Setare, M. R.; Adami, H.
2018-01-01
We apply the new fall of conditions presented in the paper [1] on asymptotically flat spacetime solutions of Chern-Simons-like theories of gravity. We show that the considered fall of conditions asymptotically solve equations of motion of generalized minimal massive gravity. We demonstrate that there exist two type of solutions, one of those is trivial and the others are non-trivial. By looking at non-trivial solutions, for asymptotically flat spacetimes in the generalized minimal massive gravity, in contrast to Einstein gravity, cosmological parameter can be non-zero. We obtain the conserved charges of the asymptotically flat spacetimes in generalized minimal massive gravity, and by introducing Fourier modes we show that the asymptotic symmetry algebra is a semidirect product of a BMS3 algebra and two U (1) current algebras. Also we verify that the BMS3 algebra can be obtained by a contraction of the AdS3 asymptotic symmetry algebra when the AdS3 radius tends to infinity in the flat-space limit. Finally we find energy, angular momentum and entropy for a particular case and deduce that these quantities satisfy the first law of flat space cosmologies.
Analytical general solutions for static wormholes in f ( R , T ) gravity
Energy Technology Data Exchange (ETDEWEB)
Moraes, P.H.R.S.; Correa, R.A.C.; Lobato, R.V., E-mail: moraes.phrs@gmail.com, E-mail: fis04132@gmail.com, E-mail: ronaldo.lobato@icranet.org [ITA-Instituto Tecnológico de Aeronáutica, 12228-900, São José dos Campos, SP (Brazil)
2017-07-01
Originally proposed as a tool for teaching the general theory of relativity, wormholes are today approached in many different ways and are seeing as an efficient alternative for interstellar and time travel. Attempts to achieve observational signatures of wormholes have been growing as the subject has become more and more popular. In this article we investigate some f ( R , T ) theoretical predictions for static wormholes, i.e., wormholes whose throat radius can be considered a constant. Since the T -dependence in f ( R , T ) gravity is due to the consideration of quantum effects, a further investigation of wormholes in such a theory is well motivated. We obtain the energy conditions of static wormholes in f ( R , T ) gravity and apply an analytical approach to find their physical and geometrical solutions. We highlight that our results are in agreement with previous solutions and assumptions presented in the literature.
Analytical general solutions for static wormholes in f(R,T) gravity
Moraes, P. H. R. S.; Correa, R. A. C.; Lobato, R. V.
2017-07-01
Originally proposed as a tool for teaching the general theory of relativity, wormholes are today approached in many different ways and are seeing as an efficient alternative for interstellar and time travel. Attempts to achieve observational signatures of wormholes have been growing as the subject has become more and more popular. In this article we investigate some f(R,T) theoretical predictions for static wormholes, i.e., wormholes whose throat radius can be considered a constant. Since the T-dependence in f(R,T) gravity is due to the consideration of quantum effects, a further investigation of wormholes in such a theory is well motivated. We obtain the energy conditions of static wormholes in f(R,T) gravity and apply an analytical approach to find their physical and geometrical solutions. We highlight that our results are in agreement with previous solutions and assumptions presented in the literature.
Exact solutions to quadratic gravity
Czech Academy of Sciences Publication Activity Database
Pravda, Vojtěch; Pravdová, Alena; Podolský, J.; Švarc, J.
2017-01-01
Roč. 95, č. 8 (2017), č. článku 084025. ISSN 2470-0010 R&D Projects: GA ČR GB14-37086G Institutional support: RVO:67985840 Keywords : quadratic gravity * exact solutions * Kundt spacetimes Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 4.568, year: 2016 https://journals.aps.org/prd/abstract/10.1103/PhysRevD.95.084025
Exact solutions to quadratic gravity
Czech Academy of Sciences Publication Activity Database
Pravda, Vojtěch; Pravdová, Alena; Podolský, J.; Švarc, J.
2017-01-01
Roč. 95, č. 8 (2017), č. článku 084025. ISSN 2470-0010 R&D Projects: GA ČR GB14-37086G Institutional support: RVO:67985840 Keywords : quadratic gravity * exact solutions * Kundt spacetimes Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 4.568, year: 2016 https://journals. aps .org/prd/abstract/10.1103/PhysRevD.95.084025
Lü, H; Mei, Jianwei; Pope, C N
2009-08-28
Recently Horava proposed a nonrelativistic renormalizable theory of gravitation, which reduces to Einstein's general relativity at large distances, and that may provide a candidate for a UV completion of Einstein's theory. In this Letter, we derive the full set of equations of motion, and then we obtain spherically symmetric solutions and discuss their properties. We also obtain solutions for the Friedmann-Lemaître-Robertson-Walker cosmological metric.
Black Hole Solutions in $R^2$ Gravity
Kehagias, Alex; Lust, Dieter; Riotto, Antonio
2015-01-01
We find static spherically symmetric solutions of scale invariant $R^2$ gravity. The latter has been shown to be equivalent to General Relativity with a positive cosmological constant and a scalar mode. Therefore, one expects that solutions of the $R^2$ theory will be identical to that of Einstein theory. Indeed, we find that the solutions of $R^2$ gravity are in one-to-one correspondence with solutions of General Relativity in the case of non-vanishing Ricci scalar. However, scalar-flat $R=0$ solutions are global minima of the $R^2$ action and they cannot in general be mapped to solutions of the Einstein theory. As we will discuss, the $R=0$ solutions arise in Einstein gravity as solutions in the tensionless, strong coupling limit $M_P\\rightarrow 0$. As a further result, there is no corresponding Birkhoff theorem and the Schwarzschild black hole is by no means unique in this framework. In fact, $R^2$ gravity has a rich structure of vacuum static spherically symmetric solutions partially uncovered here. We al...
Exact solutions in three-dimensional gravity
Garcia-Diaz, Alberto A
2017-01-01
A self-contained text, systematically presenting the determination and classification of exact solutions in three-dimensional Einstein gravity. This book explores the theoretical framework and general physical and geometrical characteristics of each class of solutions, and includes information on the researchers responsible for their discovery. Beginning with the physical character of the solutions, these are identified and ordered on the basis of their geometrical invariant properties, symmetries, and algebraic classifications, or from the standpoint of their physical nature, for example electrodynamic fields, fluid, scalar field, or dilaton. Consequently, this text serves as a thorough catalogue on 2+1 exact solutions to the Einstein equations coupled to matter and fields, and on vacuum solutions of topologically massive gravity with a cosmological constant. The solutions are also examined from different perspectives, enabling a conceptual bridge between exact solutions of three- and four-dimensional gravit...
Nerem, R. S.; Tapley, B. D.; Shum, C. K.; Yuan, D. N.
1989-01-01
If the geoid and the satellite position are known accurately, satellite altimetry can be used to determine the geostrophic velocity of the surface ocean currents. The purpose of this investigation is to simultaneously estimate the sea surface topography, zeta, the model for the gravity field, and the satellite orbit. Satellite tracking data from fourteen satellites were used; along with Seasat and Geosat altimeter data as well as surface gravity data for the solution. The estimated model of zeta compares well at long wavelengths with the hydrographic model of zeta. Covariance studies show that the geoid is separable from zeta up to degree 9, at which point geoid error becomes comparable to the signal of zeta.
f( R) gravity solutions for evolving wormholes
Bhattacharya, Subhra; Chakraborty, Subenoy
2017-08-01
The scalar-tensor f( R) theory of gravity is considered in the framework of a simple inhomogeneous space-time model. In this research we use the reconstruction technique to look for possible evolving wormhole solutions within viable f( R) gravity formalism. These f( R) models are then constrained so that they are consistent with existing experimental data. Energy conditions related to the matter threading the wormhole are analyzed graphically and are in general found to obey the null energy conditions (NEC) in regions around the throat, while in the limit f(R)=R, NEC can be violated at large in regions around the throat.
Charged black holes in generalized teleparallel gravity
Energy Technology Data Exchange (ETDEWEB)
Rodrigues, M.E. [Faculdade de Física, Universidade Federal do Pará, Belém, Pará, 66075–110 (Brazil); Houndjo, M.J.S.; Tossa, J. [Institut de Mathématiques et de Sciences Physiques (IMSP) - Porto-Novo, 01 BP 613 (Benin); Momeni, D.; Myrzakulov, R., E-mail: esialg@gmail.com, E-mail: sthoundjo@yahoo.fr, E-mail: joel.tossa@imsp-uac.org, E-mail: d.momeni@yahoo.com, E-mail: rmyrzakulov@gmail.com [Eurasian International Center for Theoretical Physics - Eurasian National University, Astana, 010008 (Kazakhstan)
2013-11-01
In this paper we investigate charged static black holes in 4D for generalized teleparallel models of gravity, based on torsion as the geometric object for describing gravity according to the equivalence principle. As a motivated idea, we introduce a set of non-diagonal tetrads and derive the full system of non linear differential equations. We prove that the common Schwarzschild gauge is applicable only when we study linear f(T) case. We reobtain the Reissner-Nordstrom-de Sitter (or RN-AdS) solution for the linear case of f(T) and perform a parametric cosmological reconstruction for two nonlinear models. We also study in detail a type of the no-go theorem in the framework of this modified teleparallel gravity.
Perturbation of an exact strong gravity solution
International Nuclear Information System (INIS)
Baran, S.A.
1982-10-01
Perturbations of an exact strong gravity solution are investigated. It is shown, by using the new multipole expansions previously presented, that this exact and static spherically symmetric solution is stable under odd parity perturbations. (author)
Global solutions of 1 + 1 gravity
International Nuclear Information System (INIS)
Kloesch, T.
1997-03-01
A classification of all global solutions for generalized 2D dilaton gravity models (with Lorentzian signature) including generalizations with non-trivial torsion is presented. After reviewing several coordinate systems (and - as a by-product - finding global coordinates for the Reissner-Nordstroem solution), the equations of motion are solved locally. The maximally extended universal covering solutions are then constructed by applying a simple gluing procedure to the Eddington-Finkelstein coordinate patches. This is demonstrated at a few examples, and some subtleties concerning the concept of Penrose diagrams are pointed out. The multiply connected solutions are obtained from the simply connected ones by factorization by discrete symmetry subgroups. It will be found that for generic models maximally extended solutions on noncompact surfaces of arbitrary genus with an arbitrary non-zero number of holes can be obtained. Furthermore, we determine all discrete and continuous parameters labeling these factor solutions and specify their geometrical interpretation. Remarks on a few cases not covered by the above approach and some pathological examples conclude the work. (author)
Brane solutions of gravity-dilaton-axion systems
Bergshoeff, E; Collinucci, A; Gran, U; Roest, D; Vandoren, S; Lukierski, J; Sorokin, D
2005-01-01
We consider general properties of brane solutions of gravity-dilaton-axion systems. We focus on the case of 7-branes and instantons. In both cases we show that besides the standard solutions there are new deformed solutions whose charges take value in any of the three conjugacy classes of SL(2, R).
Generalized geometry and non-symmetric gravity
Jurco, Branislav; Khoo, Fech Scen; Schupp, Peter; Vysoky, Jan
2015-01-01
Generalized geometry provides the framework for a systematic approach to non-symmetric metric gravity theory and naturally leads to an Einstein-Kalb-Ramond gravity theory with totally anti-symmetric contortion. The approach is related to the study of the low-energy effective closed string gravity actions.
From thermodynamics to the solutions in gravity theory
Directory of Open Access Journals (Sweden)
Hongsheng Zhang
2014-10-01
Full Text Available In a recent work, we present a new point of view to the relation of gravity and thermodynamics, in which we derive the Schwarzschild solution through thermodynamic considerations by the aid of the Misner–Sharp mass in an adiabatic system. In this Letter we continue to investigate the relation between gravity and thermodynamics for obtaining solutions via thermodynamics. We generalize our studies on gravi-thermodynamics in Einstein gravity to modified gravity theories. By using the first law with the assumption that the Misner–Sharp mass is the mass for an adiabatic system, we reproduce the Boulware–Deser–Cai solution in Gauss–Bonnet gravity. Using this gravi-thermodynamic thought, we obtain a NEW class of solution in F(R gravity in an n-dimensional (n≥3 spacetime which permits three-type (n−2-dimensional maximally symmetric subspace, as an extension of our recent three-dimensional black hole solution, and four-dimensional Clifton–Barrow solution in F(R gravity.
From thermodynamics to the solutions in gravity theory
International Nuclear Information System (INIS)
Zhang, Hongsheng; Li, Xin-Zhou
2014-01-01
In a recent work, we present a new point of view to the relation of gravity and thermodynamics, in which we derive the Schwarzschild solution through thermodynamic considerations by the aid of the Misner–Sharp mass in an adiabatic system. In this Letter we continue to investigate the relation between gravity and thermodynamics for obtaining solutions via thermodynamics. We generalize our studies on gravi-thermodynamics in Einstein gravity to modified gravity theories. By using the first law with the assumption that the Misner–Sharp mass is the mass for an adiabatic system, we reproduce the Boulware–Deser–Cai solution in Gauss–Bonnet gravity. Using this gravi-thermodynamic thought, we obtain a NEW class of solution in F(R) gravity in an n-dimensional (n≥3) spacetime which permits three-type (n−2)-dimensional maximally symmetric subspace, as an extension of our recent three-dimensional black hole solution, and four-dimensional Clifton–Barrow solution in F(R) gravity
Cosmology in general massive gravity theories
International Nuclear Information System (INIS)
Comelli, D.; Nesti, F.; Pilo, L.
2014-01-01
We study the cosmological FRW flat solutions generated in general massive gravity theories. Such a model are obtained adding to the Einstein General Relativity action a peculiar non derivative potentials, function of the metric components, that induce the propagation of five gravitational degrees of freedom. This large class of theories includes both the case with a residual Lorentz invariance as well as the case with rotational invariance only. It turns out that the Lorentz-breaking case is selected as the only possibility. Moreover it turns out that that perturbations around strict Minkowski or dS space are strongly coupled. The upshot is that even though dark energy can be simply accounted by massive gravity modifications, its equation of state w eff has to deviate from -1. Indeed, there is an explicit relation between the strong coupling scale of perturbations and the deviation of w eff from -1. Taking into account current limits on w eff and submillimiter tests of the Newton's law as a limit on the possible strong coupling scale, we find that it is still possible to have a weakly coupled theory in a quasi dS background. Future experimental improvements on short distance tests of the Newton's law may be used to tighten the deviation of w eff form -1 in a weakly coupled massive gravity theory
Black hole conserved charges in Generalized Minimal Massive Gravity
Directory of Open Access Journals (Sweden)
M.R. Setare
2015-05-01
Full Text Available In this paper we construct mass, angular momentum and entropy of black hole solution of Generalized Minimal Massive Gravity (GMMG in asymptotically Anti-de Sitter (AdS spacetimes. The Generalized Minimal Massive Gravity theory is realized by adding the CS deformation term, the higher derivative deformation term, and an extra term to pure Einstein gravity with a negative cosmological constant. We apply our result for conserved charge Qμ(ξ¯ to the rotating BTZ black hole solution of GMMG, and find energy, angular momentum and entropy. Then we show that our results for these quantities are consistent with the first law of black hole thermodynamics.
6D supergravity. Warped solution and gravity mediated supersymmetry breaking
International Nuclear Information System (INIS)
Luedeling, C.
2006-07-01
We consider compactified six-dimensional gauged supergravity and find the general warped solution with four-dimensional maximal symmetry. Important features of the solution such as the number and position of singularities are determined by a free holomorphic function. Furthermore, in a particular torus compactification we derive the supergravity coupling of brane fields by the Noether procedure and investigate gravity-mediated supersymmetry breaking. The effective Kaehler potential is not sequestered, yet tree level gravity mediation is absent as long as the superpotential is independent of the radius modulus. (orig.)
6D supergravity. Warped solution and gravity mediated supersymmetry breaking
Energy Technology Data Exchange (ETDEWEB)
Luedeling, C.
2006-07-15
We consider compactified six-dimensional gauged supergravity and find the general warped solution with four-dimensional maximal symmetry. Important features of the solution such as the number and position of singularities are determined by a free holomorphic function. Furthermore, in a particular torus compactification we derive the supergravity coupling of brane fields by the Noether procedure and investigate gravity-mediated supersymmetry breaking. The effective Kaehler potential is not sequestered, yet tree level gravity mediation is absent as long as the superpotential is independent of the radius modulus. (orig.)
Three dimensional magnetic solutions in massive gravity with (nonlinear field
Directory of Open Access Journals (Sweden)
S.H. Hendi
2017-12-01
Full Text Available The Noble Prize in physics 2016 motivates one to study different aspects of topological properties and topological defects as their related objects. Considering the significant role of the topological defects (especially magnetic strings in cosmology, here, we will investigate three dimensional horizonless magnetic solutions in the presence of two generalizations: massive gravity and nonlinear electromagnetic field. The effects of these two generalizations on properties of the solutions and their geometrical structure are investigated. The differences between de Sitter and anti de Sitter solutions are highlighted and conditions regarding the existence of phase transition in geometrical structure of the solutions are studied.
Generalized modified gravity in large extra dimensions
International Nuclear Information System (INIS)
Aslan, Onder; Demir, Durmus A.
2006-01-01
We discuss effective interactions among brane matter induced by modifications of higher-dimensional Einstein gravity through the replacement of Einstein-Hilbert term with a generic function f(R,R AB R AB ,R ABCD R ABCD ) of the curvature tensors. We determine gravi-particle spectrum of the theory, and perform a comparative analysis of its predictions with those of the Einstein gravity within Arkani-Hamed-Dvali-Dimopoulos (ADD) setup. We find that this general higher-curvature quantum gravity theory contributes to scatterings among both massive and massless brane matter (in contrast to much simpler generalization of the Einstein gravity, f(R), which influences only the massive matter), and therefore, can be probed via various scattering processes at present and future colliders and directly confronted with the ADD expectations. In addition to collision processes which proceed with tree-level gravi-particle exchange, effective interactions among brane matter are found to exhibit a strong sensitivity to higher-curvature gravity via the gravi-particle loops. Furthermore, particle collisions with missing energy in their final states are found to be sensitive to additional gravi-particles not found in Einstein gravity. In general, road to a correct description of quantum gravity above Fermi energies depends crucially on if collider and other search methods end up with a negative or positive answer for the presence of higher-curvature gravitational interactions
Generalized gravity from modified DFT
Energy Technology Data Exchange (ETDEWEB)
Sakatani, Yuho [Department of Physics, Kyoto Prefectural University of Medicine,Kyoto 606-0823 (Japan); Fields, Gravity and Strings, CTPU,Institute for Basic Sciences, Daejeon 34047 (Korea, Republic of); Uehara, Shozo [Department of Physics, Kyoto Prefectural University of Medicine,Kyoto 606-0823 (Japan); Yoshida, Kentaroh [Department of Physics, Kyoto University,Kitashirakawa Oiwake-cho, Kyoto 606-8502 (Japan)
2017-04-20
Recently, generalized equations of type IIB supergravity have been derived from the requirement of classical kappa-symmetry of type IIB superstring theory in the Green-Schwarz formulation. These equations are covariant under generalized T-duality transformations and hence one may expect a formulation similar to double field theory (DFT). In this paper, we consider a modification of the DFT equations of motion by relaxing a condition for the generalized covariant derivative with an extra generalized vector. In this modified double field theory (mDFT), we show that the flatness condition of the modified generalized Ricci tensor leads to the NS-NS part of the generalized equations of type IIB supergravity. In particular, the extra vector fields appearing in the generalized equations correspond to the extra generalized vector in mDFT. We also discuss duality symmetries and a modification of the string charge in mDFT.
Observational constraints on transverse gravity: A generalization of unimodular gravity
International Nuclear Information System (INIS)
Lopez-Villarejo, J J
2010-01-01
We explore the hypothesis that the set of symmetries enjoyed by the theory that describes gravity is not the full group of diffeomorphisms (Diff(M)), as in General Relativity, but a maximal subgroup of it (TransverseDiff(M)), with its elements having a jacobian equal to unity; at the infinitesimal level, the parameter describing the coordinate change x μ → x μ + ξ μ (x) is transverse, i.e., δ μ ξ μ = 0. Incidentally, this is the smaller symmetry one needs to propagate consistently a graviton, which is a great theoretical motivation for considering these theories. Also, the determinant of the metric, g, behaves as a 'transverse scalar', so that these theories can be seen as a generalization of the better-known unimodular gravity. We present our results on the observational constraints on transverse gravity, in close relation with the claim of equivalence with general scalar-tensor theory. We also comment on the structure of the divergences of the quantum theory to the one-loop order.
Gravity: An Introduction to Einstein's General Relativity
International Nuclear Information System (INIS)
Fabris, Julio C
2004-01-01
General relativity is one of the cornerstones of modern physics. In spite of this, the teaching of general relativity at undergraduate level remains quite marginal. The reasons for this particular situation are quite well known. We can quote, for example, two of them: general relativity requires specific mathematical tools that are somehow outside the mainstream of undergraduate technical development; moreover, this is a branch of physics whose observational and experimental applications have remained rare until recent times, and even though this scenario has changed dramatically in the last few years, the new situation has not yet been absorbed into undergraduate teaching. In this new book, Hartle attempts to address the difficulties that must be faced by anyone who teaches general relativity at undergraduate level. In order to not scare the student with the hard technical preparation needed to obtain the basic equations of general relativity, Einstein's equations, he simply gives up the idea of introducing these equations at the very beginning. Instead, he chooses to present Einstein's equations, with most of the mathematics needed to do them, in the last part of the book. This delicate (and of course dangerous) choice has the advantage of introducing the reader first to the physical aspects of general relativity. This approach can be dangerous because the relevant solutions of the equations necessary to discuss the physical content of general relativity are presented first without a formal derivation. The book is divided into three parts. In the first, covering five chapters of the 24 in the whole book, Newtonian physics and special relativity are reviewed. This review is done in a manner that prepares the reader for the subsequent discussion of general relativity itself. The principle of relativity, the variational principle, the geometrical content of Newtonian theory and the main ideas behind special relativity are all presented. The heart of the book is, in
Impulsive gravitational waves in general massive 3D gravity
Baykal, Ahmet; Dereli, Tekin
2017-10-01
Impulsive, nondiverging, Petrov-Segre type-N gravitational wave solutions to a general massive three-dimensional gravity in the de Sitter, anti-de Sitter, and flat Minkowski backgrounds are constructed in a unified manner by using the exterior algebra of differential forms.
f(R) gravity solutions for evolving wormholes
Energy Technology Data Exchange (ETDEWEB)
Bhattacharya, Subhra [Presidency University, Department of Mathematics, Kolkata (India); Chakraborty, Subenoy [Jadavpur University, Department of Mathematics, Kolkata (India)
2017-08-15
The scalar-tensor f(R) theory of gravity is considered in the framework of a simple inhomogeneous space-time model. In this research we use the reconstruction technique to look for possible evolving wormhole solutions within viable f(R) gravity formalism. These f(R) models are then constrained so that they are consistent with existing experimental data. Energy conditions related to the matter threading the wormhole are analyzed graphically and are in general found to obey the null energy conditions (NEC) in regions around the throat, while in the limit f(R) = R, NEC can be violated at large in regions around the throat. (orig.)
Towards combined global monthly gravity field solutions
Jaeggi, Adrian; Meyer, Ulrich; Beutler, Gerhard; Weigelt, Matthias; van Dam, Tonie; Mayer-Gürr, Torsten; Flury, Jakob; Flechtner, Frank; Dahle, Christoph; Lemoine, Jean-Michel; Bruinsma, Sean
2014-05-01
Currently, official GRACE Science Data System (SDS) monthly gravity field solutions are generated independently by the Centre for Space Research (CSR) and the German Research Centre for Geosciences (GFZ). Additional GRACE SDS monthly fields are provided by the Jet Propulsion Laboratory (JPL) for validation and outside the SDS by a number of other institutions worldwide. Although the adopted background models and processing standards have been harmonized more and more by the various processing centers during the past years, notable differences still exist and the users are more or less left alone with a decision which model to choose for their individual applications. This procedure seriously limits the accessibility of these valuable data. Combinations are well established in the area of other space geodetic techniques, such as the Global Navigation Satellite Systems (GNSS), Satellite Laser Ranging (SLR), and Very Long Baseline Interferometry (VLBI). Regularly comparing and combining space-geodetic products has tremendously increased the usefulness of the products in a wide range of disciplines and scientific applications. Therefore, we propose in a first step to mutually compare the large variety of available monthly GRACE gravity field solutions, e.g., by assessing the signal content over selected regions, by estimating the noise over the oceans, and by performing significance tests. We make the attempt to assign different solution characteristics to different processing strategies in order to identify subsets of solutions, which are based on similar processing strategies. Using these subsets we will in a second step explore ways to generate combined solutions, e.g., based on a weighted average of the individual solutions using empirical weights derived from pair-wise comparisons. We will also assess the quality of such a combined solution and discuss the potential benefits for the GRACE and GRACE-FO user community, but also address minimum processing
An unusual cosmological solution in the context of higher-derivative gravity
International Nuclear Information System (INIS)
Accioly, A.J.
1988-01-01
A general vacuum solution to the higher-derivative gravity field equations is presented in case of a model that exhibits symmetries of the Goedel-type. The solution possesses unusual properties. (author) [pt
Quantum mechanics vs. general covariance in gravity and string models
International Nuclear Information System (INIS)
Martinec, E.J.
1984-01-01
Quantization of simple low-dimensional systems embodying general covariance is studied. Functional methods are employed in the calculation of effective actions for fermionic strings and 1 + 1 dimensional gravity. The author finds that regularization breaks apparent symmetries of the theory, providing new dynamics for the string and non-trivial dynamics for 1 + 1 gravity. The author moves on to consider the quantization of some generally covariant systems with a finite number of physical degrees of freedom, assuming the existence of an invariant cutoff. The author finds that the wavefunction of the universe in these cases is given by the solution to simple quantum mechanics problems
Contribution of the GOCE gradiometer components to regional gravity solutions
Naeimi, Majid; Bouman, Johannes
2017-05-01
The contribution of the GOCE gravity gradients to regional gravity field solutions is investigated in this study. We employ radial basis functions to recover the gravity field on regional scales over Amazon and Himalayas as our test regions. In the first step, four individual solutions based on the more accurate gravity gradient components Txx, Tyy, Tzz and Txz are derived. The Tzz component gives better solution than the other single-component solutions despite the less accuracy of Tzz compared to Txx and Tyy. Furthermore, we determine five more solutions based on several selected combinations of the gravity gradient components including a combined solution using the four gradient components. The Tzz and Tyy components are shown to be the main contributors in all combined solutions whereas the Txz adds the least value to the regional gravity solutions. We also investigate the contribution of the regularization term. We show that the contribution of the regularization significantly decreases as more gravity gradients are included. For the solution using all gravity gradients, regularization term contributes to about 5 per cent of the total solution. Finally, we demonstrate that in our test areas, regional gravity modelling based on GOCE data provide more reliable gravity signal in medium wavelengths as compared to pre-GOCE global gravity field models such as the EGM2008.
A static axisymmetric exact solution of f(R)-gravity
Energy Technology Data Exchange (ETDEWEB)
Gutierrez-Pineres, Antonio C., E-mail: acgutierrez@correo.nucleares.unam.mx [Facultad de Ciencias Basicas, Universidad Tecnologica de Bolivar, CO 131001 Cartagena de Indias (Colombia); Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, A.P. 70-543, 04510 Mexico D.F. (Mexico); Lopez-Monsalvo, Cesar S., E-mail: cesar.slm@correo.nucleares.unam.mx [Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, A.P. 70-543, 04510 Mexico D.F. (Mexico)
2013-01-29
We present an exact, axially symmetric, static, vacuum solution for f(R)-gravity in Weyl's canonical coordinates. We obtain a general explicit expression for the dependence of df(R)/dR upon the r and z coordinates and then the corresponding explicit form of f(R), which must be consistent with the field equations. We analyze in detail the modified Schwarzschild solution in prolate spheroidal coordinates. Finally, we study the curvature invariants and show that, in the case of f(R){ne}R, this solution corresponds to a naked singularity.
Noncommutative Wormhole Solutions in Einstein Gauss-Bonnet Gravity
Directory of Open Access Journals (Sweden)
Shamaila Rani
2016-01-01
Full Text Available We explore static spherically symmetric wormhole solutions in the framework of n-dimensional Einstein Gauss-Bonnet gravity. Our objective is to find out wormhole solutions that satisfy energy conditions. For this purpose, we consider two frameworks such as Gaussian distributed and Lorentzian distributed noncommutative geometry. Taking into account constant redshift function, we obtain solutions in the form of shape function. The fifth and sixth dimensional solutions with positive as well as negative Gauss-Bonnet coefficient are discussed. Also, we check the equilibrium condition for the wormhole solutions with the help of generalized Tolman-Oppenheimer-Volkoff equation. It is interesting to mention here that we obtain fifth dimensional stable wormhole solutions in both distributions that satisfy the energy conditions.
Gravity discharge vessel revisited: An explicit Lambert W function solution
Digilov, Rafael M.
2017-07-01
Based on the generalized Poiseuille equation modified by a kinetic energy correction, an explicit solution for the time evolution of a liquid column draining under gravity through an exit capillary tube is derived in terms of the Lambert W function. In contrast to the conventional exponential behavior, as implied by the Poiseuille law, a new analytical solution gives a full account for the volumetric flow rate of a fluid through a capillary of any length and improves the precision of viscosity determination. The theoretical consideration may be of interest to students as an example of how implicit equations in the field of physics can be solved analytically using the Lambert function.
Generalized Galilean algebras and Newtonian gravity
González, N.; Rubio, G.; Salgado, P.; Salgado, S.
2016-04-01
The non-relativistic versions of the generalized Poincaré algebras and generalized AdS-Lorentz algebras are obtained. These non-relativistic algebras are called, generalized Galilean algebras of type I and type II and denoted by GBn and GLn respectively. Using a generalized Inönü-Wigner contraction procedure we find that the generalized Galilean algebras of type I can be obtained from the generalized Galilean algebras type II. The S-expansion procedure allows us to find the GB5 algebra from the Newton Hooke algebra with central extension. The procedure developed in Ref. [1] allows us to show that the nonrelativistic limit of the five dimensional Einstein-Chern-Simons gravity is given by a modified version of the Poisson equation. The modification could be compatible with the effects of Dark Matter, which leads us to think that Dark Matter can be interpreted as a non-relativistic limit of Dark Energy.
Exploring plane-symmetric solutions in f( R) gravity
Shamir, M. F.
2016-02-01
The modified theories of gravity, especially the f( R) gravity, have attracted much attention in the last decade. This paper is devoted to exploring plane-symmetric solutions in the context of metric f( R) gravity. We extend the work on static plane-symmetric vacuum solutions in f( R) gravity already available in the literature [1, 2]. The modified field equations are solved using the assumptions of both constant and nonconstant scalar curvature. Some well-known solutions are recovered with power-law and logarithmic forms of f( R) models.
Galactic Halo Wormhole Solutions in f(T Gravity
Directory of Open Access Journals (Sweden)
M. Sharif
2014-01-01
Full Text Available The proposal of galactic halo region is based on the idea that dark halos contain some characteristics needed to support traversable wormhole solutions. We explore wormhole solutions in this region in the framework of generalized teleparallel gravity. We consider static spherically symmetric wormhole spacetime with flat galactic rotational curves and obtain expressions of matter components for nondiagonal tetrad. The effective energy-momentum tensor leads to the violation of energy conditions which may impose condition on the normal matter to satisfy these conditions. We take two well-known f(T models in exponential and logarithmic forms to discuss wormhole solutions as well as the equilibrium condition. It is concluded that wormhole solutions violating weak energy condition are obtained for both models with stable configuration.
A rotating charged black hole solution in f (R) gravity
Indian Academy of Sciences (India)
properties in f (R) gravities are qualitatively similar to those of standard General Relativity. Keywords. Quantum aspects of black holes; thermodynamics. PACS Nos 04.70.Bw; 04.70.Dy; 05.70.−a; 02.40.−k. 1. Introduction. Increasing attention has been paid recently to modified theories of gravity in order to understand several ...
Infinite derivative gravity : non-singular cosmology & blackhole solutions
Mazumdar, Anupam
2017-01-01
Both Einstein's theory of General Relativity and Newton's theory of gravity possess a short dis- tance and small time scale catastrophe. The blackhole singularity and cosmological Big Bang singularity problems highlight that current theories of gravity are incomplete description at early times and
Extended DBI massive gravity with generalized fiducial metric
Energy Technology Data Exchange (ETDEWEB)
Chullaphan, Tossaporn [The Institute for Fundamental Study, Naresuan University,Phitsanulok 65000 (Thailand); Department of Physics, Faculty of Science, Udon Thani Rajabhat University,Udon Thani 41000 (Thailand); Tannukij, Lunchakorn [Department of Physics, Faculty of Science, Mahidol University,Bangkok 10400 (Thailand); Wongjun, Pitayuth [The Institute for Fundamental Study, Naresuan University,Phitsanulok 65000 (Thailand); Thailand Center of Excellence in Physics, Ministry of Education,Bangkok 10400 (Thailand)
2015-06-05
We consider an extended model of DBI massive gravity by generalizing the fiducial metric to be an induced metric on the brane corresponding to a domain wall moving in five-dimensional Schwarzschild-Anti-de Sitter spacetime. The model admits all solutions of FLRW metric including flat, closed and open geometries while the original one does not. The background solutions can be divided into two branches namely self-accelerating branch and normal branch. For the self-accelerating branch, the graviton mass plays the role of cosmological constant to drive the late-time acceleration of the universe. It is found that the number degrees of freedom of gravitational sector is not correct similar to the original DBI massive gravity. There are only two propagating degrees of freedom from tensor modes. For normal branch, we restrict our attention to a particular class of the solutions which provides an accelerated expansion of the universe. It is found that the number of degrees of freedom in the model is correct. However, at least one of them is ghost degree of freedom which always present at small scale implying that the theory is not stable.
McVittie solution in f( T) gravity
Bejarano, Cecilia; Ferraro, Rafael; Guzmán, María José
2017-12-01
We show that McVittie geometry, which describes a black hole embedded in a FLRW universe, not only solves the Einstein equations but also remains as a non-deformable solution of f( T) gravity. This search for GR solutions that survive in f( T) gravity is facilitated by a null tetrad approach. We also show that flat FLRW geometry is a consistent solution of f( T) dynamical equations not only for T=-6H2 but also for T=0, which could be a manifestation of the additional degrees of freedom involved in f( T) theories.
McVittie solution in f(T) gravity
Energy Technology Data Exchange (ETDEWEB)
Bejarano, Cecilia; Jose Guzman, Maria [Instituto de Astronomia y Fisica del Espacio (IAFE, CONICET-UBA), Buenos Aires (Argentina); Ferraro, Rafael [Instituto de Astronomia y Fisica del Espacio (IAFE, CONICET-UBA), Buenos Aires (Argentina); Universidad de Buenos Aires, Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Buenos Aires (Argentina)
2017-12-15
We show that McVittie geometry, which describes a black hole embedded in a FLRW universe, not only solves the Einstein equations but also remains as a non-deformable solution of f(T) gravity. This search for GR solutions that survive in f(T) gravity is facilitated by a null tetrad approach. We also show that flat FLRW geometry is a consistent solution of f(T) dynamical equations not only for T = -6H{sup 2} but also for T = 0, which could be a manifestation of the additional degrees of freedom involved in f(T) theories. (orig.)
Particle-like platonic solutions in scalar gravity
International Nuclear Information System (INIS)
Kleihaus, Burkhard; Kunz, Jutta; Myklevoll, Kari
2006-01-01
We construct globally regular gravitating solutions, which possess only discrete symmetries. These solutions of Yang-Mills-dilaton theory may be viewed as exact (numerical) solutions of scalar gravity, by considering the dilaton as a kind of scalar graviton, or as approximate solutions of Einstein-Yang-Mills theory. We focus on platonic solutions with cubic symmetry, related to a rational map of degree N=4. We present the first two solutions of the cubic N=4 sequence, and expect this sequence to converge to an extremal Reissner-Nordstrom solution with magnetic charge P=4
Directory of Open Access Journals (Sweden)
Claudia de Rham
2014-08-01
Full Text Available We review recent progress in massive gravity. We start by showing how different theories of massive gravity emerge from a higher-dimensional theory of general relativity, leading to the Dvali–Gabadadze–Porrati model (DGP, cascading gravity, and ghost-free massive gravity. We then explore their theoretical and phenomenological consistency, proving the absence of Boulware–Deser ghosts and reviewing the Vainshtein mechanism and the cosmological solutions in these models. Finally, we present alternative and related models of massive gravity such as new massive gravity, Lorentz-violating massive gravity and non-local massive gravity.
Black hole solutions in mimetic Born-Infeld gravity.
Chen, Che-Yu; Bouhmadi-López, Mariam; Chen, Pisin
2018-01-01
The vacuum, static, and spherically symmetric solutions in the mimetic Born-Infeld gravity are studied. The mimetic Born-Infeld gravity is a reformulation of the Eddington-inspired-Born-Infeld (EiBI) model under the mimetic approach. Due to the mimetic field, the theory contains non-trivial vacuum solutions different from those in Einstein gravity. We find that with the existence of the mimetic field, the spacelike singularity inside a Schwarzschild black hole could be altered to a lightlike singularity, even though the curvature invariants still diverge at the singularity. Furthermore, in this case, the maximal proper time for a timelike radially-infalling observer to reach the singularity is found to be infinite.
Progress towards CSR RL06 GRACE gravity solutions
Save, Himanshu
2017-04-01
The GRACE project plans to re-processes the GRACE mission data in order to be consistent with the first gravity products released by the GRACE-FO project. The next generation Release-06 (RL06) gravity products from GRACE will include the improvements in GRACE Level-1 data products, background gravity models and the processing methodology. This paper will outline the planned improvements for CSR - RL06 and discuss the preliminary results. This paper will discuss the evolution of the quality of the GRACE solutions, especially over the past few years. We will also discuss the possible challenges we may face in connecting/extending the measurements of mass fluxes from the GRACE era to the GRACE-FO era due quality of the GRACE solutions from recent years.
Scaling solutions for dilaton quantum gravity
Directory of Open Access Journals (Sweden)
T. Henz
2017-06-01
The field equations derived from this effective action can be used directly for cosmology. Scale symmetry is spontaneously broken by a non-vanishing cosmological value of the scalar field. For the cosmology corresponding to our scaling solutions, inflation arises naturally. The effective cosmological constant becomes dynamical and vanishes asymptotically as time goes to infinity.
Motivations for anti-gravity in general relativity
International Nuclear Information System (INIS)
Chardin, G.
1996-05-01
Arguments are presented showing that it is natural to interpret the negative mass part of the Kerr solution as representing the geometry experienced by antimatter. The C, P and T discrete transformations are considered for this geometry. The C and T properties of the proposed identification are found to be in agreement with the usual representation of antimatter. In addition, a property of perfect stigmatism through Kerr wormholes which allows general relativity to mimic anti-gravity is conjectured. Kerr wormholes would then act as 'super-mirrors' reversing the C, P and T images of an object seen through it. This interpretation is subjected to several experimental tests and able to provide an explanation, without any free parameter, of the 'CP'-violation observed in the neutral kaon system. (K.A.)
A rotating charged black hole solution in f (R) gravity
Indian Academy of Sciences (India)
Abstract. In the context of f (R) theories of gravity, we address the problem of finding a rotating charged black hole solution in the case of constant curvature. A new metric is obtained by solving the field equations and we show that its behaviour is typical of a rotating charged source. In addition, we analyse the ...
Generalized Noether symmetry in f(T) gravity
International Nuclear Information System (INIS)
Mohseni Sadjadi, H.
2012-01-01
We consider modified teleparallel gravity (f(T) gravity), as a framework to explain the present accelerated expansion of the universe. The matter component is assumed to be cold dark matter. To find the explicit form of the function f, we utilize generalized Noether theorem and use generalized vector fields as variational symmetries of the corresponding Lagrangian. We study the cosmological consequences of the obtained results.
Abdus Salam and quadratic curvature gravity: Classical solutions
Stelle, K. S.
2017-03-01
In 1978, Salam and Strathdee suggested on the basis of Froissart boundedness that curvature-squared terms should be included in the gravitational Lagrangian. Despite the presence of ghosts in such theories, the subject has remained a persistent topic in approaches to quantum gravity and cosmology. In this article, the space of spherically symmetric solutions to such theories is explored, highlighting horizonless solutions, wormholes and non-Schwarzschild black holes.
Combined GRACE-SLR monthly gravity field solutions
Meyer, Ulrich; Sosnica, Krzysytof; Maier, Andrea; Jäggi, Adrian
2015-04-01
Monthly gravity field solutions from GRACE GPS and GRACE K-Band data provide remarkable information about the mass transport in the system Earth by capturing the temporal variability of the gravity field at long to medium wavelengths. The GRACE solutions suffer, however, from the poor determination of the C20 coefficient from GRACE K-Band data, which describes the Earth's oblateness. C20 and its temporal variability can, on the other hand, be very well determined using satellite laser ranges (SLR) to spherical geodetic satellites such as LAGEOS and LARES. It is common practice to replace the C20 coefficient in GRACE solutions by SLR-derived values. We perform a meaningful combination of GRACE and SLR solutions at the level of normal equations using the SLR-only monthly gravity fields from the combined analysis of up to nine geodetic satellites that capture the temporal variability to degree 10 of the global spherical harmonic expansion. We present combined monthly GRACE-SLR solutions and compare them to GRACE GPS/K-Band, GRACE GPS-only, and SLR-only solutions. We discuss the relative weighting scheme of the normal equations and evaluate the secular and seasonal periodic time variations of the combined solutions at long wavelengths. We observe a positive influence of the SLR data not only on C20 but also on the formal errors of the other degree-2 spherical harmonic coefficients, which correspond to the excitation of the polar motion. A possible reduction of the influence of aliasing with the S2 tide on some GRACE-derived coefficients using a combination with SLR data will also be addressed. The analysis of SLR-only solutions indicates sensitivity to time variable signal for selected coefficients at even higher degree but special care has to be taken not to corrupt coefficients with the inferior quality in SLR solutions in the combined solutions with GRACE data. In recent years, K-Band tracking between GRACE satellites was deactivated several times resulting in
Lorentz distributed noncommutative wormhole solutions in extended teleparallel gravity
Energy Technology Data Exchange (ETDEWEB)
Jawad, Abdul; Rani, Shamaila [COMSATS Institute of Information Technology, Department of Mathematics, Lahore (Pakistan)
2015-04-01
In this paper, we study static spherically symmetric wormhole solutions in extended teleparallel gravity with the inclusion of noncommutative geometry under a Lorentzian distribution. We obtain expressions of matter components for a non-diagonal tetrad. The effective energy-momentum tensor leads to the violation of energy conditions which impose a condition on the normal matter to satisfy these conditions. We explore the noncommutative wormhole solutions by assuming a viable power-law f(T) and shape function models. For the first model, we discuss two cases in which one leads to teleparallel gravity and the other is for f(T) gravity. The normal matter violates the weak energy condition for the first case, while there exists a possibility for micro physically acceptable wormhole solution. There exists a physically acceptable wormhole solution for the power-law b(r) model. Also, we check the equilibrium condition for these solutions, which is only satisfied for the teleparallel case, while for the f(T) case, these solutions are less stable. (orig.)
On the regularization of regional gravity field solutions in spherical radial base functions
Naeimi, Majid; Flury, Jakob; Brieden, Phillip
2015-08-01
Regional refinement of the gravity field models from satellite data using spherical radial base functions (SRBF) is an ill-posed problem. This is mainly due to the regional confinement of the data and the base functions, which leads to severe instabilities in the solutions. Here, this ill-posedness as well as the related regularization process are investigated. We compare three methods for the choice of the regularization parameter, which have been frequently used in gravity modelling. These methods are (1) the variance component estimation (VCE), (2) the generalized cross validation (GCV) and (3) the L-curve criterion. A particular emphasis is put on the impact of the SRBF type on the regularization parameter. To do this, we include two types of SRBF which are often used for regional gravity field modelling. These are the Shannon SRBF or the reproducing kernel and the Spline SRBF. The investigations are performed on two months of the real GOCE ultrasensitive gravity gradients over Central Africa and Amazon. The solutions are validated against a state-of-the-art global gravity solution. We conclude that if a proper regularization method is applied, both SRBF deliver more or less the same accuracy. We show that when the Shannon wavelet is used, the L-curve method gives the best results, while with the Spline kernel, the GCV outperforms the other two methods. Moreover, we observe that the estimated coefficients for the Spline kernel cannot be spatially interpreted. In contrast, the coefficients obtained for the Shannon wavelet reflect the energy of the recovered gravity field with a correlation factor of above 95 per cent. Therefore, when combined with the L-curve method, the Shannon SRBF is advantageous for regional gravity field estimation, since it is one of the simplest band-limited SRBF. In addition, it delivers promising solutions and the estimated coefficients represent the characteristics of the gravity field within the target region.
Exact Solutions in Modified Massive Gravity and Off-Diagonal Wormhole Deformations
Vacaru, Sergiu I
2014-01-01
There are explored off-diagonal deformations of "prime" metrics in Einstein gravity (for instance, for wormhole configurations) into "target" exact solutions in f(R,T)-modified and massive/ bi-metric gravity theories. The new classes of solutions may posses, or not, Killing symmetries and can be characterized by effective induced masses, anisotropic polarized interactions and cosmological constants. For nonholonomic deformations with (conformal) ellipsoid/ toroid and/or solitonic symmetries and, in particular, for small eccentricity rotoid configurations, we can generate wormholes like objects matching external black ellipsoid - de Sitter geometries. We conclude that there are nonholonomic transforms and/or non-trivial limits to exact solutions in general relativity when modified/ massive gravity effects are modeled by off-diagonal and/or nonholonomic parametric interactions.
Exact solutions in modified massive gravity and off-diagonal wormhole deformations
Energy Technology Data Exchange (ETDEWEB)
Vacaru, Sergiu I. [Alexandru Ioan Cuza University, Rector' s Office, Iasi (Romania); CERN, Theory Division, Geneva 23 (Switzerland)
2014-03-15
We explore off-diagonal deformations of 'prime' metrics in Einstein gravity (for instance, for wormhole configurations) into 'target' exact solutions in f(R,T)-modified and massive/bi-metric gravity theories. The new classes of solutions may, or may not, possess Killing symmetries and can be characterized by effective induced masses, anisotropic polarized interactions, and cosmological constants. For nonholonomic deformations with (conformal) ellipsoid/ toroid and/or solitonic symmetries and, in particular, for small eccentricity rotoid configurations, we can generate wormhole-like objects matching an external black ellipsoid--de Sitter geometries. We conclude that there are nonholonomic transforms and/or non-trivial limits to exact solutions in general relativity when modified/massive gravity effects are modeled by off-diagonal and/or nonholonomic parametric interactions. (orig.)
Three dimensional magnetic solutions in massive gravity with (non)linear field
Hendi, S. H.; Eslam Panah, B.; Panahiyan, S.; Momennia, M.
2017-12-01
The Noble Prize in physics 2016 motivates one to study different aspects of topological properties and topological defects as their related objects. Considering the significant role of the topological defects (especially magnetic strings) in cosmology, here, we will investigate three dimensional horizonless magnetic solutions in the presence of two generalizations: massive gravity and nonlinear electromagnetic field. The effects of these two generalizations on properties of the solutions and their geometrical structure are investigated. The differences between de Sitter and anti de Sitter solutions are highlighted and conditions regarding the existence of phase transition in geometrical structure of the solutions are studied.
Combination of monthly gravity field solutions from different processing centers
Jean, Yoomin; Meyer, Ulrich; Jäggi, Adrian
2015-04-01
Currently, the official GRACE Science Data System (SDS) monthly gravity field solutions are generated independently by the Centre for Space Research (CSR) and the German Research Centre for Geosciences (GFZ). Additional GRACE SDS monthly fields are provided by the Jet Propulsion Laboratory (JPL) for validation and outside the SDS by a number of other institutions worldwide. Although the adopted background models and processing standards have been harmonized more and more by the various processing centers during the past years, notable differences still exist and the users are more or less left alone with a decision which model to choose for their individual applications. Combinations are well-established in the area of other space geodetic techniques, such as the Global Navigation Satellite Systems (GNSS), Satellite Laser Ranging (SLR), and Very Long Baseline Interferometry (VLBI), where regular comparisons and combinations of space-geodetic products have tremendously increased the usefulness of the products in a wide range of disciplines and scientific applications. In the frame of the recently started Horizon 2020 project European Gravity Service for Improved Emergency Management (EGSIEM), a scientific combination service shall therefore be established to deliver the best gravity products for applications in Earth and environmental science research based on the unified knowledge of the European GRACE community. In a first step the large variety of available monthly GRACE gravity field solutions shall be mutually compared spatially and spectrally. We assess the noise of the raw as well as filtered solutions and compare the secular and seasonal periodic variations fitted to the monthly solutions. In a second step we will explore ways to generate combined solutions, e.g., based on a weighted average of the individual solutions using empirical weights derived from pair-wise comparisons. We will also assess the quality of such a combined solution and discuss the
Fluid/gravity correspondence and the CFM black brane solutions
Energy Technology Data Exchange (ETDEWEB)
Casadio, R. [Universita di Bologna, Dipartimento di Fisica e Astronomia, Bologna (Italy); I.N.F.N., Sezione di Bologna, Bologna (Italy); Cavalcanti, R.T. [Universita di Bologna, Dipartimento di Fisica e Astronomia, Bologna (Italy); Universidade Federal do ABC-UFABC, Centro de Ciencias Naturais e Humanas, Santo Andre (Brazil); Rocha, Roldao da [Universidade Federal do ABC-UFABC, Centro de Matematica, Computacao e Cognicao, Santo Andre (Brazil)
2016-10-15
We consider the lower bound for the shear viscosity-to-entropy density ratio, obtained from the fluid/gravity correspondence, in order to constrain the post-Newtonian parameter of brane-world metrics. In particular, we analyse the Casadio-Fabbri-Mazzacurati (CFM) effective solutions for the gravity side of the correspondence and argue that including higher-order terms in the hydrodynamic expansion can lead to a full agreement with the experimental bounds, for the Eddington-Robertson-Schiff post-Newtonian parameter in the CFM metrics. This lends further support to the physical relevance of the viscosity-to-entropy ratio lower bound and fluid/gravity correspondence. Hence we show that CFM black branes are, effectively, Schwarzschild black branes. (orig.)
Analytic rotating black-hole solutions in N-dimensional f(T) gravity
Energy Technology Data Exchange (ETDEWEB)
Nashed, G.G.L. [The British University in Egypt, Centre for Theoretical Physics, P.O. Box 43, Cairo (Egypt); Ain Shams University, Faculty of Science, Mathematics Department, Cairo (Egypt); Egyptian Relativity Group (ERG), Cairo (Egypt); El Hanafy, W. [The British University in Egypt, Centre for Theoretical Physics, P.O. Box 43, Cairo (Egypt); Egyptian Relativity Group (ERG), Cairo (Egypt)
2017-02-15
A non-diagonal vielbein ansatz is applied to the N-dimension field equations of f(T) gravity. An analytical vacuum solution is derived for the quadratic polynomial f(T)=T+εT{sup 2} and an inverse relation between the coupling constant ε and the cosmological constant Λ. Since the induced metric has off-diagonal components, it cannot be removed by a mere coordinate transformation, the solution has a rotating parameter. The curvature and torsion scalars invariants are calculated to study the singularities and horizons of the solution. In contrast to general relativity, the Cauchy horizon differs from the horizon which shows the effect of the higher order torsion. The general expression of the energy-momentum vector of f(T) gravity is used to calculate the energy of the system. Finally, we have shown that this kind of solution satisfies the first law of thermodynamics in the framework of f(T) gravitational theories. (orig.)
The de Sitter spacetime as an attractor solution in fourth-order gravity
International Nuclear Information System (INIS)
Schmidt, H.-J.
1988-01-01
We investigate the general vacuum solution of fourth-order gravity, and include the Bach tensor. For L 2 = 1.3μR 2 + 1/2αC 2 the expanding de Sitter spacetime is an attractor in the set of axially symmetric Bianchi type-I models if and only if αμ ≤ 0 or α > 4μ holds. It will be argued that this result holds true for a large class of inhomogeneous models. As a byproduct, a new closed-form cosmological solution, is obtained. It is also shown that the de Sitter spacetime is an attractor for the Bach-Einstein gravity with a minimally coupled scalar field φ. Specialised to Einstein gravity (i.e. α = 0 above) this conformal equivalence remains a non-trivial one. (author)
Energy Technology Data Exchange (ETDEWEB)
Shu, Fu-Wen [Institute for Advanced Physics Mathematics, Zhejiang University of Technology,Hangzhou 310032 (China); Center for Relativistic Astrophysics and High Energy Physics, Nanchang University,Nanchang 330031 (China); Lin, Kai [Institute for Advanced Physics Mathematics, Zhejiang University of Technology,Hangzhou 310032 (China); Instituto de Física, Universidade de São Paulo,CP 66318, 05315-970, São Paulo (Brazil); Wang, Anzhong [Institute for Advanced Physics Mathematics, Zhejiang University of Technology,Hangzhou 310032 (China); GCAP-CASPER, Physics Department, Baylor University,Waco, TX 76798-7316 (United States); Wu, Qiang [Institute for Advanced Physics Mathematics, Zhejiang University of Technology,Hangzhou 310032 (China)
2014-04-08
In this paper, we study static vacuum solutions of quantum gravity at a fixed Lifshitz point in (2+1) dimensions, and present all the diagonal solutions in closed forms in the infrared limit. The exact solutions represent spacetimes with very rich structures: they can represent generalized BTZ black holes, Lifshitz space-times or Lifshitz solitons, in which the spacetimes are free of any kind of space-time singularities, depending on the choices of the free parameters of the solutions. We also find several classes of exact static non-diagonal solutions, which represent similar space-time structures as those given in the diagonal case. The relevance of these solutions to the non-relativistic Lifshitz-type gauge/gravity duality is discussed.
Criteria of existence for bounce solutions in false vacuum decay with gravity
Wong, Nicholas W. K.; Gong, Jiangbin; Lim, Yen-Kheng; Wang, Qing-hai
2018-02-01
The bounce solutions of self-interacting scalar fields coupled to gravity are studied using a semi-classical approach. We found that bounce solutions have a maximum required barrier curvature, in addition to the known minimum required barrier curvature. In particular, as the maximum barrier curvature is approached, the scale factor of the well-known Coleman–De Luccia (CDL) bounce solutions become divergent. Unlike the CDL or its more general oscillating bounce counterparts, this cannot be considered as a subset of the Hawking–Turok solution.
Cosmological evolution of generalized non-local gravity
Zhang, Xue; Wu, Ya-Bo; Li, Song; Liu, Yu-Chen; Chen, Bo-Hai; Chai, Yun-Tian; Shu, Shuang
2016-07-01
We construct a class of generalized non-local gravity (GNLG) model which is the modified theory of general relativity (GR) obtained by adding a term m2n-2 R□-nR to the Einstein-Hilbert action. Concretely, we not only study the gravitational equation for the GNLG model by introducing auxiliary scalar fields, but also analyse the classical stability and examine the cosmological consequences of the model for different exponent n. We find that the half of the scalar fields are always ghost-like and the exponent n must be taken even number for a stable GNLG model. Meanwhile, the model spontaneously generates three dominant phases of the evolution of the universe, and the equation of state parameters turn out to be phantom-like. Furthermore, we clarify in another way that exponent n should be even numbers by the spherically symmetric static solutions in Newtonian gauge. It is worth stressing that the results given by us can include ones in refs. [28, 34] as the special case of n=2.
Indian Academy of Sciences (India)
We study the cosmological dynamics for R p exp( λ R ) gravity theory in the metric formalism, using dynamical systems approach. Considering higher-dimensional FRW geometries in case of an imperfect fluid which has two different scale factors in the normal and extra dimensions, we find the exact solutions, and study its ...
Combination of GRACE monthly gravity field solutions from different processing strategies
Jean, Yoomin; Meyer, Ulrich; Jäggi, Adrian
2018-02-01
We combine the publicly available GRACE monthly gravity field time series to produce gravity fields with reduced systematic errors. We first compare the monthly gravity fields in the spatial domain in terms of signal and noise. Then, we combine the individual gravity fields with comparable signal content, but diverse noise characteristics. We test five different weighting schemes: equal weights, non-iterative coefficient-wise, order-wise, or field-wise weights, and iterative field-wise weights applying variance component estimation (VCE). The combined solutions are evaluated in terms of signal and noise in the spectral and spatial domains. Compared to the individual contributions, they in general show lower noise. In case the noise characteristics of the individual solutions differ significantly, the weighted means are less noisy, compared to the arithmetic mean: The non-seasonal variability over the oceans is reduced by up to 7.7% and the root mean square (RMS) of the residuals of mass change estimates within Antarctic drainage basins is reduced by 18.1% on average. The field-wise weighting schemes in general show better performance, compared to the order- or coefficient-wise weighting schemes. The combination of the full set of considered time series results in lower noise levels, compared to the combination of a subset consisting of the official GRACE Science Data System gravity fields only: The RMS of coefficient-wise anomalies is smaller by up to 22.4% and the non-seasonal variability over the oceans by 25.4%. This study was performed in the frame of the European Gravity Service for Improved Emergency Management (EGSIEM; http://www.egsiem.eu) project. The gravity fields provided by the EGSIEM scientific combination service (ftp://ftp.aiub.unibe.ch/EGSIEM/) are combined, based on the weights derived by VCE as described in this article.
Wormhole solutions in f(R) gravity satisfying energy conditions
Mazharimousavi, S. Habib; Halilsoy, M.
2016-10-01
Without reference to exotic sources construction of viable wormholes in Einstein’s general relativity remained ever a myth. With the advent of modified theories, however, specifically the f(R) theory, new hopes arose for the possibility of such objects. From this token, we construct traversable wormholes in f(R) theory supported by a fluid source which respects at least the weak energy conditions. We provide an example (Example 1) of asymptotically flat wormhole in f(R) gravity without ghosts.
de Rham, Claudia
2014-01-01
We review recent progress in massive gravity. We start by showing how different theories of massive gravity emerge from a higher-dimensional theory of general relativity, leading to the Dvali–Gabadadze–Porrati model (DGP), cascading gravity, and ghost-free massive gravity. We then explore their theoretical and phenomenological consistency, proving the absence of Boulware–Deser ghosts and reviewing the Vainshtein mechanism and the cosmological solutions in these models. Finally, we present alt...
whistler oscillitons and capillary-gravity generalized solitons
African Journals Online (AJOL)
Nonlinear stationary waveforms in two completely different systems, namely, electromagnetic-fluid waves in a magnetic plasma and capillary-gravity water waves, are compared and ... In the case of the latter, “generalized solitons”, a weakly nonlinear theory, based on a 5th order Korteweg-de Vries (KdeV) equation, is used.
Accelerated FRW solutions in Chern-Simons gravity
International Nuclear Information System (INIS)
Cataldo, Mauricio; Crisostomo, Juan; Gomez, Fernando; Salgado, Patricio; Campo, Sergio del; Quinzacara, Cristian C.
2014-01-01
We consider a five-dimensional Einstein-Chern-Simons action which is composed of a gravitational sector and a sector of matter where the gravitational sector is given by a Chern-Simons gravity action instead of the Einstein-Hilbert action and where the matter sector is given by the so-called perfect fluid. It is shown that (i) the Einstein-Chern-Simons (EChS) field equations subject to suitable conditions can be written in a similar way to the Einstein-Maxwell field equations; (ii) these equations have solutions that describe an accelerated expansion for the three possible cosmological models of the universe, namely, spherical expansion, flat expansion, and hyperbolic expansion when α a parameter of the theory, is greater than zero. This result allows us to conjecture that these solutions are compatible with the era of dark energy and that the energy-momentum tensor for the field h a , a bosonic gauge field from the Chern-Simons gravity action, corresponds to a form of positive cosmological constant. It is also shown that the EChS field equations have solutions compatible with the era of matter: (i) In the case of an open universe, the solutions correspond to an accelerated expansion (α > 0) with a minimum scale factor at initial time that, when time goes to infinity, the scale factor behaves as a hyperbolic sine function. (ii) In the case of a flat universe, the solutions describe an accelerated expansion whose scale factor behaves as an exponential function of time. (iii) In the case of a closed universe there is found only one solution for a universe in expansion, which behaves as a hyperbolic cosine function of time. (orig.)
A 'general boundary' formulation for quantum mechanics and quantum gravity
International Nuclear Information System (INIS)
Oeckl, Robert
2003-01-01
I propose to formalize quantum theories as topological quantum field theories in a generalized sense, associating state spaces with boundaries of arbitrary (and possibly finite) regions of space-time. I further propose to obtain such 'general boundary' quantum theories through a generalized path integral quantization. I show how both, non-relativistic quantum mechanics and quantum field theory can be given a 'general boundary' formulation. Surprisingly, even in the non-relativistic case, features normally associated with quantum field theory emerge from consistency conditions. This includes states with arbitrary particle number and pair creation. I also note how three-dimensional quantum gravity is an example for a realization of both proposals and suggest to apply them to four-dimensional quantum gravity
Holographic entanglement entropy for the most general higher derivative gravity
International Nuclear Information System (INIS)
Miao, Rong-Xin; Guo, Wu-zhong
2015-01-01
The holographic entanglement entropy for the most general higher derivative gravity is investigated. We find a new type of Wald entropy, which appears on entangling surface without the rotational symmetry and reduces to usual Wald entropy on Killing horizon. Furthermore, we obtain a formal formula of HEE for the most general higher derivative gravity and work it out exactly for some squashed cones. As an important application, we derive HEE for gravitational action with one derivative of the curvature when the extrinsic curvature vanishes. We also study some toy models with non-zero extrinsic curvature. We prove that our formula yields the correct universal term of entanglement entropy for 4d CFTs. Furthermore, we solve the puzzle raised by Hung, Myers and Smolkin that the logarithmic term of entanglement entropy derived from Weyl anomaly of CFTs does not match the holographic result even if the extrinsic curvature vanishes. We find that such mismatch comes from the ‘anomaly of entropy’ of the derivative of curvature. After considering such contributions carefully, we resolve the puzzle successfully. In general, we need to fix the splitting problem for the conical metrics in order to derive the holographic entanglement entropy. We find that, at least for Einstein gravity, the splitting problem can be fixed by using equations of motion. How to derive the splittings for higher derivative gravity is a non-trivial and open question. For simplicity, we ignore the splitting problem in this paper and find that it does not affect our main results.
Holographic entanglement entropy for the most general higher derivative gravity
Energy Technology Data Exchange (ETDEWEB)
Miao, Rong-Xin [Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, 14476 Golm (Germany); Guo, Wu-zhong [Kavli Institute for Theoretical Physics, Key Laboratory of Frontiers in Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190 (China); Yukawa Institute for Theoretical Physics (YITP), Kyoto University, Kyoto 606-8502 (Japan)
2015-08-07
The holographic entanglement entropy for the most general higher derivative gravity is investigated. We find a new type of Wald entropy, which appears on entangling surface without the rotational symmetry and reduces to usual Wald entropy on Killing horizon. Furthermore, we obtain a formal formula of HEE for the most general higher derivative gravity and work it out exactly for some squashed cones. As an important application, we derive HEE for gravitational action with one derivative of the curvature when the extrinsic curvature vanishes. We also study some toy models with non-zero extrinsic curvature. We prove that our formula yields the correct universal term of entanglement entropy for 4d CFTs. Furthermore, we solve the puzzle raised by Hung, Myers and Smolkin that the logarithmic term of entanglement entropy derived from Weyl anomaly of CFTs does not match the holographic result even if the extrinsic curvature vanishes. We find that such mismatch comes from the ‘anomaly of entropy’ of the derivative of curvature. After considering such contributions carefully, we resolve the puzzle successfully. In general, we need to fix the splitting problem for the conical metrics in order to derive the holographic entanglement entropy. We find that, at least for Einstein gravity, the splitting problem can be fixed by using equations of motion. How to derive the splittings for higher derivative gravity is a non-trivial and open question. For simplicity, we ignore the splitting problem in this paper and find that it does not affect our main results.
Sectors of solutions in three-dimensional gravity and black holes
Energy Technology Data Exchange (ETDEWEB)
Fjelstad, Jens E-mail: jens.fjelstad@kau.se; Hwang, Stephen E-mail: stephen.hwang@kau.se
2002-04-29
We examine the connection between three-dimensional gravity with negative cosmological constant and two-dimensional CFT via the Chern-Simons formulation. A set of generalized spectral flow transformations are shown to yield new sectors of solutions. One implication is that the microscopic calculation of the entropy of the Banados-Teitelboim-Zanelli (BTZ) black hole is corrected by a multiplicative factor with the result that it saturates the Bekenstein-Hawking expression.
Sectors of solutions in three-dimensional gravity and black holes
International Nuclear Information System (INIS)
Fjelstad, Jens; Hwang, Stephen
2002-01-01
We examine the connection between three-dimensional gravity with negative cosmological constant and two-dimensional CFT via the Chern-Simons formulation. A set of generalized spectral flow transformations are shown to yield new sectors of solutions. One implication is that the microscopic calculation of the entropy of the Banados-Teitelboim-Zanelli (BTZ) black hole is corrected by a multiplicative factor with the result that it saturates the Bekenstein-Hawking expression
General scalar-tensor cosmology: analytical solutions via noether symmetry
Energy Technology Data Exchange (ETDEWEB)
Massaeli, Erfan; Motaharfar, Meysam; Sepangi, Hamid Reza [Shahid Beheshti University, Department of Physics, Tehran (Iran, Islamic Republic of)
2017-02-15
We analyze the cosmology of a general scalar-tensor theory which encompasses generalized Brans-Dicke theory, Gauss-Bonnet gravity, non-minimal derivative gravity, generalized Galilean gravity and also the general k-essence type models. Instead of taking into account phenomenological considerations we adopt a Noether symmetry approach, as a physical criterion, to single out the form of undetermined functions in the action. These specified functions symmetrize equations of motion in the simplest possible form which result in exact solutions. Demanding de Sitter, power-law and bouncing universe solutions in the absence and presence of matter density leads to exploring new as well as well-investigated models. We show that there are models for which the dynamics of the system allows a transition from a decelerating phase (matter dominated era) to an accelerating phase (dark energy epoch) and could also lead to general Brans-Dicke with string correction without a self-interaction potential. Furthermore, we classify the models based on a phantom or quintessence dark energy point of view. Finally, we obtain the condition for stability of a de Sitter solution for which the solution is an attractor of the system. (orig.)
Generalizations of teleparallel gravity and local Lorentz symmetry
International Nuclear Information System (INIS)
Sotiriou, Thomas P.; Barrow, John D.; Li Baojiu
2011-01-01
We analyze the relation between teleparallelism and local Lorentz invariance. We show that generic modifications of the teleparallel equivalent to general relativity will not respect local Lorentz symmetry. We clarify the reasons for this and explain why the situation is different in general relativity. We give a prescription for constructing teleparallel equivalents for known theories. We also explicitly consider a recently proposed class of generalized teleparallel theories, called f(T) theories of gravity, and show why restoring local Lorentz symmetry in such theories cannot lead to sensible dynamics, even if one gives up teleparallelism.
Exact solutions for scalar field cosmology in f(R) gravity
Maharaj, S. D.; Goswami, R.; Chervon, S. V.; Nikolaev, A. V.
2017-09-01
We study scalar field FLRW cosmology in the content of f(R) gravity. Our consideration is restricted to the spatially flat Friedmann universe. We derived the general evolution equations of the model, and showed that the scalar field equation is automatically satisfied for any form of the f(R) function. We also derived representations for kinetic and potential energies, as well as for the acceleration in terms of the Hubble parameter and the form of the f(R) function. Next we found the exact cosmological solutions in modified gravity without specifying the f(R) function. With negligible acceleration of the scalar curvature, we found that the de Sitter inflationary solution is always attained. Also we obtained new solutions with special restrictions on the integration constants. These solutions contain oscillating, accelerating, decelerating and even contracting universes. For further investigation, we selected special cases which can be applied with early or late inflation. We also found exact solutions for the general case for the model with negligible acceleration of the scalar curvature in terms of special Airy functions. Using initial conditions which represent the universe at the present epoch, we determined the constants of integration. This allows for the comparison of the scale factor in the new solutions with that for current stage of the universe evolution in the ΛCDM model.
Exact solutions and critical chaos in dilaton gravity with a boundary
Energy Technology Data Exchange (ETDEWEB)
Fitkevich, Maxim [Institute for Nuclear Research of the Russian Academy of Sciences,60th October Anniversary Prospect 7a, Moscow 117312 (Russian Federation); Moscow Institute of Physics and Technology,Institutskii per. 9, Dolgoprudny 141700, Moscow Region (Russian Federation); Levkov, Dmitry [Institute for Nuclear Research of the Russian Academy of Sciences,60th October Anniversary Prospect 7a, Moscow 117312 (Russian Federation); Zenkevich, Yegor [Dipartimento di Fisica, Università di Milano-Bicocca,Piazza della Scienza 3, I-20126 Milano (Italy); INFN, sezione di Milano-Bicocca,I-20126 Milano (Italy); National Research Nuclear University MEPhI,Moscow 115409 (Russian Federation)
2017-04-19
We consider (1+1)-dimensional dilaton gravity with a reflecting dynamical boundary. The boundary cuts off the region of strong coupling and makes our model causally similar to the spherically-symmetric sector of multidimensional gravity. We demonstrate that this model is exactly solvable at the classical level and possesses an on-shell SL(2, ℝ) symmetry. After introducing general classical solution of the model, we study a large subset of soliton solutions. The latter describe reflection of matter waves off the boundary at low energies and formation of black holes at energies above critical. They can be related to the eigenstates of the auxiliary integrable system, the Gaudin spin chain. We argue that despite being exactly solvable, the model in the critical regime, i.e. at the verge of black hole formation, displays dynamical instabilities specific to chaotic systems. We believe that this model will be useful for studying black holes and gravitational scattering.
Coherent states, quantum gravity, and the Born-Oppenheimer approximation. I. General considerations
International Nuclear Information System (INIS)
Stottmeister, Alexander; Thiemann, Thomas
2016-01-01
This article, as the first of three, aims at establishing the (time-dependent) Born-Oppenheimer approximation, in the sense of space adiabatic perturbation theory, for quantum systems constructed by techniques of the loop quantum gravity framework, especially the canonical formulation of the latter. The analysis presented here fits into a rather general framework and offers a solution to the problem of applying the usual Born-Oppenheimer ansatz for molecular (or structurally analogous) systems to more general quantum systems (e.g., spin-orbit models) by means of space adiabatic perturbation theory. The proposed solution is applied to a simple, finite dimensional model of interacting spin systems, which serves as a non-trivial, minimal model of the aforesaid problem. Furthermore, it is explained how the content of this article and its companion affect the possible extraction of quantum field theory on curved spacetime from loop quantum gravity (including matter fields).
Canonical structure and extra mode of generalized unimodular gravity
Bufalo, Rodrigo; Oksanen, Markku
2018-02-01
We consider a recently proposed generalization of unimodular gravity, where the lapse function is constrained to be equal to a function of the determinant of the spatial metric f (h ), as a potential origin of a dark fluid with a generally h -dependent equation of state parameter. We establish the Hamiltonian analysis and the canonical path integral for the theory. All the special cases that do not match unimodular gravity involve the violation of general covariance, and consequently the physical content of the theory is changed significantly. Particularly, the case of a constant function f is shown to contain an extra physical degree of freedom in each point of space. Physical consequences of the extra degree of freedom are studied in a linearized theory, where the extra mode is carried by the trace of the metric perturbation. The trace mode does not propagate as a wave, since it satisfies an elliptic partial differential equation in spacetime. Consequently, the trace perturbation is shown to grow exponentially with time, which implies instability. The case of a general f (h ) involves additional second-class constraints, which implies the presence of an extra global degree of freedom that depends only on time (instead of the extra local degree of freedom in the case of a constant f ).
Generalisation for regular black holes on general relativity to f(R) gravity
Energy Technology Data Exchange (ETDEWEB)
Rodrigues, Manuel E. [Universidade Federal do Para Campus Universitario de Abaetetuba, Faculdade de Ciencias Exatas e Tecnologia, Abaetetuba, Para (Brazil); Universidade Federal do Para, Faculdade de Fisica, PPGF, Belem, Para (Brazil); Fabris, Julio C. [Universidade Federal do Espirito Santo, Vitoria, ES (Brazil); National Research Nuclear University MEPhI, Moscow (Russian Federation); Junior, Ednaldo L.B. [Universidade Federal do Para, Faculdade de Fisica, PPGF, Belem, Para (Brazil); Universidade Federal do Para, Campus Universitario de Tucurui, Faculdade de Engenharia da Computacao, Tucurui, Para (Brazil); Marques, Glauber T. [Universidade Federal Rural da Amazonia ICIBE - LASIC, Belem, PA (Brazil)
2016-05-15
IIn this paper, we determine regular black hole solutions using a very general f(R) theory, coupled to a nonlinear electromagnetic field given by a Lagrangian L{sub NED}. The functions f(R) and L{sub NED} are in principle left unspecified. Instead, the model is constructed through a choice of the mass function M(r) presented in the metric coefficients. Solutions which have a regular behaviour of the geometric invariants are found. These solutions have two horizons, the event horizon and the Cauchy horizon. All energy conditions are satisfied in the whole space-time, except the strong energy condition (SEC), which is violated near the Cauchy horizon.We present also a new theorem related to the energy conditions in f(R) gravity, re-obtaining the well-known conditions in the context of general relativity when the geometry of the solution is the same. (orig.)
Black hole hair in generalized scalar-tensor gravity.
Sotiriou, Thomas P; Zhou, Shuang-Yong
2014-06-27
The most general action for a scalar field coupled to gravity that leads to second-order field equations for both the metric and the scalar--Horndeski's theory--is considered, with the extra assumption that the scalar satisfies shift symmetry. We show that in such theories, the scalar field is forced to have a nontrivial configuration in black hole spacetimes, unless one carefully tunes away a linear coupling with the Gauss-Bonnet invariant. Hence, black holes for generic theories in this class will have hair. This contradicts a recent no-hair theorem which seems to have overlooked the presence of this coupling.
Charged black holes in a generalized scalar–tensor gravity model
Directory of Open Access Journals (Sweden)
Yves Brihaye
2017-09-01
Full Text Available We study 4-dimensional charged and static black holes in a generalized scalar–tensor gravity model, in which a shift symmetry for the scalar field exists. For vanishing scalar field the solution corresponds to the Reissner–Nordström (RN solution, while solutions of the full scalar-gravity model have to be constructed numerically. We demonstrate that these black holes support Galilean scalar hair up to a maximal value of the scalar–tensor coupling that depends on the value of the charge and can be up to roughly twice as large as that for uncharged solutions. The Hawking temperature TH of the hairy black holes at maximal scalar–tensor coupling decreases continuously with the increase of the charge and reaches TH=0 for the highest possible charge that these solutions can carry. However, in this limit, the scalar–tensor coupling needs to vanish. The limiting solution hence corresponds to the extremal RN solution, which does not support regular Galilean scalar hair due to its AdS2×S2 near-horizon geometry.
An exact solution for a rotating black hole in modified gravity
Filippini, Francesco; Tasinato, Gianmassimo
2018-01-01
Exact solutions describing rotating black holes can offer important tests for alternative theories of gravity, motivated by the dark energy and dark matter problems. We present an analytic rotating black hole solution for a class of vector-tensor theories of modified gravity, valid for arbitrary values of the rotation parameter. The new configuration is characterised by parametrically large deviations from the Kerr-Newman geometry, controlled by non-minimal couplings between vectors and gravity. It has an oblate horizon in Boyer-Lindquist coordinates, and it can rotate more rapidly and have a larger ergosphere than black holes in General Relativity (GR) with the same asymptotic properties. We analytically investigate the features of the innermost stable circular orbits for massive objects on the equatorial plane, and show that stable orbits lie further away from the black hole horizon with respect to rotating black holes in GR. We also comment on possible applications of our findings for the extraction of rotational energy from the black hole.
Exact solution to the 'auxiliary extra-dimension' model of massive gravity
International Nuclear Information System (INIS)
Hassan, S.F.; Rosen, Rachel A.
2011-01-01
The 'auxiliary extra-dimension' model was proposed in order to provide a geometrical interpretation to modifications of general relativity, in particular to non-linear massive gravity. In this context, the theory was shown to be ghost free to third order in perturbations, in the decoupling limit. In this work, we exactly solve the equation of motion in the extra dimension, to obtain a purely 4-dimensional theory. Using this solution, it is shown that the ghost appears at the fourth order and beyond. We explore potential modifications to address the ghost issue and find that their consistent implementation requires going beyond the present framework.
Li, Ping; Li, Xin-zhou; Xi, Ping
2016-06-01
We present a detailed study of the spherically symmetric solutions in Lorentz-breaking massive gravity. There is an undetermined function { F }(X,{w}1,{w}2,{w}3) in the action of Stückelberg fields {S}φ ={{{Λ }}}4\\int {{{d}}}4x\\sqrt{-g}{ F }, which should be resolved through physical means. In general relativity, the spherically symmetric solution to the Einstein equation is a benchmark and its massive deformation also plays a crucial role in Lorentz-breaking massive gravity. { F } will satisfy the constraint equation {T}01=0 from the spherically symmetric Einstein tensor {G}01=0, if we maintain that any reasonable physical theory should possess the spherically symmetric solutions. The Stückelberg field {φ }i is taken as a ‘hedgehog’ configuration {φ }i=φ (r){x}i/r, whose stability is guaranteed by the topological one. Under this ansätz, {T}01=0 is reduced to d{ F }=0. The functions { F } for d{ F }=0 form a commutative ring {R}{ F }. We obtain an expression of the solution to the functional differential equation with spherical symmetry if { F }\\in {R}{ F }. If { F }\\in {R}{ F } and \\partial { F }/\\partial X=0, the functions { F } form a subring {S}{ F }\\subset {R}{ F }. We show that the metric is Schwarzschild, Schwarzschild-AdS or Schwarzschild-dS if { F }\\in {S}{ F }. When { F }\\in {R}{ F } but { F }\
Even-dimensional General Relativity from Born–Infeld gravity
Energy Technology Data Exchange (ETDEWEB)
Concha, P.K.; Peñafiel, D.M.; Rodríguez, E.K.; Salgado, P., E-mail: pasalgad@udec.cl
2013-10-01
It is an accepted fact that requiring the Lovelock theory to have the maximum possible number of degree of freedom, fixes the parameters in terms of the gravitational and the cosmological constants. In odd dimensions, the Lagrangian is a Chern–Simons form for the (A)dS group. In even dimensions, the action has a Born–Infeld-like form. Recently was shown that standard odd-dimensional General Relativity can be obtained from Chern–Simons gravity theory for a certain Lie algebra B. Here we report on a simple model that suggests a mechanism by which standard even-dimensional General Relativity may emerge as a weak coupling constant limit of a Born–Infeld theory for a certain Lie subalgebra of the algebra B. Possible extension to the case of even-dimensional supergravity is briefly discussed.
New classes of bi-axially symmetric solutions to four-dimensional Vasiliev higher spin gravity
Energy Technology Data Exchange (ETDEWEB)
Sundell, Per; Yin, Yihao [Departamento de Ciencias Físicas, Universidad Andres Bello,Republica 220, Santiago de Chile (Chile)
2017-01-11
We present new infinite-dimensional spaces of bi-axially symmetric asymptotically anti-de Sitter solutions to four-dimensional Vasiliev higher spin gravity, obtained by modifications of the Ansatz used in https://arxiv.org/abs/1107.1217, which gave rise to a Type-D solution space. The current Ansatz is based on internal semigroup algebras (without identity) generated by exponentials formed out of the bi-axial symmetry generators. After having switched on the vacuum gauge function, the resulting generalized Weyl tensor is given by a sum of generalized Petrov type-D tensors that are Kerr-like or 2-brane-like in the asymptotic AdS{sub 4} region, and the twistor space connection is smooth in twistor space over finite regions of spacetime. We provide evidence for that the linearized twistor space connection can be brought to Vasiliev gauge.
Remarks on the Taub-NUT solution in Chern–Simons modified gravity
Energy Technology Data Exchange (ETDEWEB)
Brihaye, Yves, E-mail: yves.brihaye@umons.ac.be [Physique-Mathématique, Universite de Mons-Hainaut, Mons (Belgium); Radu, Eugen [Departamento de Física da Universidade de Aveiro and CIDMA, Campus de Santiago, 3810-183 Aveiro (Portugal)
2017-01-10
We discuss the generalization of the NUT spacetime in General Relativity (GR) within the framework of the (dynamical) Einstein–Chern–Simons (ECS) theory with a massless scalar field. These configurations approach asymptotically the NUT spacetime and are characterized by the ‘electric’ and ‘magnetic’ mass parameters and a scalar ‘charge’. The solutions are found both analytically and numerically. The analytical approach is perturbative around the Einstein gravity background. Our results indicate that the ECS configurations share all basic properties of the NUT spacetime in GR. However, when considering the solutions inside the event horizon, we find that in contrast to the GR case, the spacetime curvature grows (apparently) without bound.
Is nonrelativistic gravity possible?
Kocharyan, A. A.
2009-01-01
We study nonrelativistic gravity using the Hamiltonian formalism. For the dynamics of general relativity (relativistic gravity) the formalism is well known and called the Arnowitt-Deser-Misner (ADM) formalism. We show that if the lapse function is constrained correctly, then nonrelativistic gravity is described by a consistent Hamiltonian system. Surprisingly, nonrelativistic gravity can have solutions identical to relativistic gravity ones. In particular, (anti-)de Sitter black holes of Eins...
New features of extended wormhole solutions in the scalar field gravity theories
Energy Technology Data Exchange (ETDEWEB)
Nandi, Kamal K [Department of Mathematics, University of North Bengal, Siliguri 734 013 (India); Nigmatzyanov, Ilnur; Izmailov, Ramil; Migranov, Nail G [Joint Research Laboratory, Bashkir State Pedagogical University, Ufa 450000 (Russian Federation)], E-mail: kamalnandi1952@yahoo.co.in, E-mail: ilnur.nigmat@gmail.com, E-mail: ramil.ejik@gmail.com, E-mail: ufangm@yahoo.co.uk
2008-08-21
This paper reports new interesting features characteristic of wormhole solutions in the scalar field gravity theories. To demonstrate these, using a slightly modified form of the Matos-Nunez algorithm, we obtain an extended class of asymptotically flat wormhole solutions belonging to the Einstein minimally coupled scalar field theory. Generally, solutions in these theories do not represent traversable wormholes due to the occurrence of curvature singularities. However, the Ellis I solution of the Einstein minimally coupled theory, when Wick rotated, yields an Ellis class III solution representing a singularity-free traversable wormhole. We see that Ellis I and III are not essentially independent solutions. The Wick-rotated seed solutions, extended by the algorithm, contain two new parameters a and {delta}. The effect of the parameter a on the geodesic motion of test particles reveals some remarkable features. By arguing for Sagnac effect in the extended Wick-rotated solution, we find that the parameter a can indeed be interpreted as a rotation parameter of the wormhole. The analysis reported here has wide applicability, for it can be adopted in other scalar field theories, including string theory.
Generalized spheroidal spacetimes in 5-D Einstein-Maxwell-Gauss-Bonnet gravity
Energy Technology Data Exchange (ETDEWEB)
Hansraj, Sudan [University of KwaZulu Natal, Astrophysics and Cosmology Research Unit, Durban (South Africa)
2017-08-15
The field equations for static EGBM gravity are obtained and transformed to an equivalent form through a coordinate redefinition. A form for one of the metric potentials that generalizes the spheroidal ansatz of Vaidya-Tikekar superdense stars and additionally prescribing the electric field intensity yields viable solutions. Some special cases of the general solution are considered and analogous classes in the Einstein framework are studied. In particular the Finch-Skea ansatz is examined in detail and found to satisfy the elementary physical requirements. These include positivity of pressure and density, the existence of a pressure free hypersurface marking the boundary, continuity with the exterior metric, a subluminal sound speed as well as the energy conditions. Moreover, the solution possesses no coordinate singularities. It is found that the impact of the Gauss-Bonnet term is to correct undesirable features in the pressure profile and sound speed index when compared to the equivalent Einstein gravity model. Furthermore graphical analyses suggest that higher densities are achievable for the same radial values when compared to the 5-dimensional Einstein case. The case of a constant gravitational potential, isothermal distribution as well as an incompressible fluid are studied. All exact solutions derived exhibit an equation of state explicitly. (orig.)
Exact radial solution in 2+1 gravity with a real scalar field
Energy Technology Data Exchange (ETDEWEB)
Schmidt, Hans-Jürgen, E-mail: hjschmi@rz.uni-potsdam.de [Institut für Mathematik, Universität Potsdam Am Neuen Palais 10, D-14469 Potsdam (Germany); Singleton, Douglas, E-mail: dougs@csufresno.edu [Institut für Mathematik, Universität Potsdam Am Neuen Palais 10, D-14469 Potsdam (Germany); Department of Physics, Institut Teknologi Bandung (Indonesia); Physics Department, CSU Fresno, Fresno, CA 93740-8031 (United States)
2013-04-25
In this Letter we give some general considerations about circularly symmetric, static space–times in 2+1 dimensions, focusing first on the surprising (at the time) existence of the BTZ black hole solution. We show that BTZ black holes and Schwarzschild black holes in 3+1 dimensions originate from different definitions of a black hole. There are two by-products of this general discussion: (i) we give a new and simple derivation of (2+1)-dimensional Anti-de Sitter (AdS) space–time; (ii) we present an exact solution to (2+1)-dimensional gravity coupled to a self-interacting real scalar field. The spatial part of the metric of this solution is flat but the temporal part behaves asymptotically like AdS space–time. The scalar field has logarithmic behavior as one would expect for a massless scalar field in flat space–time. The solution can be compared to gravitating scalar field solutions in 3+1 dimensions but with certain oddities connected with the (2+1)-dimensional character of the space–time. The solution is unique to 2+1 dimensions; it does not carry over to 3+1 dimensions.
Exact radial solution in 2 + 1 gravity with a real scalar field
Schmidt, Hans-Jürgen; Singleton, Douglas
2013-04-01
In this Letter we give some general considerations about circularly symmetric, static space-times in 2 + 1 dimensions, focusing first on the surprising (at the time) existence of the BTZ black hole solution. We show that BTZ black holes and Schwarzschild black holes in 3 + 1 dimensions originate from different definitions of a black hole. There are two by-products of this general discussion: (i) we give a new and simple derivation of (2 + 1)-dimensional Anti-de Sitter (AdS) space-time; (ii) we present an exact solution to (2 + 1)-dimensional gravity coupled to a self-interacting real scalar field. The spatial part of the metric of this solution is flat but the temporal part behaves asymptotically like AdS space-time. The scalar field has logarithmic behavior as one would expect for a massless scalar field in flat space-time. The solution can be compared to gravitating scalar field solutions in 3 + 1 dimensions but with certain oddities connected with the (2 + 1)-dimensional character of the space-time. The solution is unique to 2 + 1 dimensions; it does not carry over to 3 + 1 dimensions.
Standard general relativity from Chern-Simons gravity
International Nuclear Information System (INIS)
Izaurieta, F.; Minning, P.; Perez, A.; Rodriguez, E.; Salgado, P.
2009-01-01
Chern-Simons models for gravity are interesting because they provide a truly gauge-invariant action principle in the fiber-bundle sense. So far, their main drawback has largely been its perceived remoteness from standard General Relativity, based on the presence of higher powers of the curvature in the Lagrangian (except, remarkably, for three-dimensional spacetime). Here we report on a simple model that suggests a mechanism by which standard General Relativity in five-dimensional spacetime may indeed emerge at a special critical point in the space of couplings, where additional degrees of freedom and corresponding 'anomalous' Gauss-Bonnet constraints drop out from the Chern-Simons action. To achieve this goal, both the Lie algebra g and the symmetric g-invariant tensor that define the Chern-Simons Lagrangian are constructed by means of the Lie algebra S-expansion method with a suitable finite Abelian semigroup S. The results are generalized to arbitrary odd dimensions, and the possible extension to the case of eleven-dimensional supergravity is briefly discussed.
Modeling of gravity-imbibition and gravity-drainage processes: Analytic and numerical solutions
DEFF Research Database (Denmark)
Bech, N.; Jensen, O.K.; Nielsen, B.
1991-01-01
A matrix/fracture exchange model for a fractured reservoir simulator is described. Oil/water imbibition is obtained from a diffusion equation with water saturation as the dependent variable. Gas/oil gravity drainage and imbibition are calculated by taking into account the vertical saturation...... distribution in the matrix blocks....
A Theory of Gravity and General Relativity based on Quantum Electromagnetism
Zheng-Johansson, J. X.
2018-02-01
Based on first principles solutions in a unified framework of quantum mechanics and electromagnetism we predict the presence of a universal attractive depolarisation radiation (DR) Lorentz force (F) between quantum entities, each being either an IED matter particle or light quantum, in a polarisable dielectric vacuum. Given two quantum entities i = 1, 2 of either kind, of characteristic frequencies ν _i^0, masses m_i0 = hν _i^0/{c^2} and separated at a distance r 0, the solution for F is F = - G}m_1^0m_2^0/{≤ft( {{r^2}} \\right)^2}, where G} = χ _0^2{e^4}/12{π ^2} \\in _0^2{ρ _λ };{χ _0} is the susceptibility and π λ is the reduced linear mass density of the vacuum. This force F resembles in all respects Newton’s gravity and is accurate at the weak F limit; hence ℊ equals the gravitational constant G. The DR wave fields and hence the gravity are each propagated in the dielectric vacuum at the speed of light c; these can not be shielded by matter. A test particle µ of mass m 0 therefore interacts gravitationally with all of the building particles of a given large mass M at r 0 apart, by a total gravitational force F = -GMm 0/(r 0)2 and potential V = -∂F/∂r 0. For a finite V and hence a total Hamiltonian H = m 0 c 2 + V, solution for the eigenvalue equation of µ presents a red-shift in the eigen frequency ν = ν 0(1 - GM/r 0 c 2) and hence in other wave variables. The quantum solutions combined with the wave nature of the gravity further lead to dilated gravito optical distance r = r 0/(1 - GM/r 0 c 2) and time t = t 0/(1 - GM/r 0 c 2), and modified Newton’s gravity and Einstein’s mass energy relation. Applications of these give predictions of the general relativistic effects manifested in the four classical test experiments of Einstein’s general relativity (GR), in direct agreement with the experiments and the predictions given based on GR.
Generalized second law of thermodynamics in f(T) gravity
Energy Technology Data Exchange (ETDEWEB)
Karami, K.; Abdolmaleki, A., E-mail: KKarami@uok.ac.ir, E-mail: AAbdolmaleki@uok.ac.ir [Department of Physics, University of Kurdistan, Pasdaran St., Sanandaj (Iran, Islamic Republic of)
2012-04-01
We investigate the validity of the generalized second law (GSL) of gravitational thermodynamics in the framework of f(T) modified teleparallel gravity. We consider a spatially flat FRW universe containing only the pressureless matter. The boundary of the universe is assumed to be enclosed by the Hubble horizon. For two viable f(T) models containing f(T) = T+μ{sub 1}((−T)){sup n} and f(T) = T−μ{sub 2}T(1−e{sup βT{sub 0}/T}), we first calculate the effective equation of state and deceleration parameters. Then, (we investigate the null and strong energy conditions and conclude that a sudden future singularity appears in both models. Furthermore, using a cosmographic analysis we check the viability of two models. Finally, we examine the validity of the GSL and find that for both models it) is satisfied from the early times to the present epoch. But in the future, the GSL is violated for the special ranges of the torsion scalar T.
Generalized Curvature-Matter Couplings in Modified Gravity
Directory of Open Access Journals (Sweden)
Tiberiu Harko
2014-07-01
Full Text Available In this work, we review a plethora of modified theories of gravity with generalized curvature-matter couplings. The explicit nonminimal couplings, for instance, between an arbitrary function of the scalar curvature R and the Lagrangian density of matter, induces a non-vanishing covariant derivative of the energy-momentum tensor, implying non-geodesic motion and, consequently, leads to the appearance of an extra force. Applied to the cosmological context, these curvature-matter couplings lead to interesting phenomenology, where one can obtain a unified description of the cosmological epochs. We also consider the possibility that the behavior of the galactic flat rotation curves can be explained in the framework of the curvature-matter coupling models, where the extra terms in the gravitational field equations modify the equations of motion of test particles and induce a supplementary gravitational interaction. In addition to this, these models are extremely useful for describing dark energy-dark matter interactions and for explaining the late-time cosmic acceleration.
On linear equations with general polynomial solutions
Laradji, A.
2018-04-01
We provide necessary and sufficient conditions for which an nth-order linear differential equation has a general polynomial solution. We also give necessary conditions that can directly be ascertained from the coefficient functions of the equation.
Robbins, J. W.
1985-01-01
An autonomous spaceborne gravity gradiometer mission is being considered as a post Geopotential Research Mission project. The introduction of satellite diometry data to geodesy is expected to improve solid earth gravity models. The possibility of utilizing gradiometer data for the determination of pertinent gravimetric quantities on a local basis is explored. The analytical technique of least squares collocation is investigated for its usefulness in local solutions of this type. It is assumed, in the error analysis, that the vertical gravity gradient component of the gradient tensor is used as the raw data signal from which the corresponding reference gradients are removed to create the centered observations required in the collocation solution. The reference gradients are computed from a high degree and order geopotential model. The solution can be made in terms of mean or point gravity anomalies, height anomalies, or other useful gravimetric quantities depending on the choice of covariance types. Selected for this study were 30 x 30 foot mean gravity and height anomalies. Existing software and new software are utilized to implement the collocation technique. It was determined that satellite gradiometry data at an altitude of 200 km can be used successfully for the determination of 30 x 30 foot mean gravity anomalies to an accuracy of 9.2 mgal from this algorithm. It is shown that the resulting accuracy estimates are sensitive to gravity model coefficient uncertainties, data reduction assumptions and satellite mission parameters.
On the stability of the cosmological solutions in f(R, G) gravity
International Nuclear Information System (INIS)
De la Cruz-Dombriz, Álvaro; Sáez-Gómez, Diego
2012-01-01
Modified gravity is one of the most promising candidates for explaining the current accelerating expansion of the Universe, and even its unification with the inflationary epoch. Nevertheless, the wide range of models capable of explaining the phenomena of dark energy imposes that current research focuses on a more precise study of the possible effects of modified gravity on both cosmological and local levels. In this paper, we focus on the analysis of a type of modified gravity, the so-called f(R, G) gravity, and we perform a deep analysis on the stability of important cosmological solutions. This not only can help to constrain the form of the gravitational action, but also facilitate a better understanding of the behavior of the perturbations in this class of higher order theories of gravity, which will lead to a more precise analysis of the full spectrum of cosmological perturbations in future. (paper)
Gamow, George
2003-01-01
A distinguished physicist and teacher, George Gamow also possessed a special gift for making the intricacies of science accessible to a wide audience. In Gravity, he takes an enlightening look at three of the towering figures of science who unlocked many of the mysteries behind the laws of physics: Galileo, the first to take a close look at the process of free and restricted fall; Newton, originator of the concept of gravity as a universal force; and Einstein, who proposed that gravity is no more than the curvature of the four-dimensional space-time continuum.Graced with the author's own draw
A quantum gravity tensor equation formally integrating general relativity with quantum mechanics
Duan, Xu
2016-01-01
Extending black-hole entropy to ordinary objects, we propose kinetic entropy tensor, based on which a quantum gravity tensor equation is established. Our investigation results indicate that if N=1, the quantum gravity tensor equation returns to Schrodinger integral equation. When N becomes sufficiently large, it is equivalent to Einstein field equation. This illustrates formal unification and intrinsic compatibility of general relativity with quantum mechanics. The quantum gravity equation ma...
Comment on the Exterior Solutions and Their Geometry in Scalar-Tensor Theories of Gravity
Tsuchida, T.; Watanabe, K.
1999-01-01
We study series of stationary solutions with asymptotic flatness properties in the Einstein-Maxwell-free scalar system because they are locally equivalent to the exterior solutions in some class of scalar-tensor theories of gravity. First, we classify spherical exterior solutions into two types of solutions, an apparently black hole type solution and an apparently worm hole type solution. The solutions contain three parameters, and we clarify their physical significance. Second, we reduce the field equations for the axisymmetric exterior solutions. We find that the reduced equations are partially the same as the Ernst equations. As simple examples, we derive new series of static, axisymmetric exterior solutions, which correspond to Voorhees's solutions. We then establish a non-trivial relation between the spherical exterior solutions and our new solutions. Finally, since null geodesics have conformally invariant properties, we study the local geometry of the exterior solutions by using the optical scalar equations and find some anomalous behavior of the null geodesics.
Rivera, Andrea
2017-01-01
Gravity is all around us. Learn how it is used in art, technology, and engineering. Five easy-to-read chapters explain the science behind gravity, as well as its real-world applications. Vibrant, full-color photos, bolded glossary words, and a key stats section let readers zoom in even deeper. Aligned to Common Core Standards and correlated to state standards. Abdo Zoom is a division of ABDO.
General solution of linear vector supersymmetry
International Nuclear Information System (INIS)
Blasi, Alberto; Maggiore, Nicola
2007-01-01
We give the general solution of the Ward identity for the linear vector supersymmetry which characterizes all topological models. Such a solution, whose expression is quite compact and simple, greatly simplifies the study of theories displaying a supersymmetric algebraic structure, reducing to a few lines the proof of their possible finiteness. In particular, the cohomology technology, usually involved for the quantum extension of these theories, is completely bypassed. The case of Chern-Simons theory is taken as an example
Unsteady Stokes equations: Some complete general solutions
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
making use of eq. (2), it is easy to see that the pressure is harmonic. Hence, on operating the Laplace operator on eq. (3), we find that the velocity vector satisfies the equation. ∇2. (. ∇2 −. 1 ν. ∂. ∂t. ) V = 0. (4). 1.1 A complete general solution of unsteady Stokes equations. Let (V, p) be any solution of (2) and (3). We define.
Geodesically complete BTZ-type solutions of 2 + 1 Born–Infeld gravity
International Nuclear Information System (INIS)
Bazeia, D; Losano, L; Olmo, Gonzalo J; Rubiera-Garcia, D
2017-01-01
We study Born–Infeld gravity coupled to a static, non-rotating electric field in 2 + 1 dimensions and find exact analytical solutions. Two families of such solutions represent geodesically complete, and hence nonsingular, spacetimes. Another family represents a point-like charge with a singularity at the center. Despite the absence of rotation, these solutions resemble the charged, rotating BTZ solution of general relativity but with a richer structure in terms of horizons. The nonsingular character of the first two families turn out to be attached to the emergence of a wormhole structure on their innermost region. This seems to be a generic prediction of extensions of general relativity formulated in metric-affine (or Palatini) spaces, where metric and connection are regarded as independent degrees of freedom. (paper)
Dadhich, Naresh; Pons, Josep M
We study static black hole solutions in Einstein and Einstein-Gauss-Bonnet gravity with the topology of the product of two spheres, [Formula: see text], in higher dimensions. There is an unusual new feature of the Gauss-Bonnet black hole: the avoidance of a non-central naked singularity prescribes a mass range for the black hole in terms of [Formula: see text]. For an Einstein-Gauss-Bonnet black hole a limited window of negative values for [Formula: see text] is also permitted. This topology encompasses black strings, branes, and generalized Nariai metrics. We also give new solutions with the product of two spheres of constant curvature.
Generalized solutions of nonlinear partial differential equations
Rosinger, EE
1987-01-01
During the last few years, several fairly systematic nonlinear theories of generalized solutions of rather arbitrary nonlinear partial differential equations have emerged. The aim of this volume is to offer the reader a sufficiently detailed introduction to two of these recent nonlinear theories which have so far contributed most to the study of generalized solutions of nonlinear partial differential equations, bringing the reader to the level of ongoing research.The essence of the two nonlinear theories presented in this volume is the observation that much of the mathematics concernin
Energy Technology Data Exchange (ETDEWEB)
Nashed, Gamal G.L. [The British University in Egypt, Centre for Theoretical Physics, P.O. Box 43, Sherouk City (Egypt); Ain Shams University, Mathematics Department, Faculty of Science, Cairo (Egypt)
2013-04-15
In this paper a non-diagonal, spherically symmetric, tetrad field that contains an arbitrary function, S(r), which corresponds to a local Lorentz transformation, is applied to the field equations of f(T) gravity theories. Analytic vacuum solutions with integration constants are derived. These constants are studied by calculating the total conserved charge associated with each solution. The study shows that the obtained solutions represent the Schwarzschild-Ads spacetime. (orig.)
Analysis of Factors Affecting Stress Solution at Concrete Gravity Dam Heel
Hung, Vu Hoang; Quoc Cong, Trinh; Tongchun, Li
2010-05-01
Along with Vietnam's development, various hydraulic constructions including concrete gravity dams have been being built. In some of these dams, the fractures occurred at the heel of the dams are even in small and media dams. There are various reasons cause the factures at dam heel but the main reason is the stress states at dam heel are not determined correctly while designing dam. In this paper, several factors affecting stress solution at concrete gravity dam heel such as element mesh size, crack joints of upstream foundation, execution process are investigated by using finite element model of Banve concrete gravity dam. This work is very significant when the more high concrete gravity dams will be constructed in Vietnam year after year.
On pseudoparticle solutions in Yang's theory of gravity
International Nuclear Information System (INIS)
Mielke, E.W.
1980-03-01
Within the framework of differential geometry, Yang's parallel-displacement gauge theory is considered with respect to ''pure'' gravitational fields. In a four-dimensional Riemannian manifold it is shown that the double self-dual solutions obey Einstein's vacuum equations with cosmological term, whereas the double anti-self-dual configurations satisfy the Rainich conditions of Wheeler's geometrodynamics. Conformal methods reveal that the gravitational analogue of the ''instanton'' or pseudoparticle solution of Yang-Mills theory was already known to Riemann. (author)
Directory of Open Access Journals (Sweden)
M.R. Setare
2017-01-01
Full Text Available In this paper we study the near horizon symmetry algebra of the non-extremal black hole solutions of the Chern–Simons-like theories of gravity, which are stationary but are not necessarily spherically symmetric. We define the extended off-shell ADT current which is an extension of the generalized ADT current. We use the extended off-shell ADT current to define quasi-local conserved charges such that they are conserved for Killing vectors and asymptotically Killing vectors which depend on dynamical fields of the considered theory. We apply this formalism to the Generalized Minimal Massive Gravity (GMMG and obtain conserved charges of a spacetime which describes near horizon geometry of non-extremal black holes. Eventually, we find the algebra of conserved charges in Fourier modes. It is interesting that, similar to the Einstein gravity in the presence of negative cosmological constant, for the GMMG model also we obtain the Heisenberg algebra as the near horizon symmetry algebra of the black flower solutions. Also the vacuum state and all descendants of the vacuum have the same energy. Thus these zero energy excitations on the horizon appear as soft hairs on the black hole.
Cosmological Solutions of Tensor–Vector Theories of Gravity by ...
Indian Academy of Sciences (India)
We consider tensor–vector theories by varying the space-time–matter coupling constant (varying Einstein velocity) in a spatially flat FRW universe.We examine the dynamics of this model by dynamical system method assuming a CDM background and we find some exact solutions by considering the character of critical ...
Cosmological Solutions of Tensor–Vector Theories of Gravity by ...
Indian Academy of Sciences (India)
Also we set restrictions on the varying Einstein velocity to solve the horizon problem. This gives a selection rule for choosing the appropriate stable solution. We will see that it is possible to produce the background expansion history () indicated by observations. Finally we will discuss the behavior of the speed of light ...
Gamal, G. L. Nashed
2011-11-01
A theory of (4+1)-dimensional gravity is developed on the basis of the teleparallel theory equivalent to general relativity. The fundamental gravitational field variables are the five-dimensional vector fields (pentad), defined globally on a manifold M, and gravity is attributed to the torsion. The Lagrangian density is quadratic in the torsion tensor. We then give the exact five-dimensional solution. The solution is a generalization of the familiar Schwarzschild and Kerr solutions of the four-dimensional teleparallel equivalent of general relativity. We also use the definition of the gravitational energy to calculate the energy and the spatial momentum.
21 CFR 864.9320 - Copper sulfate solution for specific gravity determinations.
2010-04-01
... determinations. 864.9320 Section 864.9320 Food and Drugs FOOD AND DRUG ADMINISTRATION, DEPARTMENT OF HEALTH AND... determinations. (a) Identification. A copper sulfate solution for specific gravity determinations is a device used to determine whether the hemoglobin content of a potential donor's blood meets the required level...
A new approach to the regularization of regional gravity field solutions in SRBF
Naeimi, Majid; Flury, Jakob
2016-04-01
We present a purely data-dependent approach to the choice of the regularization parameter for regional gravity field solutions in spherical radial base functions. The method is based on the space-localization feature of the base functions and needs a prior gravity field solution to solve for the regional gravity field coefficients. However, to be independent of any prior model, we estimate an approximate solution using a realistic first guess for the regularization parameter. The final regularization parameter and therefore the final regional solution are obtained in an iterative procedure. We apply our methodology to real GOCE gravity gradients and assess the performance of the method in several test regions. Results show that our approach outperforms the existing methods such as the L-curve, the GCV and the VCE. In addition, the estimated coefficients represent the shape of the signal (geoid) in the target region and have therefore physical meaning. More details are given and the results are discussed in this contribution.
GRIM5-C1: Combination solution of the global gravity field to degree and order 120
Gruber, Thomas; Bode, Albert; Reigber, Christoph; Schwintzer, Peter; Balmino, Georges; Biancale, Richard; Lemoine, Jean-Michel
2000-12-01
The new satellite Earth gravity field model GRIM5-S1 was recently prepared in a joint GFZ and GRGS effort. Based on this satellite solution and terrestrial and altimetric gravity anomalies from NIMA, a combined model GRIM5-C1, with full variance-covariance matrix up to degree and order 120, was computed. Surface gravity and altimetric gravity data are corrected for several systematic effects, such as ellipsoidal corrections and aliasing. A weighting scheme for gravity anomalies, according to their given standard deviations was developed. From each data set full normal equations were set up and finally combined with the GRIM5-S1 normals. To take into account good information from the satellite-only model a procedure was developed to identify such coefficients and appropriately weighed them in the final normal equation system. Internal error propagation and comparisons to external data sets show, that the GRIM5-C1 model represents the best state of long wavelength gravity field models.
Dynamic wormhole solutions in Einstein-Cartan gravity
Mehdizadeh, Mohammad Reza; Ziaie, Amir Hadi
2017-12-01
In the present work, we investigate evolving wormhole configurations described by a constant redshift function in Einstein-Cartan theory. The matter content consists of a Weyssenhoff fluid along with an anisotropic matter which together generalize the anisotropic energy momentum tensor in general relativity in order to include the effects of intrinsic angular momentum (spin) of particles. Using a generalized Friedmann-Robertson-Walker spacetime, we derive analytical evolving wormhole geometries by assuming a particular equation of state for energy density and pressure profiles. We introduce exact asymptotically flat and anti-de Sitter spacetimes that admit traversable wormholes and respect energy conditions throughout the spacetime. The rate of expansion of these evolving wormholes is determined only by the Friedmann equation in the presence of spin effects.
Cosmic string solution in a Born-Infeld type theory of gravity
International Nuclear Information System (INIS)
Rocha, W.J. da; Guimaraes, M.E.X.
2009-01-01
Full text. Advances in the formal structure of string theory point to the emergence, and necessity, of a scalar-tensorial theory of gravity. It seems that, at least at high energy scales, the Einstein's theory is not enough to explain the gravitational phenomena. In other words, the existence of a scalar (gravitational) field acting as a mediator of the gravitational interaction together with the usual purely rank-2 tensorial field is, indeed, a natural prediction of unification models as supergravity, superstrings and M-theory. This type of modified gravitation was first introduced in a different context in the 60's in order to incorporate the Mach's principle into relativity, but nowadays it acquired different sense in cosmology and gravity theories. Although such unification theories are the most acceptable, they all exist in higher dimensional spaces. The compactification from these higher dimensions to the 4-dimensional physics is not unique and there exist many effective theories of gravity which come from the unification process. Each of them must, of course, satisfy some predictions. Here, in this paper, we will deal with one of them. The so-called NDL theory. One important assumption in General Relativity is that all field interact in the same way with gravity. This is the so called Strong Equivalence Principle (SEP). It is well known, with good accuracy, that this is true when we concern with matter to matter interaction, i.e, the Weak Equivalence Principle(WEP) is tested. But, until now, there is no direct observational confirmation of this affirmation to the gravity to gravity interaction. In an extension of the field theoretical description of General Relativity constructed by is used to propose an alternative field theory of gravity. In this theory gravitons propagate in a different spacetime. The velocity of propagation of the gravitational waves in this theory does not coincide with the General Relativity predictions. (author)
Types III and N solutions to quadratic gravity
Czech Academy of Sciences Publication Activity Database
Málek, T.; Pravda, Vojtěch
2011-01-01
Roč. 84, č. 2 (2011), 024047 ISSN 1550-7998 R&D Projects: GA ČR GAP203/10/0749 Institutional research plan: CEZ:AV0Z10190503 Keywords : constant scalar invariants * higher dimensions * spacetimes * identities * supergravity Subject RIV: BA - General Mathematics Impact factor: 4.558, year: 2011 http://prd.aps.org/abstract/PRD/v84/i2/e024047
General proof of the entropy principle for self-gravitating fluid in f ( R) gravity
Fang, Xiongjun; Guo, Minyong; Jing, Jiliang
2016-08-01
The discussions on the connection between gravity and thermodynamics attract much attention recently. We consider a static self-gravitating perfect fluid system in f ( R) gravity, which is an important theory could explain the accelerated expansion of the universe. We first show that the Tolman-Oppenheimer-Volkoff equation of f ( R) theories can be obtained by thermodynamical method in spherical symmetric spacetime. Then we prove that the maximum entropy principle is also valid for f ( R) gravity in general static spacetimes beyond spherical symmetry. The result shows that if the constraint equation is satisfied and the temperature of fluid obeys Tolmans law, the extrema of total entropy implies other components of gravitational equations. Conversely, if f ( R) gravitational equation hold, the total entropy of the fluid should be extremum. Our work suggests a general and solid connection between f ( R) gravity and thermodynamics.
International Nuclear Information System (INIS)
Hwang, Jai-chan; Noh, Hyerim
2005-01-01
We present cosmological perturbation theory based on generalized gravity theories including string theory correction terms and a tachyonic complication. The classical evolution as well as the quantum generation processes in these varieties of gravity theories are presented in unified forms. These apply both to the scalar- and tensor-type perturbations. Analyses are made based on the curvature variable in two different gauge conditions often used in the literature in Einstein's gravity; these are the curvature variables in the comoving (or uniform-field) gauge and the zero-shear gauge. Applications to generalized slow-roll inflation and its consequent power spectra are derived in unified forms which include a wide range of inflationary scenarios based on Einstein's gravity and others
Vector theory of gravity: Universe without black holes and solution of dark energy problem
Svidzinsky, Anatoly A.
2017-12-01
We propose an alternative theory of gravity which assumes that background geometry of the Universe is fixed four dimensional Euclidean space and gravity is a vector field A k in this space which breaks the Euclidean symmetry. Direction of A k gives the time coordinate, while perpendicular directions are spatial coordinates. Vector gravitational field is coupled to matter universally and minimally through the equivalent metric f ik which is a functional of A k . We show that such assumptions yield a unique theory of gravity, it is free of black holes and, to the best of our knowledge, passes all available tests. For cosmology our theory predicts the same evolution of the Universe as general relativity with cosmological constant and zero spatial curvature. However, the present theory provides explanation of the dark energy as energy of longitudinal gravitational field induced by the Universe expansion and yields, with no free parameters, the value of {{{Ω }}}{{Λ }}=2/3≈ 0.67 which is consistent with the recent Planck result {{{Ω }}}{{Λ }}=0.686+/- 0.02. Such close agreement with cosmological data indicates that gravity has a vector, rather than tensor, origin. We demonstrate that gravitational wave signals measured by LIGO are compatible with vector gravity. They are produced by orbital inspiral of massive neutron stars which can exist in the present theory. We also quantize gravitational field and show that quantum vector gravity is equivalent to QED. Vector gravity can be tested by making more accurate measurement of the time delay of radar signal traveling near the Sun; by improving accuracy of the light deflection experiments; or by measuring propagation direction of gravitational waves relative to laser interferometer arms. Resolving the supermassive object at the center of our Galaxy with VLBA could provide another test of gravity and also shed light on the nature of dark matter.
Orbit and Gravity Field Solutions from Swarm GPS Observations - First Result
Jaeggi, A.; Dahle, C.; Arnold, D.; Bock, H.; Flechtner, F.
2014-12-01
Although ESA's Earth Explorer Mission Swarm is primarily dedicated to measure the Earth's magnetic field, it may also serve as a gravity field mission. Equipped with GPS receivers, accelerometers, star-tracker assemblies and laser retro-reflectors, the three Swarm satellites are potentially capable to be used as a high-low satellite-to-satellite tracking (hl-SST) observing system, following the missions CHAMP (first single-satellite hl-SST mission), GRACE (twin-satellite mission with additional ultra-precise low-low SST and GOCE (single-satellite mission additionally equipped with a gradiometer). GRACE, dedicated to measure the time-variability of the gravity field, is the only mission still in orbit, but its lifetime will likely end before launch of its follow-on mission GRACE-FO in August 2017 primarily due to aging of the onboard batteries after meanwhile more than 12 years of operation. Swarm is probably a good candidate to provide time-variable gravity field solutions and to close a potential gap between GRACE and GRACE-FO. Consisting of three satellites, Swarm also offers to use inter-satellite GPS-derived baselines as additional observations. However, as of today it is not clear if such information will substantially improve the gravity field solutions. Nevertheless, the properties of the Swarm constellation with two lower satellites flying in a pendulum-like orbit and a slightly differently inclined third satellite at higher altitude still represent a unique observing system raising expectations at least compared to CHAMP derived time-variable gravity field solutions. Whatever processing method will be applied for Swarm gravity field recovery, its success strongly depends on the quality of the Swarm Level 1b data as well as the quality of the derived Swarm orbits. With first Level 1b data sets available since mid of May 2014 (excluding accelerometer data), first results for Swarm orbits and baselines, as well as Swarm gravity field solutions are presented
Generalization of the Randall–Sundrum solution
Directory of Open Access Journals (Sweden)
A.V. Kisselev
2016-08-01
Full Text Available The generalization of the Randall–Sundrum solution for the warp factor exp[σ(y] in the scenario with one extra coordinate y, non-factorizable space–time geometry and two branes is obtained. It is shown that the function obtained σ(y is symmetric with respect to an interchange of two branes. It also obeys the orbifold symmetry y→−y and explicitly reproduces jumps of its derivative on both branes. This solution is defined by the Einstein–Hilbert's equations up to a constant C. It is demonstrated that different values of C result in theories with quite different spectra of the Kaluza–Klein gravitons.
Static, spherically symmetric solutions with a scalar field in Rastall gravity
Bronnikov, K. A.; Fabris, J. C.; Piattella, O. F.; Santos, E. C.
2016-12-01
Rastall's theory belongs to the class of non-conservative theories of gravity. In vacuum, the only non-trivial static, spherically symmetric solution is the Schwarzschild one, except for a very special case. When a canonical scalar field is coupled to the gravity sector in this theory, new exact solutions appear for some values of the Rastall parameter a. Some of these solutions describe the same space-time geometry as the recently found solutions in the k-essence theory with a power function for the kinetic term of the scalar field. There is a large class of solutions (in particular, those describing wormholes and regular black holes) whose geometry coincides with that of solutions of GR coupled to scalar fields with nontrivial self-interaction potentials; the form of these potentials, however, depends on the Rastall parameter a. We also note that all solutions of GR with a zero trace of the energy-momentum tensor, including black-hole and wormhole ones, may be re-interpreted as solutions of Rastall's theory.
Lauriola, I.; Felisa, G.; Petrolo, D.; Di Federico, V.; Longo, S.
2018-05-01
We present an investigation on the combined effect of fluid rheology and permeability variations on the propagation of porous gravity currents in axisymmetric geometry. The fluid is taken to be of power-law type with behaviour index n and the permeability to depend from the distance from the source as a power-law function of exponent β. The model represents the injection of a current of non-Newtonian fluid along a vertical bore hole in porous media with space-dependent properties. The injection is either instantaneous (α = 0) or continuous (α > 0). A self-similar solution describing the rate of propagation and the profile of the current is derived under the assumption of small aspect ratio between the current average thickness and length. The limitations on model parameters imposed by the model assumptions are discussed in depth, considering currents of increasing/decreasing velocity, thickness, and aspect ratio, and the sensitivity of the radius, thickness, and aspect ratio to model parameters. Several critical values of α and β discriminating between opposite tendencies are thus determined. Experimental validation is performed using shear-thinning suspensions and Newtonian mixtures in different regimes. A box filled with ballotini of different diameter is used to reproduce the current, with observations from the side and bottom. Most experimental results for the radius and profile of the current agree well with the self-similar solution except at the beginning of the process, due to the limitations of the 2-D assumption and to boundary effects near the injection zone. The results for this specific case corroborate a general model for currents with constant or time-varying volume of power-law fluids propagating in porous domains of plane or radial geometry, with uniform or varying permeability, and the possible effect of channelization. All results obtained in the present and previous papers for the key parameters governing the dynamics of power-law gravity
Extension of Loop Quantum Gravity to Metric Theories beyond General Relativity
International Nuclear Information System (INIS)
Ma Yongge
2012-01-01
The successful background-independent quantization of Loop Quantum Gravity relies on the key observation that classical General Relativity can be cast into the connection-dynamical formalism with the structure group of SU(2). Due to this particular formalism, Loop Quantum Gravity was generally considered as a quantization scheme that applies only to General Relativity. However, we will show that the nonperturbative quantization procedure of Loop Quantum Gravity can be extended to a rather general class of metric theories of gravity, which have received increased attention recently due to motivations coming form cosmology and astrophysics. In particular, we will first introduce how to reformulate the 4-dimensional metric f(R) theories of gravity, as well as Brans-Dicke theory, into connection-dynamical formalism with real SU(2) connections as configuration variables. Through these formalisms, we then outline the nonpertubative canonical quantization of the f(R) theories and Brans-Dicke theory by extending the loop quantization scheme of General Relativity.
Asymptotically spacelike warped anti-de Sitter spacetimes in generalized minimal massive gravity
Setare, M. R.; Adami, H.
2017-06-01
In this paper we show that warped AdS3 black hole spacetime is a solution of the generalized minimal massive gravity (GMMG) and introduce suitable boundary conditions for asymptotically warped AdS3 spacetimes. Then we find the Killing vector fields such that transformations generated by them preserve the considered boundary conditions. We calculate the conserved charges which correspond to the obtained Killing vector fields and show that the algebra of the asymptotic conserved charges is given as the semi direct product of the Virasoro algebra with U(1) current algebra. We use a particular Sugawara construction to reconstruct the conformal algebra. Thus, we are allowed to use the Cardy formula to calculate the entropy of the warped black hole. We demonstrate that the gravitational entropy of the warped black hole exactly coincides with what we obtain via Cardy’s formula. As we expect, the warped Cardy formula also gives us exactly the same result as we obtain from the usual Cardy’s formula. We calculate mass and angular momentum of the warped black hole and then check that obtained mass, angular momentum and entropy to satisfy the first law of the black hole mechanics. According to the results of this paper we believe that the dual theory of the warped AdS3 black hole solution of GMMG is a warped CFT.
Asymptotically spacelike warped anti-de Sitter spacetimes in generalized minimal massive gravity
International Nuclear Information System (INIS)
Setare, M R; Adami, H
2017-01-01
In this paper we show that warped AdS 3 black hole spacetime is a solution of the generalized minimal massive gravity (GMMG) and introduce suitable boundary conditions for asymptotically warped AdS 3 spacetimes. Then we find the Killing vector fields such that transformations generated by them preserve the considered boundary conditions. We calculate the conserved charges which correspond to the obtained Killing vector fields and show that the algebra of the asymptotic conserved charges is given as the semi direct product of the Virasoro algebra with U (1) current algebra. We use a particular Sugawara construction to reconstruct the conformal algebra. Thus, we are allowed to use the Cardy formula to calculate the entropy of the warped black hole. We demonstrate that the gravitational entropy of the warped black hole exactly coincides with what we obtain via Cardy’s formula. As we expect, the warped Cardy formula also gives us exactly the same result as we obtain from the usual Cardy’s formula. We calculate mass and angular momentum of the warped black hole and then check that obtained mass, angular momentum and entropy to satisfy the first law of the black hole mechanics. According to the results of this paper we believe that the dual theory of the warped AdS 3 black hole solution of GMMG is a warped CFT. (paper)
Bouncing solutions from generalized EoS
Energy Technology Data Exchange (ETDEWEB)
Contreras, F. [Universidad de Santiago de Chile, Departamento de Matematicas, Santiago (Chile); Cruz, N.; Palma, G. [Universidad de Santiago, Departamento de Fisica, Santiago (Chile)
2017-12-15
We present an exact analytical bouncing solution for a closed universe filled with only one exotic fluid with negative pressure, obeying a generalized equation of state (GEoS) of the form p(ρ) = Aρ+Bρ{sup λ}, where A, B and λ are constants. In our solution A = -1/3, λ = 1/2, and B < 0 is kept as a free parameter. For particular values of the initial conditions, we find that our solution obeys the null energy condition (NEC), which allows us to reinterpret the matter source as that of a real scalar field, φ, with a positive kinetic energy and a potential V(φ). We numerically compute the scalar field as a function of time as well as its potential V(φ), and we find an analytical function for the potential that fits very accurately with the numerical data obtained. The shape of this potential can be well described by a Gaussian-type of function, and hence there is no spontaneous symmetry minimum of V(φ). We show numerically that the bouncing scenario is structurally stable in a small vicinity of the value A = -1/3. We also include the study of the evolution of the linear fluctuations due to linear perturbations in the metric. These perturbations show an oscillatory behavior near the bouncing and approach a constant at large scales. (orig.)
Solution for a local straight cosmic string in the braneworld gravity
Energy Technology Data Exchange (ETDEWEB)
Abdalla, M.C.B.; Carlesso, P.F. [UNESP, Universidade Estadual Paulista, Instituto de Fisica Teorica, Rua Dr. Bento Teobaldo Ferraz 271, Bloco II, Barra-Funda, Caixa Postal 70532-2, Sao Paulo, SP (Brazil); Hoff da Silva, J.M. [UNESP, Universidade Estadual Paulista, Departamento de Fisica e Quimica, Guaratingueta, SP (Brazil)
2015-09-15
In this work we deal with the spacetime shaped by a straight cosmic string, emerging from local gauge theories, in the braneworld gravity context. We search for physical consequences of string features due to the modified gravitational scenario encoded in the projected gravitational equations. It is shown that cosmic strings in braneworld gravity may present significant differences when compared to the general relativity predictions, since its linear density is modified and the deficit angle produced by the cosmic string is attenuated. Furthermore, the existence of cosmic strings in that scenario requires a strong restriction to the braneworld tension: λ ≥ 3 x 10{sup -17}, in Planck units. (orig.)
Black hole continuum spectra as a test of general relativity: quadratic gravity
Ayzenberg, Dimitry; Yunes, Nicolás
2017-06-01
Observations of the continuum spectrum emitted by accretion disks around black holes allows us to infer their properties, including possibly whether black holes are described by the Kerr metric. Some modified gravity theories do not admit the Kerr metric as a solution, and thus, continuum spectrum observations could be used to constrain these theories. We here investigate whether current and next generation x-ray observations of the black hole continuum spectrum can constrain such deviations from Einstein’s theory, focusing on two well-motivated modified quadratic gravity theories: dynamical Chern-Simons gravity and Einstein-dilaton-Gauss-Bonnet gravity. We do so by determining whether the non-Kerr deviations in the continuum spectrum introduced by these theories are larger than the observational error intrinsic to the observations. We find that dynamical Chern-Simons gravity cannot be constrained better than current bounds with current or next generation continuum spectrum observations. Einstein-dilaton-Gauss-Bonnet gravity, however, may be constrained better than current bounds with next generation telescopes, as long as the systematic error inherent in the accretion disk modeling is decreased below the predicted observational error.
Thermodynamic laws for generalized f(R) gravity with curvature-matter coupling
Energy Technology Data Exchange (ETDEWEB)
Wu Yabo, E-mail: ybwu61@163.com [Department of Physics, Liaoning Normal University, Dalian 116029 (China); Zhao Yueyue, E-mail: zhaoyueyue198737@163.com [Department of Physics, Liaoning Normal University, Dalian 116029 (China); Cai Ronggen [Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190 (China); Lu Jianbo; Lu Junwang; Gao Xiaojing [Department of Physics, Liaoning Normal University, Dalian 116029 (China)
2012-10-31
The first law and the generalized second law (GSL) of thermodynamics for the generalized f(R) gravity with curvature-matter coupling are studied in the spatially homogeneous, isotropic FRW universe. The research results show that the field equations of the generalized f(R) gravity with curvature-matter coupling can be cast to the form of the first law of thermodynamics with the so-called the entropy production terms dS{sup Macron} and the GSL can be given by considering the FRW universe filled only with ordinary matter enclosed by the dynamical apparent horizon with the Hawking temperature. Furthermore, as a concrete example, by utilizing the GSL the constraints on the gravitational model with f{sub 1}(R)=R+{alpha}R{sup l} and f{sub 2}(R)=R{sup m} are also discussed. It is worth noting these results given by us are quite general and can degenerate to the ones in Einstein's general relativity and pure f(R) gravity with non-coupling and non-minimal coupling as special cases. Comparing with the case of Einstein's general relativity, the appearance of the entropy production term dS{sup Macron} in the first law of thermodynamics demonstrates that the horizon thermodynamics is non-equilibrium one for generalized f(R) gravity with curvature-matter coupling, which is consistent with the arguments given in Akbar and Cai (2007) [13] and Eling et al. (2006) [18].
Explicit solutions of a gravity-induced film flow along a convectively heated vertical wall.
Raees, Ammarah; Xu, Hang
2013-01-01
The gravity-driven film flow has been analyzed along a vertical wall subjected to a convective boundary condition. The Boussinesq approximation is applied to simplify the buoyancy term, and similarity transformations are used on the mathematical model of the problem under consideration, to obtain a set of coupled ordinary differential equations. Then the reduced equations are solved explicitly by using homotopy analysis method (HAM). The resulting solutions are investigated for heat transfer effects on velocity and temperature profiles.
Estimating the Earth's gravity field using a multi-satellite SLR solution
Bloßfeld, Mathis; Stefka, Vojtech; Müller, Horst; Gerstl, Michael
2013-04-01
Satellite Laser Ranging (SLR) is the unique technique to determine station coordinates, Earth Orientation Parameter (EOP) and Stokes coefficients of the Earth's gravity field in one common adjustment. These parameters form the so called "three pillars" (Plag & Pearlman, 2009) of the Global Geodetic Observing System (GGOS). In its function as official analysis center of the International Laser Ranging Service (ILRS), DGFI is developing and maintaining software to process SLR observations called "DGFI Orbit and Geodetic parameter estimation Software" (DOGS). The software is used to analyze SLR observations and to compute multi-satellite solutions. To take benefit of different orbit performances (e.g. inclination and altitude), a solution using ten different spherical satellites (ETALON1/2, LAGEOS1/2, STELLA, STARLETTE, AJISAI, LARETS, LARES, BLITS) covering 12 years of observations is computed. The satellites are relatively weighted using a variance component estimation (VCE). The obtained weights are analyzed w.r.t. the potential of the satellite to monitor changes in the Earths geometry, rotation and gravity field. The estimated parameters (station coordinates and EOP) are validated w.r.t. official time series of the IERS. The obtained Stokes coefficients are compared to recent gravity field solutions and discussed in detail.
Estimating the Earth's geometry, rotation and gravity field using a multi-satellite SLR solution
Stefka, V.; Blossfeld, M.; Mueller, H.; Gerstl, M.; Panafidina, N.
2012-12-01
Satellite Laser Ranging (SLR) is the unique technique to determine station coordinates, Earth Orientation Parameter (EOP) and Stokes coefficients of the Earth's gravity field in one common adjustment. These parameters form the so called "three pillars" (Plag & Pearlman, 2009) of the Global Geodetic Observing System (GGOS). In its function as official analysis center of the International Laser Ranging Service (ILRS), DGFI is developing and maintaining software to process SLR observations called "DGFI Orbit and Geodetic parameter estimation Software" (DOGS). The software is used to analyze SLR observations and to compute multi-satellite solutions. To take benefit of different orbit performances (e.g. inclination and altitude), a solution using ten different spherical satellites (ETALON1/2, LAGEOS1/2, STELLA, STARLETTE, AJISAI, LARETS, LARES, BLITS) covering the period of 12 years of observations is computed. The satellites are relatively weighted using a variance component estimation (VCE). The obtained weights are analyzed w.r.t. the potential of the satellite to monitor changes in the Earths geometry, rotation and gravity field. The estimated parameters (station coordinates and EOP) are validated w.r.t. official time series of the IERS. The Stokes coefficients are compared to recent gravity field solutions.
GENERAL SOLUTIONS FOR VISCOPLASTIC DEBRIS FLOW.
Chen, Cheng-lung
1988-01-01
Theoretical velocity profile and theoretical pressure and concentration distributions for (steady) uniform debris flow in wide channels are derived from a generalized viscoplastic fluid (GVF) model without imposing R. A. Bagnold's assumption of constant grain concentration. Good agreement between the theoretical velocity profile and the experimental data of Japanese scientists strongly supports the validity of both the GVF model and the proposed method of solution from the model. It is shown that both E. C. Bingham and Bagnold versions (or submodels) of the GVF model can be used to simulate debris flow at the dynamic state. Although Bagnold's dilatant submodel appears to fit the Japanese data better than the Bingham submodel for flow of noncohesive grains, the choice between them is by no means clear-cut.
Bezerra, V. B.; Christiansen, H. R.; Cunha, M. S.; Muniz, C. R.
2017-07-01
We obtain the exact (confluent Heun) solutions to the massive scalar field in a gravity's rainbow Schwarzschild metric. With these solutions at hand, we study the Hawking radiation resulting from the tunneling rate through the event horizon. We show that the emission spectrum obeys nonextensive statistics and is halted when a certain mass remnant is reached. Next, we infer constraints on the rainbow parameters from recent LHC particle physics experiments and Hubble STIS astrophysics measurements. Finally, we study the low frequency limit in order to find the modified energy spectrum around the source.
International Nuclear Information System (INIS)
Melendez L, L.
2004-01-01
In the first part of this work, starting from Einstein's equations of the Classical General Relativity, a new kind of solutions for the Mixmaster model are explored. By dispensing with the extension to the complex variable field, which is usual in problems such as the Laplace equation or the harmonic oscillator, in a similar manner to that of Quantum Mechanics, the equations appear to have solutions that belong to the complex General Relativity. A first integral is performed by establishing a separation of the first derivatives. Then a second integral is obtained once the respective equations with separate variables are found and whose integrals provide a family of complex solutions. However, reality conditions do not seem to be easily imposed at this stage. Above all, it is significant that the classical Einstein's equations for the debatably integrable Mixmaster model present complex solutions. In the second part of this work, following a specific strategy in which the cosmological time variables are operated upon, a new family of solutions to the empty Taub universe is found. Among the characteristics of such a family, it stands the positive acceleration provided by the tri-curvature property of this universe to two of the three scale factors of the Taub model. This effect of the tri-curvature results not in a restoring force such as normal gravity but in the conversion of the Taub cosmology into an accelerating universe. (Author)
Generalized Residual Terrain Model and Its Application in Regional Gravity Field Approximation
Directory of Open Access Journals (Sweden)
WU Yihao
2016-05-01
Full Text Available We studied the so-called non-harmonic problem in residual terrain model (RTM and compared the RTM corrections based on prisms and tesseroids. Moreover, we proposed the generalized RTM based on tesseroids, together with which the regional gravity field was modeled based on Poisson wavelets basis function by using heterogeneous gravity data sets. The results show that the RTM correction based on prism integral has a poor performance in mountainous regions, which may introduce errors with the magnitude of several mGal. Thus, we suggest using RTM based on tesseroids, which lead to a better approximation of the topography. Compared to original residual terrain model,the generalized one leads a better approximation of the regional gravity filed at the high-frequency part caused by local topographical variation.
AdS and dS black hole solutions in analogue gravity: The relativistic and nonrelativistic cases
Dey, Ramit; Liberati, Stefano; Turcati, Rodrigo
2016-11-01
We show that Schwarzschild black hole solutions in asymptotically anti-de Sitter (AdS) and de Sitter spaces may, up to a conformal factor, be reproduced in the framework of analogue gravity. The aforementioned derivation is performed using relativistic and nonrelativistic Bose-Einstein condensates. In addition, we demonstrate that the (2 +1 ) planar AdS black hole can be mapped into the nonrelativistic acoustic metric. Given that AdS black holes are extensively employed in the gauge/gravity duality, we then comment on the possibility of studying the AdS/CFT correspondence and gravity/fluid duality from an analogue gravity perspective.
Black hole complementarity with the generalized uncertainty principle in Gravity's Rainbow
Gim, Yongwan; Um, Hwajin; Kim, Wontae
2018-02-01
When gravitation is combined with quantum theory, the Heisenberg uncertainty principle could be extended to the generalized uncertainty principle accompanying a minimal length. To see how the generalized uncertainty principle works in the context of black hole complementarity, we calculate the required energy to duplicate information for the Schwarzschild black hole. It shows that the duplication of information is not allowed and black hole complementarity is still valid even assuming the generalized uncertainty principle. On the other hand, the generalized uncertainty principle with the minimal length could lead to a modification of the conventional dispersion relation in light of Gravity's Rainbow, where the minimal length is also invariant as well as the speed of light. Revisiting the gedanken experiment, we show that the no-cloning theorem for black hole complementarity can be made valid in the regime of Gravity's Rainbow on a certain combination of parameters.
Exact solution for the generalized Telegraph Fisher's equation
International Nuclear Information System (INIS)
Abdusalam, H.A.; Fahmy, E.S.
2009-01-01
In this paper, we applied the factorization scheme for the generalized Telegraph Fisher's equation and an exact particular solution has been found. The exact particular solution for the generalized Fisher's equation was obtained as a particular case of the generalized Telegraph Fisher's equation and the two-parameter solution can be obtained when n=2.
Hoseinzadeh, S.; Rezaei-Aghdam, A.
2017-10-01
We introduce a four-dimensional extension of the Poincaré algebra (N) in (1 + 1)-dimensional space-time and obtain a (1 + 1)-dimensional gauge symmetric gravity model using the algebra N. We show that the obtained gravity model is dual (canonically transformed) to the (1 + 1)-dimensional anti de Sitter (AdS) gravity. We also obtain some black hole and Friedmann-Robertson-Walker (FRW) solutions by solving its classical equations of motion. Then, we study A4,8A1/⊗A1 gauged Wess-Zumino-Witten (WZW) model and obtain some exact black hole and cosmological solutions in string theory. We show that some obtained black hole and cosmological metrics in string theory are same as the metrics obtained in solutions of our gauge symmetric gravity model.
Energy Technology Data Exchange (ETDEWEB)
Peralta, J.; López-Valverde, M. A. [Instituto de Astrofísica de Andalucía (CSIC), Glorieta de la Astronomía, 18008 Granada (Spain); Imamura, T. [Institute of Space and Astronautical Science-Japan Aerospace Exploration Agency 3-1-1, Yoshinodai, Chuo-ku, Sagamihara, Kanagawa 252-5210 (Japan); Read, P. L. [Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford (United Kingdom); Luz, D. [Centro de Astronomia e Astrofísica da Universidade de Lisboa (CAAUL), Observatório Astronómico de Lisboa, Tapada da Ajuda, 1349-018 Lisboa (Portugal); Piccialli, A., E-mail: peralta@iaa.es [LATMOS, UVSQ, 11 bd dAlembert, 78280 Guyancourt (France)
2014-07-01
This paper is the first of a two-part study devoted to developing tools for a systematic classification of the wide variety of atmospheric waves expected on slowly rotating planets with atmospheric superrotation. Starting with the primitive equations for a cyclostrophic regime, we have deduced the analytical solution for the possible waves, simultaneously including the effect of the metric terms for the centrifugal force and the meridional shear of the background wind. In those cases when the conditions for the method of the multiple scales in height are met, these wave solutions are also valid when vertical shear of the background wind is present. A total of six types of waves have been found and their properties were characterized in terms of the corresponding dispersion relations and wave structures. In this first part, only waves that are direct solutions of the generic dispersion relation are studied—acoustic and inertia-gravity waves. Concerning inertia-gravity waves, we found that in the cases of short horizontal wavelengths, null background wind, or propagation in the equatorial region, only pure gravity waves are possible, while for the limit of large horizontal wavelengths and/or null static stability, the waves are inertial. The correspondence between classical atmospheric approximations and wave filtering has been examined too, and we carried out a classification of the mesoscale waves found in the clouds of Venus at different vertical levels of its atmosphere. Finally, the classification of waves in exoplanets is discussed and we provide a list of possible candidates with cyclostrophic regimes.
A General Solution for Troesch's Problem
Directory of Open Access Journals (Sweden)
Hector Vazquez-Leal
2012-01-01
Full Text Available The homotopy perturbation method (HPM is employed to obtain an approximate solution for the nonlinear differential equation which describes Troesch’s problem. In contrast to other reported solutions obtained by using variational iteration method, decomposition method approximation, homotopy analysis method, Laplace transform decomposition method, and HPM method, the proposed solution shows the highest degree of accuracy in the results for a remarkable wide range of values of Troesch’s parameter.
Classical Weyl transverse gravity
Energy Technology Data Exchange (ETDEWEB)
Oda, Ichiro [University of the Ryukyus, Department of Physics, Faculty of Science, Nishihara, Okinawa (Japan)
2017-05-15
We study various classical aspects of the Weyl transverse (WTDiff) gravity in a general space-time dimension. First of all, we clarify a classical equivalence among three kinds of gravitational theories, those are, the conformally invariant scalar tensor gravity, Einstein's general relativity and the WTDiff gravity via the gauge-fixing procedure. Secondly, we show that in the WTDiff gravity the cosmological constant is a mere integration constant as in unimodular gravity, but it does not receive any radiative corrections unlike the unimodular gravity. A key point in this proof is to construct a covariantly conserved energy-momentum tensor, which is achieved on the basis of this equivalence relation. Thirdly, we demonstrate that the Noether current for the Weyl transformation is identically vanishing, thereby implying that the Weyl symmetry existing in both the conformally invariant scalar tensor gravity and the WTDiff gravity is a ''fake'' symmetry. We find it possible to extend this proof to all matter fields, i.e. the Weyl-invariant scalar, vector and spinor fields. Fourthly, it is explicitly shown that in the WTDiff gravity the Schwarzschild black hole metric and a charged black hole one are classical solutions to the equations of motion only when they are expressed in the Cartesian coordinate system. Finally, we consider the Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmology and provide some exact solutions. (orig.)
Post-Newtonian parameter γ in generalized non-local gravity
Zhang, Xue; Wu, YaBo; Yang, WeiQiang; Zhang, ChengYuan; Chen, BoHai; Zhang, Nan
2017-10-01
We investigate the post-Newtonian parameter γ and derive its formalism in generalized non-local (GNL) gravity, which is the modified theory of general relativity (GR) obtained by adding a term m 2 n-2 R☐-n R to the Einstein-Hilbert action. Concretely, based on parametrizing the generalized non-local action in which gravity is described by a series of dynamical scalar fields ϕ i in addition to the metric tensor g μν, the post-Newtonian limit is computed, and the effective gravitational constant as well as the post-Newtonian parameters are directly obtained from the generalized non-local gravity. Moreover, by discussing the values of the parametrized post-Newtonian parameters γ, we can compare our expressions and results with those in Hohmann and Järv et al. (2016), as well as current observational constraints on the values of γ in Will (2006). Hence, we draw restrictions on the nonminimal coupling terms F̅ around their background values.
General classical solutions in the noncommutative CPN-1 model
International Nuclear Information System (INIS)
Foda, O.; Jack, I.; Jones, D.R.T.
2002-01-01
We give an explicit construction of general classical solutions for the noncommutative CP N-1 model in two dimensions, showing that they correspond to integer values for the action and topological charge. We also give explicit solutions for the Dirac equation in the background of these general solutions and show that the index theorem is satisfied
Is there vacuum when there is mass? Vacuum and non-vacuum solutions for massive gravity
International Nuclear Information System (INIS)
Martín-Moruno, Prado; Visser, Matt
2013-01-01
Massive gravity is a theory which has a tremendous amount of freedom to describe different cosmologies, but at the same time, the various solutions one encounters must fulfil some rather nontrivial constraints. Most of the freedom comes not from the Lagrangian, which contains only a small number of free parameters (typically three depending on counting conventions), but from the fact that one is in principle free to choose the reference metric almost arbitrarily—which effectively introduces a non-denumerable infinity of free parameters. In the current paper, we stress that although changing the reference metric would lead to a different cosmological model, this does not mean that the dynamics of the universe can be entirely divorced from its matter content. That is, while the choice of reference metric certainly influences the evolution of the physically observable foreground metric, the effect of matter cannot be neglected. Indeed the interplay between matter and geometry can be significantly changed in some specific models; effectively since the graviton would be able to curve the spacetime by itself, without the need of matter. Thus, even the set of vacuum solutions for massive gravity can have significant structure. In some cases, the effect of the reference metric could be so strong that no conceivable material content would be able to drastically affect the cosmological evolution. Dedicated to the memory of Professor Pedro F González–Díaz (paper)
Is there vacuum when there is mass? Vacuum and non-vacuum solutions for massive gravity
Martín-Moruno, Prado; Visser, Matt
2013-08-01
Massive gravity is a theory which has a tremendous amount of freedom to describe different cosmologies, but at the same time, the various solutions one encounters must fulfil some rather nontrivial constraints. Most of the freedom comes not from the Lagrangian, which contains only a small number of free parameters (typically three depending on counting conventions), but from the fact that one is in principle free to choose the reference metric almost arbitrarily—which effectively introduces a non-denumerable infinity of free parameters. In the current paper, we stress that although changing the reference metric would lead to a different cosmological model, this does not mean that the dynamics of the universe can be entirely divorced from its matter content. That is, while the choice of reference metric certainly influences the evolution of the physically observable foreground metric, the effect of matter cannot be neglected. Indeed the interplay between matter and geometry can be significantly changed in some specific models; effectively since the graviton would be able to curve the spacetime by itself, without the need of matter. Thus, even the set of vacuum solutions for massive gravity can have significant structure. In some cases, the effect of the reference metric could be so strong that no conceivable material content would be able to drastically affect the cosmological evolution. Dedicated to the memory of Professor Pedro F González-Díaz
Energy Technology Data Exchange (ETDEWEB)
Tajahmad, Behzad [University of Tabriz, Faculty of Physics, Tabriz (Iran, Islamic Republic of)
2017-04-15
In this paper, we present the Noether symmetries of flat FRW spacetime in the context of a new action in teleparallel gravity which we construct based on the f(R) version. This modified action contains a coupling between the scalar field potential and magnetism. Also, we introduce an innovative approach, the beyond Noether symmetry (B.N.S.) approach, for exact solutions which carry more conserved currents than the Noether approach. By data analysis of the exact solutions, obtained from the Noether approach, late-time acceleration and phase crossing are realized, and some deep connections with observational data such as the age of the universe, the present value of the scale factor as well as the state and deceleration parameters are observed. In the B.N.S. approach, we consider the dark energy dominated era. (orig.)
Koga, Jun-ichirou; Maeda, Kei-ichi
1998-01-01
We analyze black hole thermodynamics in a generalized theory of gravity whose Lagrangian is an arbitrary function of the metric, the Ricci tensor and a scalar field. We can convert the theory into the Einstein frame via a "Legendre" transformation or a conformal transformation. We calculate thermodynamical variables both in the original frame and in the Einstein frame, following the Iyer--Wald definition which satisfies the first law of thermodynamics. We show that all thermodynamical variabl...
Quark confinement and the short-range component of general affine gauge gravity
International Nuclear Information System (INIS)
Sijacki, D.
1982-01-01
Within the framework of a gauge field theory based on the general affine space-time symmetry, we propose a certain purely quadratic gauge field lagrangian. In the large-scale region it yields an Einstein-Cartan-like gravity with Newton's constand generated spontaneously, while in the particle domain it yields a renormalizable theory with a confining potential applying to quarks and not to leptons. (orig.)
Lemaître-Tolman-Bondi dust solutions in f (R) gravity
Sussman, Roberto A.; Jaime, Luisa G.
2017-12-01
We derive a class of non-static inhomogeneous dust solutions in f(R) gravity described by the Lemaître-Tolman-Bondi (LTB) metric. The field equations are fully integrated for all parameter subcases and compared with analogous subcases of LTB dust solutions of GR. Since the solutions do not admit regular symmetry centres, we have two possibilities: (i) a spherical dust cloud with angle deficit acting as the source of a vacuum Schwarzschild-like solution associated with a global monopole, or (ii) fully regular dust wormholes without angle deficit, whose rest frames are homeomorphic to the Schwarzschild-Kruskal manifold or to a 3d torus. The compatibility between the LTB metric and generic f(R) ansatzes furnishes an ‘inverse procedure’ to generate LTB solutions whose sources are found from the f(R) geometry. While the resulting fluids may have an elusive physical interpretation, they can be used as exact non-perturbative toy models in theoretical and cosmological applications of f(R) theories.
The solution of the generalized Kepler's equation
López, Rosario; Hautesserres, Denis; San-Juan, Juan Félix
2018-01-01
In the context of general perturbation theories, the main problem of the artificial satellite analyses the motion of an orbiter around an Earth-like planet, only perturbed by its equatorial bulge or J2 effect. By means of a Lie transform and the Krylov-Bogoliubov-Mitropolsky method, a first-order theory in closed form of the eccentricity is produced. During the evaluation of the theory, it is necessary to solve a generalization of the classical Kepler's equation. In this work, the application of a numerical technique and three initial guesses to the generalized Kepler's equation are discussed.
Wang, Jun; Meng, Xiaohong; Li, Fang
2017-11-01
Generalized inversion is one of the important steps in the quantitative interpretation of gravity data. With appropriate algorithm and parameters, it gives a view of the subsurface which characterizes different geological bodies. However, generalized inversion of gravity data is time consuming due to the large amount of data points and model cells adopted. Incorporating of various prior information as constraints deteriorates the above situation. In the work discussed in this paper, a method for fast nonlinear generalized inversion of gravity data is proposed. The fast multipole method is employed for forward modelling. The inversion objective function is established with weighted data misfit function along with model objective function. The total objective function is solved by a dataspace algorithm. Moreover, depth weighing factor is used to improve depth resolution of the result, and bound constraint is incorporated by a transfer function to limit the model parameters in a reliable range. The matrix inversion is accomplished by a preconditioned conjugate gradient method. With the above algorithm, equivalent density vectors can be obtained, and interpolation is performed to get the finally density model on the fine mesh in the model domain. Testing on synthetic gravity data demonstrated that the proposed method is faster than conventional generalized inversion algorithm to produce an acceptable solution for gravity inversion problem. The new developed inversion method was also applied for inversion of the gravity data collected over Sichuan basin, southwest China. The established density structure in this study helps understanding the crustal structure of Sichuan basin and provides reference for further oil and gas exploration in this area.
International Nuclear Information System (INIS)
Giribet, G E
2005-01-01
Claus Kiefer presents his book, Quantum Gravity, with his hope that '[the] book will convince readers of [the] outstanding problem [of unification and quantum gravity] and encourage them to work on its solution'. With this aim, the author presents a clear exposition of the fundamental concepts of gravity and the steps towards the understanding of its quantum aspects. The main part of the text is dedicated to the analysis of standard topics in the formulation of general relativity. An analysis of the Hamiltonian formulation of general relativity and the canonical quantization of gravity is performed in detail. Chapters four, five and eight provide a pedagogical introduction to the basic concepts of gravitational physics. In particular, aspects such as the quantization of constrained systems, the role played by the quadratic constraint, the ADM decomposition, the Wheeler-de Witt equation and the problem of time are treated in an expert and concise way. Moreover, other specific topics, such as the minisuperspace approach and the feasibility of defining extrinsic times for certain models, are discussed as well. The ninth chapter of the book is dedicated to the quantum gravitational aspects of string theory. Here, a minimalistic but clear introduction to string theory is presented, and this is actually done with emphasis on gravity. It is worth mentioning that no hard (nor explicit) computations are presented, even though the exposition covers the main features of the topic. For instance, black hole statistical physics (within the framework of string theory) is developed in a pedagogical and concise way by means of heuristical arguments. As the author asserts in the epilogue, the hope of the book is to give 'some impressions from progress' made in the study of quantum gravity since its beginning, i.e., since the end of 1920s. In my opinion, Kiefer's book does actually achieve this goal and gives an extensive review of the subject. (book review)
A generalized action for (2 + 1)-dimensional Chern–Simons gravity
International Nuclear Information System (INIS)
Díaz, J; Fierro, O; Merino, N; Salgado, P; Valdivia, O; Izaurieta, F; Rodriguez, E
2012-01-01
We show that the so-called semi-simple extended Poincaré (SSEP) algebra in D dimensions can be obtained from the anti-de Sitter algebra so(D-1,2) by means of the S-expansion procedure with an appropriate semigroup S. A general prescription is given for computing Casimir operators for S-expanded algebras, and the method is exemplified for the SSEP algebra. The S-expansion method also allows us to extract the corresponding invariant tensor for the SSEP algebra, which is a key ingredient in the construction of a generalized action for Chern–Simons gravity in (2 + 1) dimensions. (paper)
Generalized Poincaré algebras and Lovelock–Cartan gravity theory
Directory of Open Access Journals (Sweden)
P.K. Concha
2015-03-01
Full Text Available We show that the Lagrangian for Lovelock–Cartan gravity theory can be reformulated as an action which leads to General Relativity in a certain limit. In odd dimensions the Lagrangian leads to a Chern–Simons theory invariant under the generalized Poincaré algebra B2n+1, while in even dimensions the Lagrangian leads to a Born–Infeld theory invariant under a subalgebra of the B2n+1 algebra. It is also shown that torsion may occur explicitly in the Lagrangian leading to new torsional Lagrangians, which are related to the Chern–Pontryagin character for the B2n+1 group.
Birkhoff’s theorem in Lovelock gravity for general base manifolds
Ray, Sourya
2015-10-01
We extend the Birkhoff’s theorem in Lovelock gravity for arbitrary base manifolds using an elementary method. In particular, it is shown that any solution of the form of a warped product of a two-dimensional transverse space and an arbitrary base manifold must be static. Moreover, the field equations restrict the base manifold such that all the non-trivial intrinsic Lovelock tensors of the base manifold are constants, which can be chosen arbitrarily, and the metric in the transverse space is determined by a single function of a spacelike coordinate which satisfies an algebraic equation involving the constants characterizing the base manifold along with the coupling constants.
Zebrafish Bone and General Physiology Are Differently Affected by Hormones or Changes in Gravity.
Directory of Open Access Journals (Sweden)
Jessica Aceto
Full Text Available Teleost fish such as zebrafish (Danio rerio are increasingly used for physiological, genetic and developmental studies. Our understanding of the physiological consequences of altered gravity in an entire organism is still incomplete. We used altered gravity and drug treatment experiments to evaluate their effects specifically on bone formation and more generally on whole genome gene expression. By combining morphometric tools with an objective scoring system for the state of development for each element in the head skeleton and specific gene expression analysis, we confirmed and characterized in detail the decrease or increase of bone formation caused by a 5 day treatment (from 5dpf to 10 dpf of, respectively parathyroid hormone (PTH or vitamin D3 (VitD3. Microarray transcriptome analysis after 24 hours treatment reveals a general effect on physiology upon VitD3 treatment, while PTH causes more specifically developmental effects. Hypergravity (3g from 5dpf to 9 dpf exposure results in a significantly larger head and a significant increase in bone formation for a subset of the cranial bones. Gene expression analysis after 24 hrs at 3g revealed differential expression of genes involved in the development and function of the skeletal, muscular, nervous, endocrine and cardiovascular systems. Finally, we propose a novel type of experimental approach, the "Reduced Gravity Paradigm", by keeping the developing larvae at 3g hypergravity for the first 5 days before returning them to 1g for one additional day. 5 days exposure to 3g during these early stages also caused increased bone formation, while gene expression analysis revealed a central network of regulatory genes (hes5, sox10, lgals3bp, egr1, edn1, fos, fosb, klf2, gadd45ba and socs3a whose expression was consistently affected by the transition from hyper- to normal gravity.
Zebrafish Bone and General Physiology Are Differently Affected by Hormones or Changes in Gravity.
Aceto, Jessica; Nourizadeh-Lillabadi, Rasoul; Marée, Raphael; Dardenne, Nadia; Jeanray, Nathalie; Wehenkel, Louis; Aleström, Peter; van Loon, Jack J W A; Muller, Marc
2015-01-01
Teleost fish such as zebrafish (Danio rerio) are increasingly used for physiological, genetic and developmental studies. Our understanding of the physiological consequences of altered gravity in an entire organism is still incomplete. We used altered gravity and drug treatment experiments to evaluate their effects specifically on bone formation and more generally on whole genome gene expression. By combining morphometric tools with an objective scoring system for the state of development for each element in the head skeleton and specific gene expression analysis, we confirmed and characterized in detail the decrease or increase of bone formation caused by a 5 day treatment (from 5dpf to 10 dpf) of, respectively parathyroid hormone (PTH) or vitamin D3 (VitD3). Microarray transcriptome analysis after 24 hours treatment reveals a general effect on physiology upon VitD3 treatment, while PTH causes more specifically developmental effects. Hypergravity (3g from 5dpf to 9 dpf) exposure results in a significantly larger head and a significant increase in bone formation for a subset of the cranial bones. Gene expression analysis after 24 hrs at 3g revealed differential expression of genes involved in the development and function of the skeletal, muscular, nervous, endocrine and cardiovascular systems. Finally, we propose a novel type of experimental approach, the "Reduced Gravity Paradigm", by keeping the developing larvae at 3g hypergravity for the first 5 days before returning them to 1g for one additional day. 5 days exposure to 3g during these early stages also caused increased bone formation, while gene expression analysis revealed a central network of regulatory genes (hes5, sox10, lgals3bp, egr1, edn1, fos, fosb, klf2, gadd45ba and socs3a) whose expression was consistently affected by the transition from hyper- to normal gravity.
General solution of the scattering equations
Energy Technology Data Exchange (ETDEWEB)
Dolan, Louise [Department of Physics, University of North Carolina,Chapel Hill, NC 27599 (United States); Goddard, Peter [School of Natural Sciences, Institute for Advanced Study,Princeton, NJ 08540 (United States)
2016-10-26
The scattering equations, originally introduced by Fairlie and Roberts in 1972 and more recently shown by Cachazo, He and Yuan to provide a kinematic basis for describing tree amplitudes for massless particles in arbitrary space-time dimension, have been reformulated in polynomial form. The scattering equations for N particles are equivalent to N−3 polynomial equations h{sub m}=0, 1≤m≤N−3, in N−3 variables, where h{sub m} has degree m and is linear in the individual variables. Facilitated by this linearity, elimination theory is used to construct a single variable polynomial equation, Δ{sub N}=0, of degree (N−3)! determining the solutions. Δ{sub N} is the sparse resultant of the system of polynomial scattering equations and it can be identified as the hyperdeterminant of a multidimensional matrix of border format within the terminology of Gel’fand, Kapranov and Zelevinsky. Macaulay’s Unmixedness Theorem is used to show that the polynomials of the scattering equations constitute a regular sequence, enabling the Hilbert series of the variety determined by the scattering equations to be calculated, independently showing that they have (N−3)! solutions.
International Nuclear Information System (INIS)
Kopeikin, Sergei M
2004-01-01
According to Einstein, the notions of geodesic, parallel transport (affine connection) and curvature of the spacetime manifold have a pure geometric origin and do not correlate with any electromagnetic concepts. At the same time, curvature is generated by matter which is not affiliated with the spacetime geometric concepts. For this reason, the fundamental constant c entering the geometric and matter sectors of the general theory of relativity has different conceptual meanings. Specifically, the letter c on the left-hand side of the Einstein equations (geometric sector) entering the Christoffel symbols and its time derivatives is the ultimate speed of gravity characterizing the upper limit on the speed of its propagation as well as the maximal rate of change of time derivatives of the metric tensor, that is gravitational field. The letter c on the right-hand side of the Einstein equations (matter sector) is the maximal speed of propagation of any other field rather than gravity. Einstein's general principle of relativity extends his principle of special relativity and equates the numerical value of the ultimate speed of gravity to that of the speed of light in the special theory of relativity but this general principle must be tested experimentally. To this end, we work out the speed of gravity parametrization of the Einstein equations (c g -parametrization) to keep track of the time-dependent effects associated with the geometric sector of general relativity and to separate them from the time-dependent effects of the matter sector. Parametrized post-Newtonian (PPN) approximation of the Einstein equations is derived in order to explain the gravitational physics of the Jovian deflection VLBI experiment conducted on 8 September 2002. The post-Newtonian series expansion in the c g -parametrized general relativity is with respect to a small parameter that is proportional to the ratio of the characteristic velocity of the bodies to the speed of propagation of the
Exact solutions to the generalized Lienard equation and its ...
Indian Academy of Sciences (India)
and the solutions of the equation are applied to solve nonlinear wave equations with nonlin- ... Lienard equation (1) corresponds to the p = 2 case of the generalized Lienard equation. Some exact solutions of the generalized Lienard equation (2) and their applications have been ...... In order to make the left-hand side of eq.
Energy Technology Data Exchange (ETDEWEB)
Shabani, Hamid [University of Sistan and Baluchestan, Physics Department, Faculty of Sciences, Zahedan (Iran, Islamic Republic of); Ziaie, Amir Hadi [Islamic Azad University, Department of Physics, Kahnooj Branch, Kerman (Iran, Islamic Republic of)
2017-05-15
Very recently, Josset and Perez (Phys. Rev. Lett. 118:021102, 2017) have shown that a violation of the energy-momentum tensor (EMT) could result in an accelerated expansion state via the appearance of an effective cosmological constant, in the context of unimodular gravity. Inspired by this outcome, in this paper we investigate cosmological consequences of a violation of the EMT conservation in a particular class of f(R,T) gravity when only the pressure-less fluid is present. In this respect, we focus on the late time solutions of models of the type f(R,T) = R + βΛ(-T). As the first task, we study the solutions when the conservation of EMT is respected, and then we proceed with those in which violation occurs. We have found, provided that the EMT conservation is violated, that there generally exist two accelerated expansion solutions of which the stability properties depend on the underlying model. More exactly, we obtain a dark energy solution for which the effective equation of state depends on the model parameters and a de Sitter solution. We present a method to parametrize the Λ(-T) function, which is useful in a dynamical system approach and has been employed in the model. Also, we discuss the cosmological solutions for models with Λ(-T) = 8πG(-T){sup α} in the presence of ultra-relativistic matter. (orig.)
Vacaru, Sergiu I.; Yazici, Enis
2014-01-01
We show that a geometric techniques can be elaborated and applied for constructing generic off-diagonal exact solutions in $f(R,T)$--modified gravity for systems of gravitational-Yang-Mills-Higgs equations. The corresponding classes of metrics and generalized connections are determined by generating and integration functions which depend, in general, on all space and time coordinates and may possess, or not, Killing symmetries. For nonholonomic constraints resulting in Levi-Civita configurations, we can extract solutions of the Einstein-Yang-Mills-Higgs equations. We show that the constructions simplify substantially for metrics with at least one Killing vector. There are provided and analyzed some examples of exact solutions describing generic off-diagonal modifications to black hole/ellipsoid and solitonic configurations.
Vacaru, Sergiu I.; Veliev, Elşen Veli; Yazici, Enis
2014-09-01
We show that geometric techniques can be elaborated and applied for constructing generic off-diagonal exact solutions in f(R, T)-modified gravity for systems of gravitational-Yang-Mills-Higgs equations. The corresponding classes of metrics and generalized connections are determined by generating and integration functions which depend, in general, on all space and time coordinates and may possess, or not, Killing symmetries. For nonholonomic constraints resulting in Levi-Civita configurations, we can extract solutions of the Einstein-Yang-Mills-Higgs equations. We show that the constructions simplify substantially for metrics with at least one Killing vector. Some examples of exact solutions describing generic off-diagonal modifications to black hole/ellipsoid and solitonic configurations are provided and analyzed.
Generalized Recursion Relations for Correlators in the Gauge-Gravity Correspondence
Raju, Suvrat
2011-03-01
We show that a generalization of the Britto-Cachazo-Feng-Witten recursion relations gives a new and efficient method of computing correlation functions of the stress tensor or conserved currents in conformal field theories with an (d+1)-dimensional anti-de Sitter space dual, for d≥4, in the limit where the bulk theory is approximated by tree-level Yang-Mills theory or gravity. In supersymmetric theories, additional correlators of operators that live in the same multiplet as a conserved current or stress tensor can be computed by these means.
Generalized recursion relations for correlators in the gauge-gravity correspondence.
Raju, Suvrat
2011-03-04
We show that a generalization of the Britto-Cachazo-Feng-Witten recursion relations gives a new and efficient method of computing correlation functions of the stress tensor or conserved currents in conformal field theories with an (d+1)-dimensional anti-de Sitter space dual, for d≥4, in the limit where the bulk theory is approximated by tree-level Yang-Mills theory or gravity. In supersymmetric theories, additional correlators of operators that live in the same multiplet as a conserved current or stress tensor can be computed by these means.
Spherically symmetric solution in higher-dimensional teleparallel equivalent of general relativity
Gamal, G. L. Nashed
2013-02-01
A theory of (N+1)-dimensional gravity is developed on the basis of the teleparallel equivalent of general relativity (TEGR). The fundamental gravitational field variables are the (N+1)-dimensional vector fields, defined globally on a manifold M, and the gravitational field is attributed to the torsion. The form of Lagrangian density is quadratic in torsion tensor. We then give an exact five-dimensional spherically symmetric solution (Schwarzschild (4+1)-dimensions). Finally, we calculate energy and spatial momentum using gravitational energy—momentum tensor and superpotential 2-form.
Generalized plane waves in Poincaré gauge theory of gravity
Blagojević, Milutin; Cvetković, Branislav; Obukhov, Yuri N.
2017-09-01
A family of exact vacuum solutions, representing generalized plane waves propagating on the (anti-)de Sitter background, is constructed in the framework of Poincaré gauge theory. The wave dynamics is defined by the general Lagrangian that includes all parity even and parity odd invariants up to the second order in the gauge field strength. The structure of the solution shows that the wave metric significantly depends on the spacetime torsion.
A general polynomial solution to convection–dispersion equation ...
Indian Academy of Sciences (India)
Jiao Wang
s12040-017-0820-4. A general polynomial solution to convection–dispersion equation using ... water pollution of groundwater, numerical models are increasingly used in .... to convective transport by water flow is negligi- ble. Equation (4) is ...
General solution for first order elliptic systems in the plane
International Nuclear Information System (INIS)
Mshimba, A.S.
1990-01-01
It is shown that a system of 2n real-valued partial differential equations of first order, which under certain assumptions can be transformed to the so-called 'complex normal form', admits a general solution. 15 refs
New exact solutions of the generalized Zakharov–Kuznetsov ...
Indian Academy of Sciences (India)
YUSUF PANDIR. Department of Mathematics, Faculty of Science and Arts, Bozok University, 66100 Yozgat, Turkey ... The extended trial equation method; generalized Zakharov–Kuznetsov equation; soliton solution; elliptic ... these, some new exact solutions are obtained by using the trial equation methods. Some of them ...
New exact solutions of the generalized Zakharov–Kuznetsov ...
Indian Academy of Sciences (India)
In this paper, new exact solutions, including soliton, rational and elliptic integral function solutions, for the generalized Zakharov–Kuznetsov modified equal-width equation are obtained using a new approach called the extended trial equation method. In this discussion, a new version of the trial equation method for the ...
Minimal solution of general dual fuzzy linear systems
International Nuclear Information System (INIS)
Abbasbandy, S.; Otadi, M.; Mosleh, M.
2008-01-01
Fuzzy linear systems of equations, play a major role in several applications in various area such as engineering, physics and economics. In this paper, we investigate the existence of a minimal solution of general dual fuzzy linear equation systems. Two necessary and sufficient conditions for the minimal solution existence are given. Also, some examples in engineering and economic are considered
A self-tuning exact solution and the non-existence of horizons in 5d gravity-scalar system
International Nuclear Information System (INIS)
Zhu Chuan-Jie; Abdus Salam International Centre for Theoretical Physics, Trieste
2000-05-01
We present an exact thick domain wall solution with naked singularities to five dimensional gravity coupled with a scalar field with exponential potential. In our solution we found exactly the special coefficient of the exponent as coming from compactification of string theory with cosmological constant. We show that this solution is self-tuning when a 3-brane is included. In searching for a solution with horizon we found a similar exact solution with fine-tuned exponent coefficient with an integration constant. Failing to find a solution with horizon we prove the non-existence of horizons. These naked singularities actually can't be resolved by horizon. We also comment on the physical relevance of this solution. (author)
Solutions to the strong-CP problem in a world with gravity
International Nuclear Information System (INIS)
Holman, R.; Watkins, R.; Widrow, L.M.; Toronto Univ., ON
1992-01-01
We examine various solutions of the strong-CP problem to determine their sensitivity to possible violations of global symmetries by Plauck scale physics. While some solutions remain viable even in the face of such effects. Violations of the Peccei-Quinn (PQ) symmetry by non-renormalizable operators of dimension less than 10 will generally shift the value of bar θ to values inconsistent with the experimental bound bar θ approx-lt 10 - 9. We show that it is possible to construct axion models where gauge symmetries protect PQ symmetry to the requisite level
Gravity, black holes and the very early Universe an introduction to general relativity and cosmology
Chow, Tai L
2008-01-01
In the early 1900s, Albert Einstein formulated two theories that would forever change the landscape of physics: the Special Theory of Relativity and the General Theory of Relativity. By 1925, quantum mechanics had been born out of the dissection of these two theories, and shortly after that, relativistic quantum field theory. We now had in place some important ties between the laws of physics and the types of particle interactions the new physics was uncovering. Gravity is one of the four types of forces that are found throughout the universe. In fact, although it is a relatively weak force, it operates at huge distances, and so must be accounted for in any cosmological system. Unfortunately, gravity continues to defy our neat categorization of how all the forces in nature work together. Professor Tai Chow, from the California State University at Stanislaus in Turlock, lays out for us the basic ideas of Einstein, including his law of gravitation, explains the physics behind black holes, and weaves into this a...
A Generalized Field Theory: Charged Spherical Symmetric Solution
Wanas, M. I.
1985-06-01
Three solutions with spherical symmetry are obtained for the field equations of the generalized field theory established recently by Mikhail and Wanas. The solutions found are in agreement with classical known results. The solution representing a generalized field, outside a spherical symmetric charged body, is found to have an extra term compared with the Reissner-Nordström metric. The space used for application is of type FIGI, so the solutions obtained correspond to a field in a matter-free space. A brief comparison between the solutions obtained and those given by other field theories is given. Two methods have been used to get physical results: the first is the type analysis, and the second is the comparison with classical known results by writing down the metric of the associated Riemannian space.
Directory of Open Access Journals (Sweden)
R. Pail
2003-01-01
Full Text Available The recovery of a full set of gravity field parameters from satellite gravity gradiometry (SGG is a huge numerical and computational task. In practice, parallel computing has to be applied to estimate the more than 90 000 harmonic coefficients parameterizing the Earth’s gravity field up to a maximum spherical harmonic degree of 300. Three independent solution strategies, i.e. two iterative methods (preconditioned conjugate gradient method, semi-analytic approach and a strict solver (Distributed Non-approximative Adjustment, which are operational on a parallel platform (‘Graz Beowulf Cluster’, are assessed and compared both theoretically and on the basis of a realistic-as-possible numerical simulation, regarding the accuracy of the results, as well as the computational effort. Special concern is given to the correct treatment of the coloured noise characteristics of the gradiometer. The numerical simulations show that there are no significant discrepancies among the solutions of the three methods. The newly proposed Distributed Nonapproximative Adjustment approach, which is the only one of the three methods that solves the inverse problem in a strict sense, also turns out to be a feasible method for practical applications.Key words. Spherical harmonics – satellite gravity gradiometry – GOCE – parallel computing – Beowulf cluster
Gravity Probe B: final results of a space experiment to test general relativity.
Everitt, C W F; DeBra, D B; Parkinson, B W; Turneaure, J P; Conklin, J W; Heifetz, M I; Keiser, G M; Silbergleit, A S; Holmes, T; Kolodziejczak, J; Al-Meshari, M; Mester, J C; Muhlfelder, B; Solomonik, V G; Stahl, K; Worden, P W; Bencze, W; Buchman, S; Clarke, B; Al-Jadaan, A; Al-Jibreen, H; Li, J; Lipa, J A; Lockhart, J M; Al-Suwaidan, B; Taber, M; Wang, S
2011-06-03
Gravity Probe B, launched 20 April 2004, is a space experiment testing two fundamental predictions of Einstein's theory of general relativity (GR), the geodetic and frame-dragging effects, by means of cryogenic gyroscopes in Earth orbit. Data collection started 28 August 2004 and ended 14 August 2005. Analysis of the data from all four gyroscopes results in a geodetic drift rate of -6601.8±18.3 mas/yr and a frame-dragging drift rate of -37.2±7.2 mas/yr, to be compared with the GR predictions of -6606.1 mas/yr and -39.2 mas/yr, respectively ("mas" is milliarcsecond; 1 mas=4.848×10(-9) rad).
Vatankhah, Saeed; Renaut, Rosemary A.; Ardestani, Vahid E.
2018-04-01
We present a fast algorithm for the total variation regularization of the 3-D gravity inverse problem. Through imposition of the total variation regularization, subsurface structures presenting with sharp discontinuities are preserved better than when using a conventional minimum-structure inversion. The associated problem formulation for the regularization is nonlinear but can be solved using an iteratively reweighted least-squares algorithm. For small-scale problems the regularized least-squares problem at each iteration can be solved using the generalized singular value decomposition. This is not feasible for large-scale, or even moderate-scale, problems. Instead we introduce the use of a randomized generalized singular value decomposition in order to reduce the dimensions of the problem and provide an effective and efficient solution technique. For further efficiency an alternating direction algorithm is used to implement the total variation weighting operator within the iteratively reweighted least-squares algorithm. Presented results for synthetic examples demonstrate that the novel randomized decomposition provides good accuracy for reduced computational and memory demands as compared to use of classical approaches.
Numerical Solution of Laminar Incompressible Generalized Newtonian Fluids Flow
Keslerová, R.; Kozel, K.
2009-09-01
This paper deals with the numerical solution of laminar viscous incompressible flows for generalized Newtonian (Newtonian and non-Newtonian) fluids in the branching channel. The mathematical model is the generalized system of Navier-Stokes equations. The right hand side of this system is defined by power-law model. The finite volume method combined with an artificial compressibility method is used for spatial discretization. For time discretization the explicit multistage Runge-Kutta numerical scheme is considered. Numerical solution is divided into two parts, steady and unsteady. Steady state solution is achieved for t→∞ using steady boundary conditions and followed by steady residual behavior. For unsteady solution a dual-time stepping method is considered. Numerical results for flows in two dimensional and three dimensional branching channel are presented.
Isotropic extensions of the vacuum solutions in general relativity
Energy Technology Data Exchange (ETDEWEB)
Molina, C. [Universidade de Sao Paulo (USP), SP (Brazil); Martin-Moruno, Prado [Victoria University of Wellington (New Zealand); Gonzalez-Diaz, Pedro F. [Consejo Superior de Investigaciones Cientificas, Madrid (Spain)
2012-07-01
Full text: Spacetimes described by spherically symmetric solutions of Einstein's equations are of paramount importance both in astrophysical applications and theoretical considerations. And among those, black holes are highlighted. In vacuum, Birkhoff's theorem and its generalizations to non-asymptotically flat cases uniquely fix the metric as the Schwarzschild, Schwarzschild-de Sitter or Schwarzschild-anti-de Sitter geometries, the vacuum solutions of the usual general relativity with zero, positive or negative values for the cosmological constant, respectively. In this work we are mainly interested in black holes in a cosmological environment. Of the two main assumptions of the cosmological principle, homogeneity is lost when compact objects are considered. Nevertheless isotropy is still possible, and we enforce this condition. Within this context, we investigate spatially isotropic solutions close - continuously deformable - to the usual vacuum solutions. We obtain isotropic extensions of the usual spherically symmetric vacuum geometries in general relativity. Exact and perturbative solutions are derived. Maximal extensions are constructed and their causal structures are discussed. The classes of geometries obtained include black holes in compact and non-compact universes, wormholes in the interior region of cosmological horizons, and anti-de Sitter geometries with excess/deficit solid angle. The tools developed here are applicable in more general contexts, with extensions subjected to other constraints. (author)
Fast 3D inversion of gravity data using solution space priorconditioned lanczos bidiagonalization
Rezaie, Mohammad; Moradzadeh, Ali; Kalateh, Ali Nejati
2017-01-01
Inversion of gravity data is one of the most important steps in the quantitative interpretation of practical data. Inversion is a mathematical technique that automatically constructs a subsurface geophysical model from measured data, incorporating some priori information. Inversion of gravity data is time consuming because of increase in data and model parameters. Some efforts have been made to deal with this problem, one of them is using fast algorithms for solving system of equations in inverse problem. Lanczos bidiagonalization method is a fast algorithm that works based on Krylov subspace iterations and projection method, but cannot always provide a good basis for a projection method. So in this study, we combined the Krylov method with a regularization method applied to the low-dimensional projected problem. To achieve the goal, the orthonormal basis vectors of the discrete cosine transform (DCT) were used to build the low-dimensional subspace. The forward operator matrix replaced with a matrix of lower dimension, thus, the required memory and running time of the inverse modeling is decreased by using the proposed algorithm. It is shown that this algorithm can be appropriate to solve a Tikhonov cost function for inversion of gravity data. The proposed method has been applied on a noise-corrupted synthetic data and field gravity data (Mobrun gravity data) to demonstrate its reliability for three dimensional (3D) gravity inversion. The obtained results of 3D inversion both synthetic and field gravity data (Mobrun gravity data) indicate the proposed inversion algorithm could produce density models consistent with true structures.
Directory of Open Access Journals (Sweden)
Antonio Gledson Goulart
2013-12-01
Full Text Available In this paper, the equation for the gravity wave spectra in mean atmosphere is analytically solved without linearization by the Adomian decomposition method. As a consequence, the nonlinear nature of problem is preserved and the errors found in the results are only due to the parameterization. The results, with the parameterization applied in the simulations, indicate that the linear solution of the equation is a good approximation only for heights shorter than ten kilometers, because the linearization the equation leads to a solution that does not correctly describe the kinetic energy spectra.
Periodic solution for the stochastic chemostat with general response function
Wang, Liang; Jiang, Daqing
2017-11-01
This paper addresses a stochastic chemostat model with periodic dilution rate and general class of response functions. The general functional response is assumed to satisfy two classifications of conditions, and these assumptions on the functional response are relative weak that are valid for many forms of growth response. For the chemostat with periodic dilution rate, we derive the sufficient criteria for the existence of the stochastic nontrivial positive periodic solution, by utilizing Khasminskii's theory on periodic Markov process.
Butterfly effect in 3D gravity
Qaemmaqami, Mohammad M.
2017-11-01
We study the butterfly effect by considering shock wave solutions near the horizon of the anti-de Sitter black hole in some three-dimensional gravity models including 3D Einstein gravity, minimal massive 3D gravity, new massive gravity, generalized massive gravity, Born-Infeld 3D gravity, and new bigravity. We calculate the butterfly velocities of these models and also we consider the critical points and different limits in some of these models. By studying the butterfly effect in the generalized massive gravity, we observe a correspondence between the butterfly velocities and right-left moving degrees of freedom or the central charges of the dual 2D conformal field theories.
Classification of single travelling wave solutions to the generalized ...
Indian Academy of Sciences (India)
c Indian Academy of Sciences. Vol. 80, No. 5. — journal of. May 2013 physics pp. 771–783. Classification of single travelling wave solutions to the generalized Zakharov–Kuznetsov equation ... linear ion-acoustic waves in a strongly magnetized lossless plasma composed of cold ions and hot isothermal electrons [10].
Solitary wave solution to a singularly perturbed generalized Gardner ...
Indian Academy of Sciences (India)
2015-11-27
Home; Journals; Pramana – Journal of Physics; Volume 88; Issue 4. Solitary wave solution to a singularly perturbed generalized ... Proceedings of the International Workshop/Conference on Computational Condensed Matter Physics and Materials Science (IWCCMP-2015). Posted on November 27, 2015. Guest Editors: ...
On The Existence And Uniqueness Of Solutions Of A Generalized ...
African Journals Online (AJOL)
In this paper, the existence and uniqueness theorem for the solutions of the initial value problem (1.1), (1.2) and (3.12) shall be proven, where the function f, in (1.1) and (3.12) satisfy generalized Lipschitz continuous. IFE Journal of Science Vol. 9 (2) 2007 pp. 241-246 ...
General analytical shakedown solution for structures with kinematic hardening materials
Guo, Baofeng; Zou, Zongyuan; Jin, Miao
2016-09-01
The effect of kinematic hardening behavior on the shakedown behaviors of structure has been investigated by performing shakedown analysis for some specific problems. The results obtained only show that the shakedown limit loads of structures with kinematic hardening model are larger than or equal to those with perfectly plastic model of the same initial yield stress. To further investigate the rules governing the different shakedown behaviors of kinematic hardening structures, the extended shakedown theorem for limited kinematic hardening is applied, the shakedown condition is then proposed, and a general analytical solution for the structural shakedown limit load is thus derived. The analytical shakedown limit loads for fully reversed cyclic loading and non-fully reversed cyclic loading are then given based on the general solution. The resulting analytical solution is applied to some specific problems: a hollow specimen subjected to tension and torsion, a flanged pipe subjected to pressure and axial force and a square plate with small central hole subjected to biaxial tension. The results obtained are compared with those in literatures, they are consistent with each other. Based on the resulting general analytical solution, rules governing the general effects of kinematic hardening behavior on the shakedown behavior of structure are clearly.
Approximating a common solution of a finite family of generalized ...
African Journals Online (AJOL)
In this paper, we introduce and investigate an iterative scheme for finding a common element of the set of common solutions of a finite family of generalized equilibrium problems and the set of fixed points of a Lipschitz and hemicontractive-type multi-valued mapping. We obtain strong convergence theorems of the proposed ...
A New Solution for Einstein Field Equation in General Relativity
Mousavi, Sadegh
2006-05-01
There are different solutions for Einstein field equation in general relativity that they have been proposed by different people the most important solutions are Schwarzchild, Reissner Nordstrom, Kerr and Kerr Newmam. However, each one of these solutions limited to special case. I've found a new solution for Einstein field equation which is more complete than all previous ones and this solution contains the previous solutions as its special forms. In this talk I will present my new metric for Einstein field equation and the Christofel symbols and Richi and Rieman tensor components for the new metric that I have calculated them by GR TENSOR software. As a result I will determine the actual movement of black holes which is different From Kerr black hole's movement. Finally this new solution predicts, existence of a new and constant field in the nature (that nobody can found it up to now), so in this talk I will introduce this new field and even I will calculate the amount of this field. SADEGH MOUSAVI, Amirkabir University of Technology.
New generalized Noh solutions for HEDP hydrocode verification
Velikovich, A. L.; Giuliani, J. L.; Zalesak, S. T.; Tangri, V.
2017-10-01
The classic Noh solution describing stagnation of a cold ideal gas in a strong accretion shock wave has been the workhorse of compressible hydrocode verification for over three decades. We describe a number of its generalizations available for HEDP code verification. First, for an ideal gas, we have obtained self-similar solutions that describe adiabatic convergence either of a finite-pressure gas into an empty cavity or of a finite-amplitude sound wave into a uniform resting gas surrounding the center or axis of symmetry. At the moment of collapse such a flow produces a uniform gas whose velocity at each point is constant and directed towards the axis or the center, i. e. the initial condition similar to the classic solution but with a finite pressure of the converging gas. After that, a constant-velocity accretion shock propagates into the incident gas whose pressure and velocity profiles are not flat, in contrast with the classic solution. Second, for an arbitrary equation of state, we demonstrate the existence of self-similar solutions of the Noh problem in cylindrical and spherical geometry. Examples of such solutions with a three-term equation of state that includes cold, thermal ion/lattice, and thermal electron contributions are presented for aluminum and copper. These analytic solutions are compared to our numerical simulation results as an example of their use for code verification. Work supported by the US DOE/NNSA.
Massive gravity from bimetric gravity
International Nuclear Information System (INIS)
Baccetti, Valentina; Martín-Moruno, Prado; Visser, Matt
2013-01-01
We discuss the subtle relationship between massive gravity and bimetric gravity, focusing particularly on the manner in which massive gravity may be viewed as a suitable limit of bimetric gravity. The limiting procedure is more delicate than currently appreciated. Specifically, this limiting procedure should not unnecessarily constrain the background metric, which must be externally specified by the theory of massive gravity itself. The fact that in bimetric theories one always has two sets of metric equations of motion continues to have an effect even in the massive gravity limit, leading to additional constraints besides the one set of equations of motion naively expected. Thus, since solutions of bimetric gravity in the limit of vanishing kinetic term are also solutions of massive gravity, but the contrary statement is not necessarily true, there is no complete continuity in the parameter space of the theory. In particular, we study the massive cosmological solutions which are continuous in the parameter space, showing that many interesting cosmologies belong to this class. (paper)
Newton law on the generalized singular brane with and without 4d induced gravity
International Nuclear Information System (INIS)
Jung, Eylee; Kim, Sung-Hoon; Park, D.K.
2003-01-01
Newton law arising due to the gravity localized on the general singular brane embedded in AdS 5 bulk is examined in the absence or presence of the 4d induced Einstein term. For the RS brane, apart from the subleading correction, Newton potential obeys 4d- and 5d-type gravitational law at long- and short-ranges if it were not for the induced Einstein term. The 4d induced Einstein term generates an intermediate range at short distance, in which the 5d Newton potential 1/r 2 emerges. For Neumann brane the long-range behavior of Newton potential is exponentially suppressed regardless of the existence of the induced Einstein term. For Dirichlet brane the expression of Newton potential is dependent on the renormalized coupling constant v ren . At particular value of v ren Newton potential on Dirichlet brane exhibits a similar behavior to that on RS brane. For other values the long-range behavior of Newton potential is exponentially suppressed as that in Neumann brane
Directory of Open Access Journals (Sweden)
G. M. N’Guérékata
2018-01-01
Full Text Available The main aim of this paper is to investigate generalized asymptotical almost periodicity and generalized asymptotical almost automorphy of solutions to a class of abstract (semilinear multiterm fractional differential inclusions with Caputo derivatives. We illustrate our abstract results with several examples and possible applications.
Analytical Solution of Unsteady Gravity Flows of A Power-Law Fluid ...
African Journals Online (AJOL)
We investigate the power-law viscosity index, the Darcy parameter on the temperature profiles and the results were discussed. Keywords: Unsteady gravity flows; Porous media; Non – Newtonian power- law fluid. Journal of the Nigerian Association of Mathematical Physics, Volume 19 (November, 2011), pp 223 – 228 ...
Wouters, B.; Schrama, E.J.O.
2007-01-01
One of the major problems one has to deal with when working with Gravity Recovery and Climate Experiment (GRACE) data is the increasing error spectrum at higher degrees in the provided Stokes coefficients, appearing as unphysical North?South striping patterns in the maps of equivalent water height
Polko, P.; Meier, D.L.; Markoff, S.
2013-01-01
We present a new, approximate method for modelling the acceleration and collimation of relativistic jets in the presence of gravity. This method is self-similar throughout the computational domain where gravitational effects are negligible and, where significant, self-similar within a flux tube.
Particular solutions of generalized Euler-Poisson-Darboux equation
Directory of Open Access Journals (Sweden)
Rakhila B. Seilkhanova
2015-01-01
Full Text Available In this article we consider the generalized Euler-Poisson-Darboux equation $$ {u}_{tt}+\\frac{2\\gamma }{t}{{u}_{t}}={u}_{xx}+{u}_{yy} +\\frac{2\\alpha }{x}{{u}_{x}}+\\frac{2\\beta }{y}{{u}_y},\\quad x>0,\\;y>0,\\;t>0. $$ We construct particular solutions in an explicit form expressed by the Lauricella hypergeometric function of three variables. Properties of each constructed solutions have been investigated in sections of surfaces of the characteristic cone. Precisely, we prove that found solutions have singularity $1/r$ at $r\\to 0$, where ${{r}^2}={{( x-{{x}_0}}^2}+{{( y-{{y}_0}}^2}-{{( t-{{t}_0}}^2}$.
On the General Analytical Solution of the Kinematic Cosserat Equations
Michels, Dominik L.
2016-09-01
Based on a Lie symmetry analysis, we construct a closed form solution to the kinematic part of the (partial differential) Cosserat equations describing the mechanical behavior of elastic rods. The solution depends on two arbitrary analytical vector functions and is analytical everywhere except a certain domain of the independent variables in which one of the arbitrary vector functions satisfies a simple explicitly given algebraic relation. As our main theoretical result, in addition to the construction of the solution, we proof its generality. Based on this observation, a hybrid semi-analytical solver for highly viscous two-way coupled fluid-rod problems is developed which allows for the interactive high-fidelity simulations of flagellated microswimmers as a result of a substantial reduction of the numerical stiffness.
Numerical solution of pipe flow problems for generalized Newtonian fluids
International Nuclear Information System (INIS)
Samuelsson, K.
1993-01-01
In this work we study the stationary laminar flow of incompressible generalized Newtonian fluids in a pipe with constant arbitrary cross-section. The resulting nonlinear boundary value problems can be written in a variational formulation and solved using finite elements and the augmented Lagrangian method. The solution of the boundary value problem is obtained by finding a saddle point of the augmented Lagrangian. In the algorithm the nonlinear part of the equations is treated locally and the solution is obtained by iteration between this nonlinear problem and a global linear problem. For the solution of the linear problem we use the SSOR preconditioned conjugate gradient method. The approximating problem is solved on a sequence of adaptively refined grids. A scheme for adjusting the value of the crucial penalization parameter of the augmented Lagrangian is proposed. Applications to pipe flow and a problem from the theory of capacities are given. (author) (34 refs.)
A database for extract solutions in general relativity
International Nuclear Information System (INIS)
Horvath, I.; Horvath, Zs.; Lukacs, B.
1993-07-01
The field of equations of General Relativity are coupled second order partial differential equations. Therefore no general method is known to generate solutions for prescribed initial and boundary conditions. In addition, the meaning of the particular coordinates cannot be known until the metric is not found. Therefore the result must permit arbitrary coordinate transformations, i.e. most kinds of approximating methods are improper. So exact solutions are necessary and each one is an individual product. For storage, retrieval and comparison database handling techniques are needed. A database of 1359 articles is shown (cross-referred at least once) published in 156 more important journals. It can be handled by dBase III plus on IBM PC's. (author) 5 refs.; 5 tabs
Multipolar electromagnetic fields around neutron stars: general-relativistic vacuum solutions
Pétri, J.
2017-12-01
Magnetic fields inside and around neutron stars are at the heart of pulsar magnetospheric activity. Strong magnetic fields are responsible for quantum effects, an essential ingredient to produce leptonic pairs and the subsequent broad-band radiation. The variety of electromagnetic field topologies could lead to the observed diversity of neutron star classes. Thus, it is important to include multipolar components to a presumably dominant dipolar magnetic field. Exact analytical solutions for these multipoles in Newtonian gravity have been computed in recent literature. However, flat space-time is not adequate to describe physics in the immediate surroundings of neutron stars. We generalize the multipole expressions to the strong gravity regime by using a slowly rotating metric approximation such as the one expected around neutron stars. Approximate formulae for the electromagnetic field including frame dragging are computed from which we estimate the Poynting flux and the braking index. Corrections to leading order in compactness and spin parameter are presented. As far as spin-down luminosity is concerned, it is shown that frame dragging remains irrelevant. For high-order multipoles starting from the quadrupole, the electric part can radiate more efficiently than the magnetic part. Both analytical and numerical tools are employed.
Quantum solutions for Prisoner's Dilemma game with general parameters
International Nuclear Information System (INIS)
Sun, Z.W.; Jin, H.; Zhao, H.
2008-01-01
The quantum game of the Prisoner's Dilemma with general payoff matrix was studied in L. Marinatto and T. Weber's scheme presented in [Phys. Lett. A 272 (2000) 291, so that the results of two schemes of the quantum game can be compared. The Nash equilibria and the solutions of the game are obtained. They are related to initial state, matrix parameters and the intervals among the parameters. It can be concluded from the results that the quantum PD game in Marinatto and Weber's scheme matches the one in Eisert et al.'s scheme, one with general unitary operations.
Automatic computation and solution of generalized harmonic balance equations
Peyton Jones, J. C.; Yaser, K. S. A.; Stevenson, J.
2018-02-01
Generalized methods are presented for generating and solving the harmonic balance equations for a broad class of nonlinear differential or difference equations and for a general set of harmonics chosen by the user. In particular, a new algorithm for automatically generating the Jacobian of the balance equations enables efficient solution of these equations using continuation methods. Efficient numeric validation techniques are also presented, and the combined algorithm is applied to the analysis of dc, fundamental, second and third harmonic response of a nonlinear automotive damper.
Generalized Fokker-Planck equation: Derivation and exact solutions
Denisov, S. I.; Horsthemke, W.; Hänggi, P.
2009-04-01
We derive the generalized Fokker-Planck equation associated with the Langevin equation (in the Ito sense) for an overdamped particle in an external potential driven by multiplicative noise with an arbitrary distribution of the increments of the noise generating process. We explicitly consider this equation for various specific types of noises, including Poisson white noise and Lévy stable noise, and show that it reproduces all Fokker-Planck equations that are known for these noises. Exact analytical, time-dependent and stationary solutions of the generalized Fokker-Planck equation are derived and analyzed in detail for the cases of a linear, a quadratic, and a tailored potential.
A general method for enclosing solutions of interval linear equations
Czech Academy of Sciences Publication Activity Database
Rohn, Jiří
2012-01-01
Roč. 6, č. 4 (2012), s. 709-717 ISSN 1862-4472 R&D Projects: GA ČR GA201/09/1957; GA ČR GC201/08/J020 Institutional research plan: CEZ:AV0Z10300504 Keywords : interval linear equations * solution set * enclosure * absolute value inequality Subject RIV: BA - General Mathematics Impact factor: 1.654, year: 2012
Analytical Solution of Generalized Space-Time Fractional Cable Equation
Ram K. Saxena; Zivorad Tomovski; Trifce Sandev
2015-01-01
In this paper, we consider generalized space-time fractional cable equation in presence of external source. By using the Fourier-Laplace transform we obtain the Green function in terms of infinite series in H-functions. The fractional moments of the fundamental solution are derived and their asymptotic behavior in the short and long time limit is analyzed. Some previously obtained results are compared with those presented in this paper. By using the Bernstein characterization theorem we find ...
Magnetotail equilibrium theory - The general three-dimensional solution
Birn, J.
1987-01-01
The general magnetostatic equilibrium problem for the geomagnetic tail is reduced to the solution of ordinary differential equations and ordinary integrals. The theory allows the integration of the self-consistent magnetotail equilibrium field from the knowledge of four functions of two space variables: the neutral sheet location, the total pressure, the magnetic field strength, and the z component of the magnetic field at the neutral sheet.
Hughes, Kyle M.; Knittel, Jeremy M.; Englander, Jacob A.
2017-01-01
This work presents an automated method of calculating mass (or time) optimal gravity-assist trajectories without a priori knowledge of the flyby-body combination. Since gravity assists are particularly crucial for reaching the outer Solar System, we use the Ice Giants, Uranus and Neptune, as example destinations for this work. Catalogs are also provided that list the most attractive trajectories found over launch dates ranging from 2024 to 2038. The tool developed to implement this method, called the Python EMTG Automated Trade Study Application (PEATSA), iteratively runs the Evolutionary Mission Trajectory Generator (EMTG), a NASA Goddard Space Flight Center in-house trajectory optimization tool. EMTG finds gravity-assist trajectories with impulsive maneuvers using a multiple-shooting structure along with stochastic methods (such as monotonic basin hopping) and may be run with or without an initial guess provided. PEATSA runs instances of EMTG in parallel over a grid of launch dates. After each set of runs completes, the best results within a neighborhood of launch dates are used to seed all other cases in that neighborhood---allowing the solutions across the range of launch dates to improve over each iteration. The results here are compared against trajectories found using a grid-search technique, and PEATSA is found to outperform the grid-search results for most launch years considered.
AdS and dS black hole solutions in analogue gravity: The relativistic and non-relativistic cases
Dey, Ramit; Liberati, Stefano; Turcati, Rodrigo
2016-01-01
We show that Schwarzschild black hole solutions in asymptotically Anti-de Sitter (AdS) and de Sitter (dS) spaces may, up to a conformal factor, be reproduced in the framework of analogue gravity. The aforementioned derivation is performed using relativistic and non-relativistic Bose-Einstein condensates. In addition, we demonstrate that the (2+1) planar AdS black hole can be mapped into the non-relativistic acoustic metric. Given that AdS black holes are extensively employed in the gauge/grav...
Exact solutions of the Bach field equations of general relativity
Fiedler, B.; Schimming, R.
1980-02-01
Conformally invariant gravitational field equations on the hand and fourth order field equations on the other were discussed in the early history of general relativity (Weyl Einstein, Bach et al.) and have recently gained some new interest (Deser, P. Günther, Treder, et al.). The equations Bαβ=0 or Bαβ= ϰTαβ, where Bαβ denotes the Bach tensor and Tαβ a suitable energy-momentum tensor, possess both the mentioned properties. We construct exact solutions ds2= gαβdxαdxβ of the Bach equations: (2, 2)-decomposable, centrally symmetric and pp-wave solutions. The gravitational field gαβ is coupled by Bαβ= ϰTαβ to an electromagnetic field Fαβ=- Fαβ obeying the Maxwell equations or to a neutrino field ϕ A obeying the Weyl equations respectively. Among interesting new metrics ds2 there appear some physically well-known ones, such as the De Sitter universe, the Weyl-Trefftz metric. and the plane-fronted gravitational waves with parallel rays (pp-waves) known from Einstein's theory. The solutions are built up by means of special techniques: A separation method for (2, 2)-decomposable solutions, simplification of centrally symmetric metrics by a suitable conformal transformation, and complex function methods for pp-wave solutions.
General terms and rigidity: another solution to the trivialization problem
Directory of Open Access Journals (Sweden)
Eleonora Orlando
2014-06-01
Full Text Available In this paper I am concerned with the problem of applying the notion of rigidity to general terms. In Naming and Necessity, Kripke has clearly suggested that we should include some general terms among the rigid ones, namely, those common nouns semantically correlated with natural substances, species and phenomena, in general, natural kinds -'water', 'tiger', 'heat'- and some adjectives -'red', 'hot', 'loud'. However, the notion of rigidity has been defined for singular terms; after all, the notion that Kripke has provided us with is the notion of a rigid designator. But general terms do not designate single individuals: rather, they apply to many of them. In sum, the original concept of rigidity cannot be straightforwardly applied to general terms: it has to be somehow redefined in order to make it cover them. As is known, two main positions have been put forward to accomplish that task: the identity of designation conception, according to which a rigid general term is one that designates the same property or kind in all possible worlds, and the essentialist conception, which conceives of a rigid general term as an essentialist one, namely, a term that expresses an essential property of an object. My purpose in the present paper is to defend a particular version of the identity of designation conception: on the proposed approach, a rigid general term will be one that expresses the same property in all possible worlds and names the property it expresses. In my opinion, the position can be established on the basis of an inference to the best explanation of our intuitive interpretation and evaluation, relative to counterfactual circumstances, of statements containing different kinds of general terms, which is strictly analogous to our intuitive interpretation and evaluation, relative to such circumstances, of statements containing different kinds of singular ones. I will argue that it is possible to offer a new solution to the trivialization
Nonsingular universe in massive gravity's rainbow
Hendi, S. H.; Momennia, M.; Eslam Panah, B.; Panahiyan, S.
2017-06-01
One of the fundamental open questions in cosmology is whether we can regard the universe evolution without singularity like a Big Bang or a Big Rip. This challenging subject stimulates one to regard a nonsingular universe in the far past with an arbitrarily large vacuum energy. Considering the high energy regime in the cosmic history, it is believed that Einstein gravity should be corrected to an effective energy dependent theory which could be acquired by gravity's rainbow. On the other hand, employing massive gravity provided us with solutions to some of the long standing fundamental problems of cosmology such as cosmological constant problem and self acceleration of the universe. Considering these aspects of gravity's rainbow and massive gravity, in this paper, we initiate studying FRW cosmology in the massive gravity's rainbow formalism. At first, we show that although massive gravity modifies the FRW cosmology, but it does not itself remove the big bang singularity. Then, we generalize the massive gravity to the case of energy dependent spacetime and find that massive gravity's rainbow can remove the early universe singularity. We bring together all the essential conditions for having a nonsingular universe and the effects of both gravity's rainbow and massive gravity generalizations on such criteria are determined.
On generalized Melvin solution for the Lie algebra E6
International Nuclear Information System (INIS)
Bolokhov, S.V.; Ivashchuk, V.D.
2017-01-01
A multidimensional generalization of Melvin's solution for an arbitrary simple Lie algebra G is considered. The gravitational model in D dimensions, D ≥ 4, contains n 2-forms and l ≥ n scalar fields, where n is the rank of G. The solution is governed by a set of n functions H s (z) obeying n ordinary differential equations with certain boundary conditions imposed. It was conjectured earlier that these functions should be polynomials (the so-called fluxbrane polynomials). The polynomials H s (z), s = 1,.., 6, for the Lie algebra E 6 are obtained and a corresponding solution for l = n = 6 is presented. The polynomials depend upon integration constants Q s , s = 1,.., 6. They obey symmetry and duality identities. The latter ones are used in deriving asymptotic relations for solutions at large distances. The power-law asymptotic relations for E 6 -polynomials at large z are governed by the integer-valued matrix ν = A -1 (I + P), where A -1 is the inverse Cartan matrix, I is the identity matrix and P is a permutation matrix, corresponding to a generator of the Z 2 -group of symmetry of the Dynkin diagram. The 2-form fluxes Φ s , s = 1,.., 6, are calculated. (orig.)
International Nuclear Information System (INIS)
Alexandre, Jean; Pasipoularides, Pavlos
2011-01-01
In this note we examine whether spherically symmetric solutions in covariant Horava-Lifshitz gravity can reproduce Newton's Law in the IR limit λ→1. We adopt the position that the auxiliary field A is independent of the space-time metric [J. Alexandre and P. Pasipoularides, Phys. Rev. D 83, 084030 (2011).][J. Greenwald, V. H. Satheeshkumar, and A. Wang, J. Cosmol. Astropart. Phys. 12 (2010) 007.], and we assume, as in [A. M. da Silva, Classical Quantum Gravity 28, 055011 (2011).], that λ is a running coupling constant. We show that under these assumptions, spherically symmetric solutions fail to restore the standard Newtonian physics in the IR limit λ→1, unless λ does not run, and has the fixed value λ=1. Finally, we comment on the Horava and Melby-Thompson approach [P. Horava and C. M. Melby-Thompson, Phys. Rev. D 82, 064027 (2010).] in which A is assumed as a part of the space-time metric in the IR.
International Nuclear Information System (INIS)
Rodrigues, Davi C.; Piattella, Oliver F.; Chauvineau, Bertrand
2015-01-01
We show that Renormalization Group extensions of the Einstein-Hilbert action for large scale physics are not, in general, a particular case of standard Scalar-Tensor (ST) gravity. We present a new class of ST actions, in which the potential is not necessarily fixed at the action level, and show that this extended ST theory formally contains the Renormalization Group case. We also propose here a Renormalization Group scale setting identification that is explicitly covariant and valid for arbitrary relativistic fluids
Clément, Gilles
2007-01-01
Protecting the health, safety, and performance of exploration-class mission crews against the physiological deconditioning resulting from long-term weightlessness during transit and long-term reduced gravity during surface operations will require effective, multi-system countermeasures. Artificial gravity, which would replace terrestrial gravity with inertial forces generated by rotating the transit vehicle or by short-radius human centrifuge devices within the transit vehicle or surface habitat, has long been considered a potential solution. However, despite its attractiveness as an efficient
Exact Solutions of a Generalized Weighted Scale Free Network
Directory of Open Access Journals (Sweden)
Li Tan
2013-01-01
Full Text Available We investigate a class of generalized weighted scale-free networks, where the new vertex connects to m pairs of vertices selected preferentially. The key contribution of this paper is that, from the standpoint of random processes, we provide rigorous analytic solutions for the steady state distributions, including the vertex degree distribution, the vertex strength distribution and the edge weight distribution. Numerical simulations indicate that this network model yields three power law distributions for the vertex degrees, vertex strengths and edge weights, respectively.
A general solution to some plane problems of micropolar elasticity
DEFF Research Database (Denmark)
Warren, William E.; Byskov, Esben
2008-01-01
that micropolar effects are most significant in material regions subjected to large deformation gradients. Specific results are presented for the classical crack problem, the half plane loaded uniformly on the surface, Flamant's problem, and the circular cylinder compressed by equal and opposite oncentrated......We obtain a general solution to the field equations of plane micropolar elasticity for materials characterized by a hexagonal or equilateral triangular structure. These materials exhibit 3-fold symmetry in the plane and the elastic response is isotropic. Utilizing two displacement potential...
Analytical Solution of Generalized Space-Time Fractional Cable Equation
Directory of Open Access Journals (Sweden)
Ram K. Saxena
2015-04-01
Full Text Available In this paper, we consider generalized space-time fractional cable equation in presence of external source. By using the Fourier-Laplace transform we obtain the Green function in terms of infinite series in H-functions. The fractional moments of the fundamental solution are derived and their asymptotic behavior in the short and long time limit is analyzed. Some previously obtained results are compared with those presented in this paper. By using the Bernstein characterization theorem we find the conditions under which the even moments are non-negative.
Localizing gravity on exotic thick 3-branes
International Nuclear Information System (INIS)
Castillo-Felisola, Oscar; Melfo, Alejandra; Pantoja, Nelson; Ramirez, Alba
2004-01-01
We consider localization of gravity on thick branes with a nontrivial structure. Double walls that generalize the thick Randall-Sundrum solution, and asymmetric walls that arise from a Z 2 symmetric scalar potential, are considered. We present a new asymmetric solution: a thick brane interpolating between two AdS 5 spacetimes with different cosmological constants, which can be derived from a 'fake supergravity' superpotential, and show that it is possible to confine gravity on such branes
Mashhoon, Bahram
2017-01-01
Relativity theory is based on a postulate of locality, which means that the past history of the observer is not directly taken into account. This book argues that the past history should be taken into account. In this way, nonlocality---in the sense of history dependence---is introduced into relativity theory. The deep connection between inertia and gravitation suggests that gravity could be nonlocal, and in nonlocal gravity the fading gravitational memory of past events must then be taken into account. Along this line of thought, a classical nonlocal generalization of Einstein's theory of gravitation has recently been developed. A significant consequence of this theory is that the nonlocal aspect of gravity appears to simulate dark matter. According to nonlocal gravity theory, what astronomers attribute to dark matter should instead be due to the nonlocality of gravitation. Nonlocality dominates on the scale of galaxies and beyond. Memory fades with time; therefore, the nonlocal aspect of gravity becomes wea...
Multi-loop correlators for rational theories of 2D gravity from the generalized Kontsevich models
DEFF Research Database (Denmark)
Kristjansen, C.
1994-01-01
functions of the susceptibilities and the eigenvalues of the external field. We furthermore use the moment technique to derive a closed expression for the genus zero multi-loop correlators for $(3,3m-1)$ and $(3,3m-2)$ rational matter fields coupled to gravity. We comment on the relation between the two-matrix...
Quasi-local conserved charges in Lorenz-diffeomorphism covariant theory of gravity
Energy Technology Data Exchange (ETDEWEB)
Adami, H.; Setare, M.R. [University of Kurdistan, Department of Science, Sanandaj (Iran, Islamic Republic of)
2016-04-15
In this paper, using the combined Lorenz-diffeomorphism symmetry, we find a general formula for the quasi-local conserved charge of the covariant gravity theories in a first order formalism of gravity. We simplify the general formula for the Lovelock theory of gravity. Afterwards, we apply the obtained formula on BHT gravity to obtain the energy and angular momentum of the rotating OTT black hole solution in the context of this theory. (orig.)
Totani, Tomonori
2017-10-01
In standard general relativity the universe cannot be started with arbitrary initial conditions, because four of the ten components of the Einstein's field equations (EFE) are constraints on initial conditions. In the previous work it was proposed to extend the gravity theory to allow free initial conditions, with a motivation to solve the cosmological constant problem. This was done by setting four constraints on metric variations in the action principle, which is reasonable because the gravity's physical degrees of freedom are at most six. However, there are two problems about this theory; the three constraints in addition to the unimodular condition were introduced without clear physical meanings, and the flat Minkowski spacetime is unstable against perturbations. Here a new set of gravitational field equations is derived by replacing the three constraints with new ones requiring that geodesic paths remain geodesic against metric variations. The instability problem is then naturally solved. Implications for the cosmological constant Λ are unchanged; the theory converges into EFE with nonzero Λ by inflation, but Λ varies on scales much larger than the present Hubble horizon. Then galaxies are formed only in small Λ regions, and the cosmological constant problem is solved by the anthropic argument. Because of the increased degrees of freedom in metric dynamics, the theory predicts new non-oscillatory modes of metric anisotropy generated by quantum fluctuation during inflation, and CMB B -mode polarization would be observed differently from the standard predictions by general relativity.
Action growth for black holes in modified gravity
Sebastiani, Lorenzo; Vanzo, Luciano; Zerbini, Sergio
2018-02-01
The general form of the action growth for a large class of static black hole solutions in modified gravity which includes F (R ) -gravity models is computed. The cases of black hole solutions with nonconstant Ricci scalar are also considered, generalizing the results previously found and valid only for black holes with constant Ricci scalar. An argument is put forward to provide a physical interpretation of the results, which seem tightly connected with the generalized second law of black hole thermodynamics.
Generalized Virasoro constructions and higher spin gravity: An SL(3) example
International Nuclear Information System (INIS)
Mohammedi, N.
1990-06-01
We consider a SL(3) current algebra and construct bilinears in the currents. A multitude of new Virasoro algebras, differing from the usual Sugawara and coset constructions, are then obtained. Since the SL(3) current algebra is a hidden symmetry of W 3 -gravity, we apply our results to calculate the allowed range for the values of the matter central charge. We find that this depends crucially on a parameter arising from the Sugawara-like constructions. (author). 23 refs
Renormalization group equation and scaling solutions for f(R) gravity in exponential parametrization
International Nuclear Information System (INIS)
Ohta, Nobuyoshi; Percacci, Roberto; Vacca, Gian Paolo
2016-01-01
We employ the exponential parametrization of the metric and a ''physical'' gauge fixing procedure to write a functional flow equation for the gravitational effective average action in an f(R) truncation. The background metric is a four-sphere and the coarse-graining procedure contains three free parameters. We look for scaling solutions, i.e. non-Gaussian fixed points for the function f. For a discrete set of values of the parameters, we find simple global solutions of quadratic polynomial form. For other values, global solutions can be found numerically. Such solutions can be extended in certain regions of parameter space and have two relevant directions. We discuss the merits and the shortcomings of this procedure. (orig.)
Spherically Symmetric Solutions on a Non-Trivial Frame in f(T) Theories of Gravity
Gamal, G. L. Nashed
2012-05-01
A new solution with constant torsion is derived using the field equations of f(T). Asymptotic forms of energy density, radial and transversal pressures are shown to meet the standard energy conditions, i.e., weak and null energy conditions according to some restrictions on T0, f(T0) and fT(T0). Other solutions are obtained for vanishing radial pressure and for specific choices of f(T). The physics relevant to the resulting models is discussed.
Generalized nonlinear Proca equation and its free-particle solutions
Nobre, F. D.; Plastino, A. R.
2016-06-01
We introduce a nonlinear extension of Proca's field theory for massive vector (spin 1) bosons. The associated relativistic nonlinear wave equation is related to recently advanced nonlinear extensions of the Schrödinger, Dirac, and Klein-Gordon equations inspired on the non-extensive generalized thermostatistics. This is a theoretical framework that has been applied in recent years to several problems in nuclear and particle physics, gravitational physics, and quantum field theory. The nonlinear Proca equation investigated here has a power-law nonlinearity characterized by a real parameter q (formally corresponding to the Tsallis entropic parameter) in such a way that the standard linear Proca wave equation is recovered in the limit q → 1. We derive the nonlinear Proca equation from a Lagrangian, which, besides the usual vectorial field Ψ ^{μ }(ěc {x},t), involves an additional field Φ ^{μ }(ěc {x},t). We obtain exact time-dependent soliton-like solutions for these fields having the form of a q-plane wave, and we show that both field equations lead to the relativistic energy-momentum relation E2 = p2c2 + m2c4 for all values of q. This suggests that the present nonlinear theory constitutes a new field theoretical representation of particle dynamics. In the limit of massless particles the present q-generalized Proca theory reduces to Maxwell electromagnetism, and the q-plane waves yield localized, transverse solutions of Maxwell equations. Physical consequences and possible applications are discussed.
Generalized nonlinear Proca equation and its free-particle solutions
Energy Technology Data Exchange (ETDEWEB)
Nobre, F.D. [Centro Brasileiro de Pesquisas Fisicas and National Institute of Science and Technology for Complex Systems, Rio de Janeiro, RJ (Brazil); Plastino, A.R. [Universidad Nacional Buenos Aires-Noreoeste, CeBio y Secretaria de Investigacion, Junin (Argentina)
2016-06-15
We introduce a nonlinear extension of Proca's field theory for massive vector (spin 1) bosons. The associated relativistic nonlinear wave equation is related to recently advanced nonlinear extensions of the Schroedinger, Dirac, and Klein-Gordon equations inspired on the non-extensive generalized thermostatistics. This is a theoretical framework that has been applied in recent years to several problems in nuclear and particle physics, gravitational physics, and quantum field theory. The nonlinear Proca equation investigated here has a power-law nonlinearity characterized by a real parameter q (formally corresponding to the Tsallis entropic parameter) in such a way that the standard linear Proca wave equation is recovered in the limit q → 1. We derive the nonlinear Proca equation from a Lagrangian, which, besides the usual vectorial field Ψ{sup μ}(vector x,t), involves an additional field Φ{sup μ}(vector x,t). We obtain exact time-dependent soliton-like solutions for these fields having the form of a q-plane wave, and we show that both field equations lead to the relativistic energy-momentum relation E{sup 2} = p{sup 2}c{sup 2} + m{sup 2}c{sup 4} for all values of q. This suggests that the present nonlinear theory constitutes a new field theoretical representation of particle dynamics. In the limit of massless particles the present q-generalized Proca theory reduces to Maxwell electromagnetism, and the q-plane waves yield localized, transverse solutions of Maxwell equations. Physical consequences and possible applications are discussed. (orig.)
New exact solutions of the generalized Zakharov–Kuznetsov ...
Indian Academy of Sciences (India)
soliton, elliptic integral function and Jacobi elliptic function solutions. Apart from all these, some new exact solutions are obtained by using the trial equation methods. Some of them are elliptic integral F, E and functions, Jacobi elliptic function solutions etc. These types of solutions are very important and encounter in various ...
New Exact Solutions for the (3+1-Dimensional Generalized BKP Equation
Directory of Open Access Journals (Sweden)
Jun Su
2016-01-01
Full Text Available The Wronskian technique is used to investigate a (3+1-dimensional generalized BKP equation. Based on Hirota’s bilinear form, new exact solutions including rational solutions, soliton solutions, positon solutions, negaton solutions, and their interaction solutions are formally derived. Moreover we analyze the strangely mechanical behavior of the Wronskian determinant solutions. The study of these solutions will enrich the variety of the dynamics of the nonlinear evolution equations.
International Nuclear Information System (INIS)
David, F.
1990-01-01
In these lectures, I shall focus on the matrix formulation of 2-d gravity. In the first one, I shall discuss the main results of the continuum formulation of 2-d gravity, starting from the first renormalization group calculations which led to the concept of the conformal anomaly, going through the Polyakov bosonic string and the Liouville action, up to the recent results on the scaling properties of conformal field theories coupled to 2-d gravity. In the second lecture, I shall discuss the discrete formulation of 2-d gravity in term of random lattices, and the mapping onto random matrix models. The occurrence of critical points in the planar limit and the scaling limit at those critical points will be described, as well as the identification of these scaling limits with continuum 2-d gravity coupled to some matter field theory. In the third lecture, the double scaling limit in the one matrix model, and its connection with continuum non perturbative 2-d gravity, will be presented. The connection with the KdV hierarchy and the general form of the string equation will be discuted. In the fourth lecture, I shall discuss the non-perturbative effects present in the non perturbative solutions, in the case of pure gravity. The Schwinger-Dyson equations for pure gravity in the double scaling limit are described and their compatibility with the solutions of the string equation for pure gravity is shown to be somewhat problematic
Pt-catalyzed ozonation of aqueous phenol solution using high-gravity rotating packed bed
International Nuclear Information System (INIS)
Chang, Chia-Chi; Chiu, Chun-Yu; Chang, Ching-Yuan; Chang, Chiung-Fen; Chen, Yi-Hung; Ji, Dar-Ren; Tseng, Jyi-Yeong; Yu, Yue-Hwa
2009-01-01
In this study, a high-gravity rotating packed bed (HGRPB or HG) was used as a catalytic ozonation (Cat-OZ) reactor to decompose phenol. The operation of HGRPB system was carried out in a semi-batch apparatus which combines two major parts, namely the rotating packed bed (RPB) and photo-reactor (PR). The high rotating speed of RPB can give a high volumetric gas-liquid mass transfer coefficient with one or two orders of magnitude higher than those in the conventional packed beds. The platinum-containing catalyst (Dash 220N, Pt/γ-Al 2 O 3 ) and activated alumina (γ-Al 2 O 3 ) were packed in the RPB respectively to adsorb molecular ozone and the target pollutant of phenol on the surface to catalyze the oxidation of phenol. An ultra violet (UV) lamp (applicable wavelength λ = 200-280 nm) was installed in the PR to enhance the self-decomposition of molecular ozone in water to form high reactive radical species. Different combinations of advanced oxidation processes (AOPs) with the HGRPB for the degradation of phenol were tested. These included high-gravity OZ (HG-OZ), HG catalytic OZ (HG-Cat-OZ), HG photolysis OZ (HG-UV-OZ) and HG-Cat-OZ with UV (HG-Cat-UV-OZ). The decomposition efficiency of total organic compound (η TOC ) of HG-UV-OZ with power of UV (P UV ) of 16 W is 54% at applied dosage of ozone per volume sample m A,in = 1200 mg L -1 (reaction time t = 20 min), while that of HG-OZ without the UV irradiation is 24%. After 80 min oxidation (m A,in = 4800 mg L -1 ), the η TOC of HG-UV-OZ is as high as 94% compared to 82% of HG-OZ process. The values of η TOC for HG-Cat-OZ process with m S = 42 g are 56% and 87% at m A,in = 1200 and 4800 mg L -1 , respectively. By increasing the catalyst mass to 77 g, the η TOC for the HG-Cat-OZ process reaches 71% and 90% at m A,in = 1200 and 4800 mg L -1 , respectively. The introduction of Pt/γ-Al 2 O 3 as well as UV irradiation in the HG-OZ process can enhance the η TOC of phenol significantly, while γ-Al 2 O 3 exhibits
Directory of Open Access Journals (Sweden)
Barceló Carlos
2005-12-01
Full Text Available Analogue models of (and for gravity have a long and distinguished history dating back to the earliest years of general relativity. In this review article we will discuss the history, aims, results, and future prospects for the various analogue models. We start the discussion by presenting a particularly simple example of an analogue model, before exploring the rich history and complex tapestry of models discussed in the literature. The last decade in particular has seen a remarkable and sustained development of analogue gravity ideas, leading to some hundreds of published articles, a workshop, two books, and this review article. Future prospects for the analogue gravity programme also look promising, both on the experimental front (where technology is rapidly advancing and on the theoretical front (where variants of analogue models can be used as a springboard for radical attacks on the problem of quantum gravity.
Semiclassical unimodular gravity
International Nuclear Information System (INIS)
Fiol, Bartomeu; Garriga, Jaume
2010-01-01
Classically, unimodular gravity is known to be equivalent to General Relativity (GR), except for the fact that the effective cosmological constant Λ has the status of an integration constant. Here, we explore various formulations of unimodular gravity beyond the classical limit. We first consider the non-generally covariant action formulation in which the determinant of the metric is held fixed to unity. We argue that the corresponding quantum theory is also equivalent to General Relativity for localized perturbative processes which take place in generic backgrounds of infinite volume (such as asymptotically flat spacetimes). Next, using the same action, we calculate semiclassical non-perturbative quantities, which we expect will be dominated by Euclidean instanton solutions. We derive the entropy/area ratio for cosmological and black hole horizons, finding agreement with GR for solutions in backgrounds of infinite volume, but disagreement for backgrounds with finite volume. In deriving the above results, the path integral is taken over histories with fixed 4-volume. We point out that the results are different if we allow the 4-volume of the different histories to vary over a continuum range. In this ''generalized'' version of unimodular gravity, one recovers the full set of Einstein's equations in the classical limit, including the trace, so Λ is no longer an integration constant. Finally, we consider the generally covariant theory due to Henneaux and Teitelboim, which is classically equivalent to unimodular gravity. In this case, the standard semiclassical GR results are recovered provided that the boundary term in the Euclidean action is chosen appropriately
Black Holes and Two-Dimensional Dilaton Gravity
Futamase, T.; Hotta, M.; Itoh, Y.
1998-01-01
We study the conditions for 2-dimensional dilaton gravity models to have dynamical formation of black holes and construct all such models. Furthermore we present a parametric representation of the general solutions of the black holes.
Kiefer, Claus
2012-01-01
The search for a quantum theory of the gravitational field is one of the great open problems in theoretical physics. This book presents a self-contained discussion of the concepts, methods and applications that can be expected in such a theory. The two main approaches to its construction - the direct quantisation of Einstein's general theory of relativity and string theory - are covered. Whereas the first attempts to construct a viable theory for the gravitational field alone, string theory assumes that a quantum theory of gravity will be achieved only through a unification of all the interactions. However, both employ the general method of quantization of constrained systems, which is described together with illustrative examples relevant for quantum gravity. There is a detailed presentation of the main approaches employed in quantum general relativity: path-integral quantization, the background-field method and canonical quantum gravity in the metric, connection and loop formulations. The discussion of stri...
A general polynomial solution to convection–dispersion equation ...
Indian Academy of Sciences (India)
Jiao Wang
A number of models have been established to simulate the behaviour of solute transport due to chemical pollution, both in croplands and groundwater systems. An approximate polynomial solution to convection–dispersion equation (CDE) based on boundary layer theory has been verified for the use to describe solute ...
Mitchell, Myles A.; He, Jian-hua; Arnold, Christian; Li, Baojiu
2018-03-01
We propose a new framework for testing gravity using cluster observations, which aims to provide an unbiased constraint on modified gravity models from Sunyaev Zel'dovich (SZ) and X-ray cluster counts and the cluster gas fraction, among other possible observables. Focusing on a popular f(R) model of gravity, we propose a novel procedure to recalibrate mass scaling relations from ΛCDM to f(R) gravity for SZ and X-ray cluster observables. We find that the complicated modified gravity effects can be simply modelled as a dependence on a combination of the background scalar field and redshift, fR(z)/(1 + z), regardless of the f(R) model parameter. By employing a large suite of N-body simulations, we demonstrate that a theoretically derived tanh fitting formula is in excellent agreement with the dynamical mass enhancement of dark matter haloes for a large range of background field parameters and redshifts. Our framework is sufficiently flexible to allow for tests of other models and inclusion of further observables, and the one-parameter description of the dynamical mass enhancement can have important implications on the theoretical modelling of observables and on practical tests of gravity.
(Compactified) black branes in four dimensional f(R)-gravity
Dimakis, N.; Giacomini, Alex; Paliathanasis, Andronikos
2018-02-01
A new family of analytical solutions in a four dimensional static spacetime is presented for f (R) -gravity. In contrast to General Relativity, we find that a non trivial black brane/string solution is supported in vacuum power law f (R) -gravity for appropriate values of the parameters characterizing the model and when axisymmetry is introduced in the line element. For the aforementioned solution, we perform a brief investigation over its basic thermodynamic quantities.
Beysens, D.A.; van Loon, J.J.W.A.; Beysens, D.A.; van Loon, J.J.W.A.
2015-01-01
It is generally thought that gravity is zero on an object travelling at constant velocity in space. This is not exactly so. We detail in the following those causes that make space gravity not strictly zero.
Unified first law and some general prescription. A redefinition of surface gravity
Energy Technology Data Exchange (ETDEWEB)
Haldar, Sourav; Bhattacharjee, Sudipto; Chakraborty, Subenoy [Jadavpur University, Department of Mathematics, Kolkata, West Bengal (India)
2017-09-15
The paper contains an extensive study of the unified first law (UFL) in the Friedmann-Robertson-Walker spacetime model. By projecting the UFL along the Kodama vector the second Friedmann equation can be obtained. Also studying the UFL on the event horizon it is found that the Clausius relation cannot be obtained from the UFL by projecting it along the tangent to the event horizon as it can be for the trapping horizon. However, it is shown in the present work that Clausius relation can be obtained by projecting the UFL along the Kodama vector on the horizon and the result is found to be true for any horizon. Finally motivated by the Unruh temperature for the Rindler observer, surface gravity is redefined and a Clausius relation is obtained from the UFL by projecting it along a vector analogous to the Kodama vector. (orig.)
Stability of Schwarzschild-like solutions in f(R,G) gravity models
International Nuclear Information System (INIS)
De Felice, Antonio; Suyama, Teruaki; Tanaka, Takahiro
2011-01-01
We study linear metric perturbations around a spherically symmetric static spacetime for general f(R,G) theories, where R is the Ricci scalar and G is the Gauss-Bonnet term. We find that, unless the determinant of the Hessian of f(R,G) is zero, even-type perturbations have a ghost for any multipole mode. In order for these theories to be plausible alternatives to general relativity, the theory should satisfy the condition that the ghost is massive enough to effectively decouple from the other fields. We study the requirement on the form of f(R,G) which satisfies this condition. We also classify the number of propagating modes both for the odd-type and the even-type perturbations and derive the propagation speeds for each mode.
Radion and holographic brane gravity
International Nuclear Information System (INIS)
Kanno, Sugumi; Soda, Jiro
2002-01-01
The low energy effective theory for the Randall-Sundrum two-brane system is investigated with an emphasis on the role of the nonlinear radion in the brane world. The equations of motion in the bulk are solved using a low energy expansion method. This allows us, through the junction conditions, to deduce the effective equations of motion for gravity on the brane. It is shown that the gravity on the brane world is described by a quasi-scalar-tensor theory with a specific coupling function ω(Ψ)=3Ψ/2(1-Ψ) on the positive tension brane and ω(Φ)=-3Φ/2(1+Φ) on the negative tension brane, where Ψ and Φ are nonlinear realizations of the radion on the positive and negative tension branes, respectively. In contrast with the usual scalar-tensor gravity, the quasi-scalar-tensor gravity couples with two kinds of matter; namely, the matter on both positive and negative tension branes, with different effective gravitational coupling constants. In particular, the radion disguised as the scalar fields Ψ and Φ couples with the sum of the traces of the energy-momentum tensor on both branes. In the course of the derivation, it is revealed that the radion plays an essential role in converting the nonlocal Einstein gravity with generalized dark radiation to local quasi-scalar-tensor gravity. For completeness, we also derive the effective action for our theory by substituting the bulk solution into the original action. It is also shown that quasi-scalar-tensor gravity works as a hologram at low energy in the sense that the bulk geometry can be reconstructed from the solution of quasi-scalar-tensor gravity
A general polynomial solution to convection–dispersion equation ...
Indian Academy of Sciences (India)
Comparison with exact solution suggests the prediction accuracy of the boundary layer solution varies with the order of polynomial expression and soil transport ... State Key Laboratory of Soil Erosion and Dryland Farming on the Loess Plateau, Northwest Agriculture and Forestry University, Yangling 712100, China.
Exact Solution of a Generalized Nonlinear Schrodinger Equation Dimer
DEFF Research Database (Denmark)
Christiansen, Peter Leth; Maniadis, P.; Tsironis, G.P.
1998-01-01
We present exact solutions for a nonlinear dimer system defined throught a discrete nonlinear Schrodinger equation that contains also an integrable Ablowitz-Ladik term. The solutions are obtained throught a transformation that maps the dimer into a double Sine-Gordon like ordinary nonlinear...
International Nuclear Information System (INIS)
Abdou, M.A.
2008-01-01
The generalized F-expansion method with a computerized symbolic computation is used for constructing a new exact travelling wave solutions for the generalized nonlinear Schrodinger equation with a source. As a result, many exact travelling wave solutions are obtained which include new periodic wave solution, trigonometric function solutions and rational solutions. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in physics
Directory of Open Access Journals (Sweden)
Bondarescu Ruxandra
2015-01-01
Full Text Available The successful miniaturisation of extremely accurate atomic clocks and atom interferometers invites prospects for satellite missions to perform precision experiments. We discuss the effects predicted by general relativity and alternative theories of gravity that can be detected by a clock, which orbits the Earth. Our experiment relies on the precise tracking of the spacecraft using its observed tick-rate. The spacecraft’s reconstructed four-dimensional trajectory will reveal the nature of gravitational perturbations in Earth’s gravitational field, potentially differentiating between different theories of gravity. This mission can measure multiple relativistic effects all during the course of a single experiment, and constrain the Parametrized Post-Newtonian Parameters around the Earth. A satellite carrying a clock of fractional timing inaccuracy of Δ f / f ∼ 10−16 in an elliptic orbit around the Earth would constrain the PPN parameters |β − 1|, |γ − 1| ≲ 10−6. We also briefly review potential constraints by atom interferometers on scalar tensor theories and in particular on Chameleon and dilaton models.
Directory of Open Access Journals (Sweden)
Carlos Barceló
2011-05-01
Full Text Available Analogue gravity is a research programme which investigates analogues of general relativistic gravitational fields within other physical systems, typically but not exclusively condensed matter systems, with the aim of gaining new insights into their corresponding problems. Analogue models of (and for gravity have a long and distinguished history dating back to the earliest years of general relativity. In this review article we will discuss the history, aims, results, and future prospects for the various analogue models. We start the discussion by presenting a particularly simple example of an analogue model, before exploring the rich history and complex tapestry of models discussed in the literature. The last decade in particular has seen a remarkable and sustained development of analogue gravity ideas, leading to some hundreds of published articles, a workshop, two books, and this review article. Future prospects for the analogue gravity programme also look promising, both on the experimental front (where technology is rapidly advancing and on the theoretical front (where variants of analogue models can be used as a springboard for radical attacks on the problem of quantum gravity.
Institutional Problems and Solutions of General Education in Chinese Universities
Meng, Weiqing; Huang, Wei
2018-01-01
Embedding general education in the Chinese university education system is a considerably complex systemic project, and a lack of institutional arrangements beneficial to general education has always been a key barrier in implementation. Currently, the main institutional restricting factors for university general education include substantial…
General classical solutions in the noncommutative CP{sup N-1} model
Energy Technology Data Exchange (ETDEWEB)
Foda, O.; Jack, I.; Jones, D.R.T
2002-10-31
We give an explicit construction of general classical solutions for the noncommutative CP{sup N-1} model in two dimensions, showing that they correspond to integer values for the action and topological charge. We also give explicit solutions for the Dirac equation in the background of these general solutions and show that the index theorem is satisfied.
Power-law cosmic expansion in f(R) gravity models
International Nuclear Information System (INIS)
Goheer, Naureen; Larena, Julien; Dunsby, Peter K. S.
2009-01-01
We show that within the class of f(R) gravity theories, Friedmann-Lemaitre-Robertson-Walker power-law perfect fluid solutions only exist for R n gravity. This significantly restricts the set of exact cosmological solutions which have similar properties to what is found in standard general relativity.
Solving the AKNS Hierarchy by Its Bilinear Form: Generalized Double Wronskian Solutions
International Nuclear Information System (INIS)
Yin Fumei; Sun Yepeng; Cai Fuqing; Chen Dengyuan
2008-01-01
Through the Wronskian technique, a simple and direct proof is presented that the AKNS hierarchy in the bilinear form has generalized double Wronskian solutions. Moreover, by using a unified way, soliton solutions, rational solutions, Matveev solutions and complexitons in double Wronskian form for it are constructed.
New explicit spike solution -- non-local component of the generalized Mixmaster attractor
Lim, Woei Chet
2007-01-01
By applying a standard solution-generating transformation to an arbitrary vacuum Bianchi type II solution, one generates a new solution with spikes commonly observed in numerical simulations. It is conjectured that the spike solution is part of the generalized Mixmaster attractor.
Exact travelling wave solutions for the generalized shallow water wave equation
International Nuclear Information System (INIS)
Elwakil, S.A.; El-labany, S.K.; Zahran, M.A.; Sabry, R.
2003-01-01
Using homogeneous balance method an auto-Baecklund transformation for the generalized shallow water wave equation is obtained. Then solitary wave solutions are found. Also, modified extended tanh-function method is applied and new exact travelling wave solutions are obtained. The obtained solutions include rational, periodical, singular and solitary wave solutions
Exact travelling wave solutions for the generalized shallow water wave equation
Energy Technology Data Exchange (ETDEWEB)
Elwakil, S.A.; El-labany, S.K.; Zahran, M.A.; Sabry, R
2003-07-01
Using homogeneous balance method an auto-Baecklund transformation for the generalized shallow water wave equation is obtained. Then solitary wave solutions are found. Also, modified extended tanh-function method is applied and new exact travelling wave solutions are obtained. The obtained solutions include rational, periodical, singular and solitary wave solutions.
Elastic stars in general relativity: III. Stiff ultrarigid exact solutions
International Nuclear Information System (INIS)
Karlovini, Max; Samuelsson, Lars
2004-01-01
We present an equation of state for elastic matter which allows for purely longitudinal elastic waves in all propagation directions, not just principal directions. The speed of these waves is equal to the speed of light whereas the transversal type speeds are also very high, comparable to but always strictly less than that of light. Clearly such an equation of state does not give a reasonable matter description for the crust of a neutron star, but it does provide a nice causal toy model for an extremely rigid phase in a neutron star core, should such a phase exist. Another reason for focusing on this particular equation of state is simply that it leads to a very simple recipe for finding stationary rigid motion exact solutions to the Einstein equations. In fact, we show that a very large class of stationary spacetimes with constant Ricci scalar can be interpreted as rigid motion solutions with this matter source. We use the recipe to derive a static spherically symmetric exact solution with constant energy density, regular centre and finite radius, having a nontrivial parameter that can be varied to yield a mass-radius curve from which stability can be read off. It turns out that the solution is stable down to a tenuity R/M slightly less than 3. The result of this static approach to stability is confirmed by a numerical determination of the fundamental radial oscillation mode frequency. We also present another solution with outwards decreasing energy density. Unfortunately, this solution only has a trivial scaling parameter and is found to be unstable
General solution of the Universal equation in n-dimensional space
International Nuclear Information System (INIS)
Fairlie, D.B.; Leznov, A.N.
1994-01-01
Using the explicit form of solution of the system it is possible to construct the general solution of the Universal Equation which was found before with the help of the method of Legendre Transform. 6 refs
Travelling Solitary Wave Solutions for Generalized Time-delayed Burgers-Fisher Equation
International Nuclear Information System (INIS)
Deng Xijun; Han Libo; Li Xi
2009-01-01
In this paper, travelling wave solutions for the generalized time-delayed Burgers-Fisher equation are studied. By using the first-integral method, which is based on the ring theory of commutative algebra, we obtain a class of travelling solitary wave solutions for the generalized time-delayed Burgers-Fisher equation. A minor error in the previous article is clarified. (general)
A generalized solution for groundwater head fluctuation in a tidal ...
Indian Academy of Sciences (India)
2Institute of Environmental Engineering, National Chiao Tung University, Hsinchu, Taiwan. ∗. Corresponding author. e-mail: hdyeh@mail.nctu.edu.tw. A new analytical solution is developed for describing groundwater level fluctuations in a coupled leaky confined aquifer system which consists of an unconfined aquifer, ...
Solitary wave solution to a singularly perturbed generalized Gardner ...
Indian Academy of Sciences (India)
2017-03-24
Mar 24, 2017 ... which is one model in plasma physics and solid physics. [3]. Hamdi et al [4] obtained an exact solitary wave solution to eq. (1.2). They also derived three conserva- tion laws and three invariants of motion for eq. (1.2). [5]. Antonova and Biswas [6] exploited the soliton perturbation theory to eq. (1.2) with γ = 1.
A generalized solution for groundwater head fluctuation in a tidal ...
Indian Academy of Sciences (India)
A new analytical solution is developed for describing groundwater level fluctuations in a coupled leaky confined aquifer system which consists of an unconfined aquifer, confined aquifer, and an aquitard in between. The aquifer system has a tidal boundary at the seashore, a no flow boundary at remote inland side, and a ...
Solution of a general pexiderized permanental functional equation
Indian Academy of Sciences (India)
49
f(ux + vy, uy − vx, zw) = g(x, y, z) h(u, v, w) is determined without any regularity assumptions. This equation arises from identities satisfied by the permanent of certain symmetric matrices. The solution so obtained are applied to deduce a number of existing related functional equations. Keywords. permanent; multiplicative ...
The generalized Schwinger-DeWitt technique and the unique effective action in quantum gravity
International Nuclear Information System (INIS)
Barvinsky, A.O.; Vilkovisky, G.A.
1983-01-01
We consider the one-loop approximation to the recently proposed unique effective action in gauge theory. The Schwinger-DeWitt technique is generalized and applied to the computation of the unique gravitational counterterms. The issue of asymptotic freedom is reexamined. (orig.)
Quantum Gravity in Everyday Life: General Relativity as an Effective Field Theory.
Burgess, Cliff P
2004-01-01
This article is meant as a summary and introduction to the ideas of effective field theory as applied to gravitational systems, ideas which provide the theoretical foundations for the modern use of general relativity as a theory from which precise predictions are possible.
Quantum Gravity in Everyday Life: General Relativity as an Effective Field Theory
Directory of Open Access Journals (Sweden)
Burgess Cliff P.
2004-01-01
Full Text Available This article is meant as a summary and introduction to the ideas of effective field theory as applied to gravitational systems, ideas which provide the theoretical foundations for the modern use of general relativity as a theory from which precise predictions are possible.
A class of doubly periodic wave solutions for the generalized Nizhnik-Novikov-Veselov equation
International Nuclear Information System (INIS)
Peng Yanze
2005-01-01
A general solution including two arbitrary functions is first obtained for the generalized Nizhnik-Novikov-Veselov equation by means of WTC truncation method. A class of doubly periodic wave solutions, which are expressed as rational functions of the Jacobi elliptic functions with different moduli, result from the general solution. Limit cases are considered and some new solitary structures are revealed. The interaction properties of periodic waves are numerically studied and found to be nonelastic. Under long wave limit, a two-dromion solution with the new solution structure is obtained and interaction between the two dromions is completely elastic
Directory of Open Access Journals (Sweden)
M. Arshad
Full Text Available In this manuscript, we constructed different form of new exact solutions of generalized coupled Zakharov–Kuznetsov and dispersive long wave equations by utilizing the modified extended direct algebraic method. New exact traveling wave solutions for both equations are obtained in the form of soliton, periodic, bright, and dark solitary wave solutions. There are many applications of the present traveling wave solutions in physics and furthermore, a wide class of coupled nonlinear evolution equations can be solved by this method. Keywords: Traveling wave solutions, Elliptic solutions, Generalized coupled Zakharov–Kuznetsov equation, Dispersive long wave equation, Modified extended direct algebraic method
Directory of Open Access Journals (Sweden)
Shiuan-Ni Liang
Full Text Available We show, contrary to expectation, that the trajectory predicted by general-relativistic mechanics for a low-speed weak-gravity system is not always well-approximated by the trajectories predicted by special-relativistic and newtonian mechanics for the same parameters and initial conditions. If the system is dissipative, the breakdown of agreement occurs for chaotic trajectories only. If the system is non-dissipative, the breakdown of agreement occurs for chaotic trajectories and non-chaotic trajectories. The agreement breaks down slowly for non-chaotic trajectories but rapidly for chaotic trajectories. When the predictions are different, general-relativistic mechanics must therefore be used, instead of special-relativistic mechanics (newtonian mechanics, to correctly study the dynamics of a weak-gravity system (a low-speed weak-gravity system.
International Nuclear Information System (INIS)
Lamon, Raphael
2010-01-01
Quantum gravity is an attempt to unify general relativity with quantum mechanics which are the two highly successful fundamental theories of theoretical physics. The main difficulty in this unification arises from the fact that, while general relativity describes gravity as a macroscopic geometrical theory, quantum mechanics explains microscopic phenomena. As a further complication, not only do both theories describe different scales but also their philosophical ramifications and the mathematics used to describe them differ in a dramatic way. Consequently, one possible starting point of an attempt at a unification is quantum mechanics, i.e. particle physics, and try to incorporate gravitation. This pathway has been chosen by particle physicists which led to string theory. On the other hand, loop quantum gravity (LQG) chooses the other possibility, i.e. it takes the geometrical aspects of gravity seriously and quantizes geometry. The first part of this thesis deals with a generalization of loop quantum cosmology (LQC) to toroidal topologies. LQC is a quantization of homogenous solutions of Einstein's field equations using tools from LQG. First the general concepts of closed topologies is introduced with special emphasis on Thurston's theorem and its consequences. It is shown that new degrees of freedom called Teichmueller parameters come into play and their dynamics can be described by a Hamiltonian. Several numerical solutions for a toroidal universe are presented and discussed. Following the guidelines of LQG this dynamics are rewritten using the Ashtekar variables and numerical solutions are shown. However, in order to find a suitable Hilbert space a canonical transformation must be performed. On the other hand this transformation makes the quantization of geometrical quantities less tractable such that two different ways are presented. It is shown that in both cases the spectrum of such geometrical operators depends on the initial value problem. Furthermore, we
Energy Technology Data Exchange (ETDEWEB)
Lamon, Raphael
2010-06-29
Quantum gravity is an attempt to unify general relativity with quantum mechanics which are the two highly successful fundamental theories of theoretical physics. The main difficulty in this unification arises from the fact that, while general relativity describes gravity as a macroscopic geometrical theory, quantum mechanics explains microscopic phenomena. As a further complication, not only do both theories describe different scales but also their philosophical ramifications and the mathematics used to describe them differ in a dramatic way. Consequently, one possible starting point of an attempt at a unification is quantum mechanics, i.e. particle physics, and try to incorporate gravitation. This pathway has been chosen by particle physicists which led to string theory. On the other hand, loop quantum gravity (LQG) chooses the other possibility, i.e. it takes the geometrical aspects of gravity seriously and quantizes geometry. The first part of this thesis deals with a generalization of loop quantum cosmology (LQC) to toroidal topologies. LQC is a quantization of homogenous solutions of Einstein's field equations using tools from LQG. First the general concepts of closed topologies is introduced with special emphasis on Thurston's theorem and its consequences. It is shown that new degrees of freedom called Teichmueller parameters come into play and their dynamics can be described by a Hamiltonian. Several numerical solutions for a toroidal universe are presented and discussed. Following the guidelines of LQG this dynamics are rewritten using the Ashtekar variables and numerical solutions are shown. However, in order to find a suitable Hilbert space a canonical transformation must be performed. On the other hand this transformation makes the quantization of geometrical quantities less tractable such that two different ways are presented. It is shown that in both cases the spectrum of such geometrical operators depends on the initial value problem
Exact periodic wave solutions to the generalized Nizhnik–Novikov ...
Indian Academy of Sciences (India)
f(ξ) = tanh ξ, g(ξ) = sech ξ, and the method is called the two-family truncation method [11,12]. It is worth noticing that when Bi ... its many doubly periodic wave solutions and study their limit cases. Substituting u = u(ξ),v = v(ξ),w = w(ξ),ξ = kx + ly ..... ematical Society, Providence, 1997). [11] R Conte and M Musette, Physica D69, ...
Solitary wave solution to a singularly perturbed generalized Gardner ...
Indian Academy of Sciences (India)
2017-03-24
Mar 24, 2017 ... This paper is concerned with the existence of travelling wave solutions to a singularly perturbed gen- eralized Gardner equation .... will be used in §3 for our purpose. For convenience, we use a version of this theory due to Jones [2]. For the system. { x (t) = f (x, y, ε), y (t) = εg(x, y, ε),. (2.1) where x ∈ Rn, y ...
A theory of general solutions of 3D problems in 1D hexagonal quasicrystals
International Nuclear Information System (INIS)
Gao Yang; Xu Sipeng; Zhao Baosheng
2008-01-01
A theory of general solutions of three-dimensional (3D) problems is developed for the coupled equilibrium equations in 1D hexagonal quasicrystals (QCs), and two new general solutions, which are called generalized Lekhnitskii-Hu-Nowacki (LHN) and Elliott-Lodge (E-L) solutions, respectively, are presented based on three theorems. As a special case, the generalized LHN solution is obtained from our previous general solution by introducing three high-order displacement functions. For further simplification, considering three cases in which three characteristic roots are distinct or possibly equal to each other, the generalized E-L solution shall take different forms, and be expressed in terms of four quasi-harmonic functions which are very simple and useful. It is proved that the general solution presented by Peng and Fan is consistent with one case of the generalized E-L solution, while does not include the other two cases. It is important to note that generalized LHN and E-L solutions are complete in z-convex domains, while incomplete in the usual non-z-convex domains
Teleparallel equivalent theory of (1+1)-dimensional gravity
Gamal, G. L. Nashed
2010-11-01
A theory of (1+1)-dimensional gravity is constructed on the basis of the teleparallel equivalent of general relativity. The fundamental field variables are the tetrad fields eiμ and the gravity is attributed to the torsion. A dilatonic spherically symmetric exact solution of the gravitational field equations characterized by two parameters M and Q is derived. The energy associated with this solution is calculated using the two-dimensional gravitational energy—momentum formula.
International Nuclear Information System (INIS)
Burkhard, N.R.
1979-01-01
The gravity inversion code applies stabilized linear inverse theory to determine the topography of a subsurface density anomaly from Bouguer gravity data. The gravity inversion program consists of four source codes: SEARCH, TREND, INVERT, and AVERAGE. TREND and INVERT are used iteratively to converge on a solution. SEARCH forms the input gravity data files for Nevada Test Site data. AVERAGE performs a covariance analysis on the solution. This document describes the necessary input files and the proper operation of the code. 2 figures, 2 tables
Energy Technology Data Exchange (ETDEWEB)
Melendez L, L
2004-07-01
In the first part of this work, starting from Einstein's equations of the Classical General Relativity, a new kind of solutions for the Mixmaster model are explored. By dispensing with the extension to the complex variable field, which is usual in problems such as the Laplace equation or the harmonic oscillator, in a similar manner to that of Quantum Mechanics, the equations appear to have solutions that belong to the complex General Relativity. A first integral is performed by establishing a separation of the first derivatives. Then a second integral is obtained once the respective equations with separate variables are found and whose integrals provide a family of complex solutions. However, reality conditions do not seem to be easily imposed at this stage. Above all, it is significant that the classical Einstein's equations for the debatably integrable Mixmaster model present complex solutions. In the second part of this work, following a specific strategy in which the cosmological time variables are operated upon, a new family of solutions to the empty Taub universe is found. Among the characteristics of such a family, it stands the positive acceleration provided by the tri-curvature property of this universe to two of the three scale factors of the Taub model. This effect of the tri-curvature results not in a restoring force such as normal gravity but in the conversion of the Taub cosmology into an accelerating universe. (Author)
Large time behaviour of solutions of a system of generalized ...
Indian Academy of Sciences (India)
j (x,t) be the solution of (1.1) and (1.2) given by (1.5). It was shown in [6] that when u0j is Lipschitz continuous, for each t > 0, except for a countable x the limits ..... To study the limit, we rewrite this formula in a convenient form by introducing the functions. Aν l,σ0 (x,t) = (2tν)1. 2 e σ2. 0 t. 2ν − σ0x ν erf c. ( tσ0 − x − l. (2tν)1. 2. ).
Quintic quasi-topological gravity
Energy Technology Data Exchange (ETDEWEB)
Cisterna, Adolfo [Vicerrectoría académica, Universidad Central de Chile,Toesca 1783 Santiago (Chile); Instituto de Ciencias Físicas y Matemáticas, Universidad Austral de Chile,Casilla 567, Valdivia (Chile); Guajardo, Luis; Hassaïne, Mokhtar [Instituto de Matemática y Física, Universidad de Talca,Casilla 747, Talca (Chile); Oliva, Julio [Departamento de Física, Universidad de Concepción,Casilla, 160-C, Concepción (Chile)
2017-04-11
We construct a quintic quasi-topological gravity in five dimensions, i.e. a theory with a Lagrangian containing R{sup 5} terms and whose field equations are of second order on spherically (hyperbolic or planar) symmetric spacetimes. These theories have recently received attention since when formulated on asymptotically AdS spacetimes might provide for gravity duals of a broad class of CFTs. For simplicity we focus on five dimensions. We show that this theory fulfils a Birkhoff’s Theorem as it is the case in Lovelock gravity and therefore, for generic values of the couplings, there is no s-wave propagating mode. We prove that the spherically symmetric solution is determined by a quintic algebraic polynomial equation which resembles Wheeler’s polynomial of Lovelock gravity. For the black hole solutions we compute the temperature, mass and entropy and show that the first law of black holes thermodynamics is fulfilled. Besides of being of fourth order in general, we show that the field equations, when linearized around AdS are of second order, and therefore the theory does not propagate ghosts around this background. Besides the class of theories originally introduced in https://arxiv.org/abs/1003.4773, the general geometric structure of these Lagrangians remains an open problem.
Possible Solutions for General Aviation of the City of Zagreb
Directory of Open Access Journals (Sweden)
Stanislav Pavlin
2007-07-01
Full Text Available General aviation, which in practice includes small aircraftin non-commercial traffic, in the City of Zagreb uses two aerodromes,Pleso and Lucko. Zagreb Airport at the Pleso locationis primarily intended for the handling of commercial aircraft,but provides also services to small aircraft in commercial andnon-commercial flying. The airfield Lucko is a sport and trainingaerodrome which accommodates operations of sport andrecreation flying, pilot training, activities of parachutists, glidersand flying-model constructors. Lucko Airfield is open to trafficabout half a year and it does not satisfy the non-commercialgeneral aviation requirements. The work presents the possibilitiesof developing the capacities for the needs of general aviationin the City of Zagreb.
Positive global solutions for a general model of size-dependent population dynamics
Kato, Nobuyuki
2000-01-01
We study size-structured population models of general type which have the growth rate depending on the size and time. The local existence and uniqueness of the solution have been shown by Kato and Torikata (1997). Here, we discuss the positivity of the solution and global existence as well as $L^\\infty$ solutions.
New exact solutions to the generalized KdV equation with ...
Indian Academy of Sciences (India)
Keywords. Improved Fan subequation method; bifurcation method; generalized KdV equation; soliton solution; kink solution; periodic solution. ... Shengqiang Tang1 Dahe Feng1. School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, Guangxi, 541004, People's Republic of China ...
Exact solutions of nonlinear generalizations of the Klein Gordon and Schrodinger equations
International Nuclear Information System (INIS)
Burt, P.B.
1978-01-01
Exact solutions of sine Gordon and multiple sine Gordon equations are constructed in terms of solutions of a linear base equation, the Klein Gordon equation and also in terms of nonlinear base equations where the nonlinearity is polynomial in the dependent variable. Further, exact solutions of nonlinear generalizations of the Schrodinger equation and of additional nonlinear generalizations of the Klein Gordon equation are constructed in terms of solutions of linear base equations. Finally, solutions with spherical symmetry, of nonlinear Klein Gordon equations are given. 14 references
A generalized exp-function method for multiwave solutions of sine ...
Indian Academy of Sciences (India)
for many nonlinear PDEs and can be used to construct multiple types of exact solutions due to its more general ansätz with arbitrary parameters. The present paper is motivated by the desire to generalize the exp-function method to construct multiwave solutions of the sine-Gordon (sG) equation [19]: utt − uxx = sin u,. (1).
Soliton solutions of the generalized sinh-Gordon equation by the ...
Indian Academy of Sciences (India)
substituting αm,...,v and the general solutions of eq. (8) into (7) we have more travelling wave solutions of the nonlinear evolution eq. (1). 3. Application to the generalized sinh-Gordon equation. First, consider the following transformation: ξ = λ(x + ct), η = λ (x + a ct) , a = c2,. (9) where λ, c are two parameters to be determined.
Tisdell, C. C.
2017-01-01
Solution methods to exact differential equations via integrating factors have a rich history dating back to Euler (1740) and the ideas enjoy applications to thermodynamics and electromagnetism. Recently, Azevedo and Valentino presented an analysis of the generalized Bernoulli equation, constructing a general solution by linearizing the problem…
International Nuclear Information System (INIS)
Markov, M.A.; West, P.C.
1984-01-01
This book discusses the state of the art of quantum gravity, quantum effects in cosmology, quantum black-hole physics, recent developments in supergravity, and quantum gauge theories. Topics considered include the problems of general relativity, pregeometry, complete cosmological theories, quantum fluctuations in cosmology and galaxy formation, a new inflationary universe scenario, grand unified phase transitions and the early Universe, the generalized second law of thermodynamics, vacuum polarization near black holes, the relativity of vacuum, black hole evaporations and their cosmological consequences, currents in supersymmetric theories, the Kaluza-Klein theories, gauge algebra and quantization, and twistor theory. This volume constitutes the proceedings of the Second Seminar on Quantum Gravity held in Moscow in 1981
International Nuclear Information System (INIS)
Isham, C.
1989-01-01
Gravitational effects are seen as arising from a curvature in spacetime. This must be reconciled with gravity's apparently passive role in quantum theory to achieve a satisfactory quantum theory of gravity. The development of grand unified theories has spurred the search, with forces being of equal strength at a unification energy of 10 15 - 10 18 GeV, with the ''Plank length'', Lp ≅ 10 -35 m. Fundamental principles of general relativity and quantum mechanics are outlined. Gravitons are shown to have spin-0, as mediators of gravitation force in the classical sense or spin-2 which are related to the quantisation of general relativity. Applying the ideas of supersymmetry to gravitation implies partners for the graviton, especially the massless spin 3/2 fermion called a gravitino. The concept of supersymmetric strings is introduced and discussed. (U.K.)
On wormholes and black holes solutions of Einstein gravity coupled to a K-massless scalar field
Energy Technology Data Exchange (ETDEWEB)
Estevez-Delgado, J [Facultad de Ciencias Fisico-Matematicas, Universidad Michoacana de San Nicolas de Hidalgo, Morelia, Mich (Mexico); Zannias, T [Ins. de Fisica y Matematicas, Universidad Michoacana de San Nicolas de Hidalgo, A.P. 2-82, 58040 Morelia, Mich (Mexico)
2007-05-15
We investigate the nature of black holes and wormholes admitted by a K-essence model involving a massless scalar field {phi}, minimally coupled to gravity. Via Weyl's formalism, we show that any axial wormhole of the theory can be generated by a unique pair of harmonic functions: U({lambda}) = {pi}/2 C + C arctan({lambda}/{lambda}{sub 0}), {phi}({lambda}) = {pi}/2 D + D arctan({lambda}/{lambda}{sub 0}) where {lambda} is one of the oblate coordinate, {lambda}{sub 0} > 0 and (C, D) real parameters. The properties of the wormholes depends crucially upon the values of the parameters (C, D). Whenever (C, D) are chosen so that 2C{sup 2} - kD{sup 2} = -2 the wormhole is spherical, while for the case where 2C{sup 2} - kD{sup 2} = -4 or 2C{sup 2} - kD{sup 2} = -6 the wormhole throat possesses toroidal topology. Those two families of wormholes exhaust all regular static and axisymmetric wormholes admitted by this theory. For completeness we add that whenever (C, D) satisfy 2C{sup 2} - kD{sup 2} = -2l with l {>=} 3/2 one still generates a spacetime possessing two asymptotically flat but the throat connecting the two ends contains a string like singularity. For the refined case where 2C{sup 2} - kD{sup 2} = -2l with l = 4,5, ... the resulting spacetime represents a multi-sheeted configuration which even though free of curvature singularities nevertheless the spacetime topology is distinct to so far accepted wormhole topology. Spacetimes generated by the pair (U({lambda}), {phi}({lambda})) and parameters (C, D) subject to 2C{sup 2} - kD{sup 2} = -2l with l < 3/2 contain naked curvature singularities. For the classes of regular wormholes, the parameters (C, D) determine the ADM masses of the asymptotically flat ends and can be positive, negative or zero. Except for the cases of zero mass wormholes, the two ends possess ADM masses of opposite sign. In contrast to wormhole sector, the black hole sector of the theory is trivial. Any static, asymptotically flat solution of the
Akram, Ghazala; Sadaf, Maasoomah
2018-02-01
A modified algorithm for homotopy analysis method (MHAM) is presented for the solution of nonlinear damped generalized regularized long-wave equation. The modified algorithm has less computational cost than standard HAM and also overcomes the difficulty in calculating complicated integrals. The MHAM is applied on different cases of the damped generalized regularized long-wave equation subject to suitable initial conditions. The numerical results show that the approximate solutions are in good agreement with the exact solutions.
On asymptotic expansion of general solution of Chew-Low equations
International Nuclear Information System (INIS)
Gerdt, V.P.; Zharkov, A.Yu.
1984-01-01
The connection between the global and local expansion of the general solution of the Chew-Low equations is considered. The reppesentations of the Chew-Low equation is used in the form of a system of nonlinear-finite difference equations. The investigation of the properties of the general solution is based on reducing the nonlinear equations to the infinite chain of inhomogeneous linear finite difference equations. It is achieved by global expansion of the general solution in series over powers of one of the arbitrary periodical function c(w), determining the structure of the general integral of the Chew-Low equations. It is shown that in each order in c(w) the asymptotic expansion of the global representation gives the well known local expansion of the general solution. It is confirmed by direct numerical investigation of the asymptotic behaviour of the physical interesting solutions possessing the Born pole
Resolving curvature singularities in holomorphic gravity
Mantz, C.L.M.; Prokopec, T.
2011-01-01
We formulate a holomorphic theory of gravity and study how the holomorphy symmetry alters the two most important singular solutions of general relativity: black holes and cosmology. We show that typical observers (freely) falling into a holomorphic black hole do not encounter a curvature
Nonsymmetric gravity has unacceptable global asymptotics
Damour, T.; Deser, S.; McCarthy, J.
1993-12-01
We analyze the radiative aspects of nonsymmetric gravity theory to show that, in contrast to General Relativity, its nonstationary solutions cannot simultaneously exhibit acceptable asymptotic behavior at both future and past null infinity: good behavior at future null infinity is only possible through the use of advanced potentials with concomitant unphysical behavior at past null infinity.
Terrestrial Gravity Fluctuations
Directory of Open Access Journals (Sweden)
Jan Harms
2015-12-01
understanding of terrestrial gravity fluctuations will have great impact on the future development of GW detectors and high-precision gravimetry in general, and many open questions need to be answered still as emphasized in this article.
Terrestrial Gravity Fluctuations
Harms, Jan
2015-12-01
terrestrial gravity fluctuations will have great impact on the future development of GW detectors and high-precision gravimetry in general, and many open questions need to be answered still as emphasized in this article.
Energy Technology Data Exchange (ETDEWEB)
Sabry, R.; Zahran, M.A.; Fan Engui
2004-05-31
A generalized expansion method is proposed to uniformly construct a series of exact solutions for general variable coefficients non-linear evolution equations. The new approach admits the following types of solutions (a) polynomial solutions, (b) exponential solutions, (c) rational solutions, (d) triangular periodic wave solutions, (e) hyperbolic and solitary wave solutions and (f) Jacobi and Weierstrass doubly periodic wave solutions. The efficiency of the method has been demonstrated by applying it to a generalized variable coefficients KdV equation. Then, new and rich variety of exact explicit solutions have been found.
Ezquiaga, Jose María; García-Bellido, Juan; Zumalacárregui, Miguel
2016-07-01
We use a description based on differential forms to systematically explore the space of scalar-tensor theories of gravity. Within this formalism, we propose a basis for the scalar sector at the lowest order in derivatives of the field and in any number of dimensions. This minimal basis is used to construct a finite and closed set of Lagrangians describing general scalar-tensor theories invariant under local Lorentz transformations in a pseudo-Riemannian manifold, which contains ten physically distinct elements in four spacetime dimensions. Subsequently, we compute their corresponding equations of motion and find which combinations are at most second order in derivatives in four as well as an arbitrary number of dimensions. By studying the possible exact forms (total derivatives) and algebraic relations between the basis components, we discover that there are only four Lagrangian combinations producing second-order equations, which can be associated with Horndeski's theory. In this process, we identify a new second-order Lagrangian, named kinetic Gauss-Bonnet, that was not previously considered in the literature. However, we show that its dynamics is already contained in Horndeski's theory. Finally, we provide a full classification of the relations between different second-order theories. This allows us to clarify, for instance, the connection between different covariantizations of Galileons theory. In conclusion, our formulation affords great computational simplicity with a systematic structure. As a first step, we focus on theories with second-order equations of motion. However, this new formalism aims to facilitate advances towards unveiling the most general scalar-tensor theories.
A General Solution Framework for Component-Commonality Problems
Directory of Open Access Journals (Sweden)
Nils Boysen
2009-05-01
Full Text Available Component commonality - the use of the same version of a component across multiple products - is being increasingly considered as a promising way to offer high external variety while retaining low internal variety in operations. However, increasing commonality has both positive and negative cost effects, so that optimization approaches are required to identify an optimal commonality level. As components influence to a greater or lesser extent nearly every process step along the supply chain, it is not surprising that a multitude of diverging commonality problems is being investigated in literature, each of which are developing a specific algorithm designed for the respective commonality problem being considered. The paper on hand aims at a general framework which is flexible and efficient enough to be applied to a wide range of commonality problems. Such a procedure based on a two-stage graph approach is presented and tested. Finally, flexibility of the procedure is shown by customizing the framework to account for different types of commonality problems.
Ciufolini, Ignazio; Paolozzi, Antonio; Pavlis, Erricos C; Koenig, Rolf; Ries, John; Gurzadyan, Vahe; Matzner, Richard; Penrose, Roger; Sindoni, Giampiero; Paris, Claudio; Khachatryan, Harutyun; Mirzoyan, Sergey
2016-01-01
We present a test of general relativity, the measurement of the Earth's dragging of inertial frames. Our result is obtained using about 3.5 years of laser-ranged observations of the LARES, LAGEOS, and LAGEOS 2 laser-ranged satellites together with the Earth gravity field model GGM05S produced by the space geodesy mission GRACE. We measure [Formula: see text], where [Formula: see text] is the Earth's dragging of inertial frames normalized to its general relativity value, 0.002 is the 1-sigma formal error and 0.05 is our preliminary estimate of systematic error mainly due to the uncertainties in the Earth gravity model GGM05S. Our result is in agreement with the prediction of general relativity.
Energy Technology Data Exchange (ETDEWEB)
Ciufolini, Ignazio [Universita del Salento, Dipartimento Ingegneria dell' Innovazione, Lecce (Italy); Sapienza Universita di Roma, Scuola di Ingegneria Aerospaziale, Rome (Italy); Paolozzi, Antonio; Paris, Claudio [Sapienza Universita di Roma, Scuola di Ingegneria Aerospaziale, Rome (Italy); Museo della Fisica e Centro Studi e Ricerche Enrico Fermi, Rome (Italy); Pavlis, Erricos C. [University of Maryland, Joint Center for Earth Systems Technology (JCET), Baltimore County (United States); Koenig, Rolf [GFZ German Research Centre for Geosciences, Helmholtz Centre Potsdam, Potsdam (Germany); Ries, John [University of Texas at Austin, Center for Space Research, Austin (United States); Gurzadyan, Vahe; Khachatryan, Harutyun; Mirzoyan, Sergey [Alikhanian National Laboratory and Yerevan State University, Center for Cosmology and Astrophysics, Yerevan (Armenia); Matzner, Richard [University of Texas at Austin, Theory Center, Austin (United States); Penrose, Roger [University of Oxford, Mathematical Institute, Oxford (United Kingdom); Sindoni, Giampiero [Sapienza Universita di Roma, DIAEE, Rome (Italy)
2016-03-15
We present a test of general relativity, the measurement of the Earth's dragging of inertial frames. Our result is obtained using about 3.5 years of laser-ranged observations of the LARES, LAGEOS, and LAGEOS 2 laser-ranged satellites together with the Earth gravity field model GGM05S produced by the space geodesy mission GRACE. We measure μ = (0.994 ± 0.002) ± 0.05, where μ is the Earth's dragging of inertial frames normalized to its general relativity value, 0.002 is the 1-sigma formal error and 0.05 is our preliminary estimate of systematic error mainly due to the uncertainties in the Earth gravity model GGM05S. Our result is in agreement with the prediction of general relativity. (orig.)
The general Lie group and similarity solutions for the one-dimensional Vlasov-Maxwell equations
Roberts, D.
1985-01-01
The general Lie point transformation group and the associated reduced differential equations and similarity forms for the solutions are derived here for the coupled (nonlinear) Vlasov-Maxwell equations in one spatial dimension. The case of one species in a background is shown to admit a larger group than the multispecies case. Previous exact solutions are shown to be special cases of the above solutions, and many of the new solutions are found to constrain the form of the distribution function much more than, for example, the BGK solutions do. The individual generators of the Lie group are used to find the possible subgroups. Finally, a simple physical argument is given to show that the asymptotic solution for a one-species, one-dimensional plasma is one of the general similarity solutions.
Gravity-driven pH adjustment for site-specific protein pKa measurement by solution-state NMR
Li, Wei
2017-12-01
To automate pH adjustment in site-specific protein pKa measurement by solution-state NMR, I present a funnel with two caps for the standard 5 mm NMR tube. The novelty of this simple-to-build and inexpensive apparatus is that it allows automatic gravity-driven pH adjustment within the magnet, and consequently results in a fully automated NMR-monitored pH titration without any hardware modification on the NMR spectrometer.
Directory of Open Access Journals (Sweden)
I. Capuzzo Dolcetta
2007-12-01
Full Text Available We analyze the validity of the Maximum Principle for viscosity solutions of fully nonlinear second order elliptic equations in general unbounded domains under suitable structure conditions on the equation allowing notably quadratic growth in the gradient terms.
New multi-soliton solutions for generalized Burgers-Huxley equation
Directory of Open Access Journals (Sweden)
Liu Jun
2013-01-01
Full Text Available The double exp-function method is used to obtain a two-soliton solution of the generalized Burgers-Huxley equation. The wave has two different velocities and two different frequencies.
Directory of Open Access Journals (Sweden)
Liu Yang
2014-01-01
Full Text Available We investigate a class of nonperiodic fourth order differential equations with general potentials. By using variational methods and genus properties in critical point theory, we obtain that such equations possess infinitely homoclinic solutions.
Analytical approximate solutions for a general class of nonlinear delay differential equations.
Căruntu, Bogdan; Bota, Constantin
2014-01-01
We use the polynomial least squares method (PLSM), which allows us to compute analytical approximate polynomial solutions for a very general class of strongly nonlinear delay differential equations. The method is tested by computing approximate solutions for several applications including the pantograph equations and a nonlinear time-delay model from biology. The accuracy of the method is illustrated by a comparison with approximate solutions previously computed using other methods.
General solution of Poisson equation in three dimensions for disk-like galaxies
International Nuclear Information System (INIS)
Tong, Y.; Zheng, X.; Peng, O.
1982-01-01
The general solution of the Poisson equation is solved by means of integral transformations for Vertical BarkVertical Barr>>1 provided that the perturbed density of disk-like galaxies distributes along the radial direction according to the Hankel function. This solution can more accurately represent the outer spiral arms of disk-like galaxies
Decay estimate of global solutions to the generalized double dispersion model in Morrey spaces
Wang, Yu-Zhu; Gu, Liuxin; Wang, Yinxia
2017-08-01
In this paper, we investigate the initial value problem for the generalized double dispersion model in Morrey spaces. Based on the decay properties of the solution operator in Morrey spaces, global existence and decay estimates of solutions are proved by Banach fixed point theorem.
Generalized Sturmian Solutions for Many-Particle Schrödinger Equations
DEFF Research Database (Denmark)
Avery, John; Avery, James Emil
2004-01-01
The generalized Sturmian method for obtaining solutions to the many-particle Schrodinger equation is reviewed. The method makes use of basis functions that are solutions of an approximate Schrodinger equation with a weighted zeroth-order potential. The weighting factors are especially chosen so...
New exact solutions for a generalized variable coefficients 2D KdV equation
Energy Technology Data Exchange (ETDEWEB)
Elwakil, S.A.; El-labany, S.K.; Zahran, M.A. E-mail: m_zahran1@mans.edu.eg; Sabry, R. E-mail: refaatsabry@mans.edu.eg
2004-03-01
Using homogeneous balance method an auto-Baecklund transformation for a generalized variable coefficients 2D KdV equation is obtained. Then new exact solutions are found which include solitary one. Also, we have found certain new analytical soliton-typed solution in terms of the variable coefficients of the studied 2D KdV equation.
Tables of generalized Airy functions for the asymptotic solution of the differential equation
Nosova, L N
1965-01-01
Tables of Generalized Airy Functions for the Asymptotic Solution of the Differential Equations contains tables of the special functions, namely, the generalized Airy functions, and their first derivatives, for real and pure imaginary values. The tables are useful for calculations on toroidal shells, laminae, rode, and for the solution of certain other problems of mathematical physics. The values of the functions were computed on the ""Strela"" highspeed electronic computer.This book will be of great value to mathematicians, researchers, and students.
Directory of Open Access Journals (Sweden)
Haci Mehmet Baskonus
2016-07-01
Full Text Available In this paper, we apply the sine-Gordon expansion method which is one of the powerful methods to the generalized-Zakharov equation with complex structure. This algorithm yields new complex hyperbolic function solutions to the generalized-Zakharov equation with complex structure. Wolfram Mathematica 9 has been used throughout the paper for plotting two- and three-dimensional surface of travelling wave solutions obtained.
Solitonlike solutions of the generalized discrete nonlinear Schrödinger equation
DEFF Research Database (Denmark)
Rasmussen, Kim; Henning, D.; Gabriel, H.
1996-01-01
We investigate the solution properties oi. a generalized discrete nonlinear Schrodinger equation describing a nonlinear lattice chain. The generalized equation interpolates between the integrable discrete Ablowitz-Ladik equation and the nonintegrable discrete Schrodinger equation. Special interest...... of the nonintegrability parameter versus the integrability parameter. The heteroclinic map orbit is derived on the basis of a variational principle. Finally, we use homoclinic and heteroclinic orbits as initial conditions to excite designed stationary localized solutions of desired width in the dynamics of the discrete...
Ghost-free F(R) gravity with Lagrange multiplier constraint
Nojiri, S.; Odintsov, S. D.; Oikonomou, V. K.
2017-12-01
We propose two new versions of ghost-free generalized F (R) gravity with Lagrange multiplier constraint. The first version of such theory for a particular degenerate choice of the Lagrange multiplier, corresponds to mimetic F (R) gravity. The second version of such theory is just the Jordan frame description of mimetic gravity with potential. As we demonstrate, it is possible to realize several cosmological scenarios in such theory. In particular, de Sitter solutions may also be found.
International Nuclear Information System (INIS)
Aros, Rodrigo; Contreras, Mauricio
2006-01-01
In this work the Poincare-Chern-Simons and anti-de Sitter-Chern-Simons gravities are studied. For both, a solution that can be cast as a black hole with manifest torsion is found. Those solutions resemble Schwarzschild and Schwarzschild-AdS solutions, respectively
Improved decay rates for solutions for a multidimensional generalized Benjamin-Bona-Mahony equation
Said-Houari, Belkacem
2014-01-01
In this paper, we study the decay rates of solutions for the generalized Benjamin-Bona-Mahony equation in multi-dimensional space. For initial data in some L1-weighted spaces, we prove faster decay rates of the solutions. More precisely, using the Fourier transform and the energy method, we show the global existence and the convergence rates of the solutions under the smallness assumption on the initial data and we give better decay rates of the solutions. This result improves early works in J. Differential Equations 158(2) (1999), 314-340 and Nonlinear Anal. 75(7) (2012), 3385-3392. © 2014-IOS Press.
Indian Academy of Sciences (India)
2016-11-02
Nov 2, 2016 ... the existence of dark energy and dark matter, several modified theories of gravitation have been proposed as alternative to Einstein's theory. By modifying the geometrical part of Einstein–Hilbert action of general relativity, we obtain the modified gravity. Modified gravity is of great importance because it can ...
Directory of Open Access Journals (Sweden)
Zayed El-Sayed Mohamed El-Sayed
2016-01-01
Full Text Available The generalized Kudryashov method is applied in this article for finding the exact solutions of nonlinear partial differential equations (PDEs in mathematical physics. Solitons and other solutions are given. To illustrate the validity of this method, we apply it to three nonlinear PDEs, namely, the diffusive predator-prey system, the nonlinear Bogoyavlenskii equations and the nonlinear telegraph equation. These equations are related to signal analysis for transmission and propagation of electrical signals. As a result, many analytical exact solutions of these equations are obtained including symmetrical Fibonacci function solutions and hyperbolic function solutions. Physical explanations for some solutions of the given three nonlinear PDEs are obtained. Comparison our new results with the well-known results are given.
Directory of Open Access Journals (Sweden)
Qinghai He
2013-01-01
Full Text Available In general Banach spaces, we consider a vector optimization problem (SVOP in which the objective is a set-valued mapping whose graph is the union of finitely many polyhedra or the union of finitely many generalized polyhedra. Dropping the compactness assumption, we establish some results on structure of the weak Pareto solution set, Pareto solution set, weak Pareto optimal value set, and Pareto optimal value set of (SVOP and on connectedness of Pareto solution set and Pareto optimal value set of (SVOP. In particular, we improved and generalize, Arrow, Barankin, and Blackwell’s classical results in Euclidean spaces and Zheng and Yang’s results in general Banach spaces.
Glueball Masses from ADS6 Gravity Theory
Cai, Bengeng; Wen, Congkao; Yang, Huanxiong
In view of the general holographic principle between gauge theories and gravity, We calculate the mass spectra of several typical QCD4 glueballs in term of AdS6 AdS-Schwarzschild black hole metric of Einstein gravity theory. The obtained mass spectra are numerically in consistent with those from the AdS7 × S4 black hole metric of the 11-dimensional supergravity. Besides, by separating the thermal circle from the extra dimensions, we find a novel exact Dp-brane solution of Type IIB supergravity, which might provide a scenario for studying the non-perturbative dynamics of QCD4 from the perspective of Type IIB supergravity.
Mass gap in Yang's theory of gravity
Mielke, Eckehard W.
2015-06-01
The quantization of a curvature-squared model of gravity, in the affine form proposed by Yang, is reconsidered in the path integral formulation. Due to its inherent Weyl invariance, sharing this with internal Yang-Mills fields, it or some of its topological generalizations are still a possible route to quantum gravity. Instanton type solutions with double duality properties exhibit a "vacuum degeneracy", i.e. a bifurcation into distinct classical Einsteinian backgrounds. For linearized fields, this conclusively induces a mass gap in the graviton spectrum, a feature which is an open problem in the quantization of internal Yang-Mills fields.
Directory of Open Access Journals (Sweden)
Xiangrong Wang
2015-01-01
Full Text Available A generalized (2+1-dimensional variable-coefficient KdV equation is introduced, which can describe the interaction between a water wave and gravity-capillary waves better than the (1+1-dimensional KdV equation. The N-soliton solutions of the (2+1-dimensional variable-coefficient fifth-order KdV equation are obtained via the Bell-polynomial method. Then the soliton fusion, fission, and the pursuing collision are analyzed depending on the influence of the coefficient eAij; when eAij=0, the soliton fusion and fission will happen; when eAij≠0, the pursuing collision will occur. Moreover, the Bäcklund transformation of the equation is gotten according to the binary Bell-polynomial and the period wave solutions are given by applying the Riemann theta function method.
Chern-Simons-like Gravity Theories
Bergshoeff, Eric A.; Hohm, Olaf; Merbis, Wout; Routh, Alasdair J.; Townsend, Paul K.
2014-01-01
A wide class of three-dimensional gravity models can be put into "Chern-Simons-like" form. We perform a Hamiltonian analysis of the general model and then specialise to Einstein-Cartan Gravity, General Massive Gravity, the recently proposed Zwei-Dreibein Gravity and a further parity violating
Evaporation/Antievaporation and energy conditions in alternative gravity
Addazi, Andrea
2018-02-01
We discuss the evaporation and antievaporation instabilities of Nariai solution in extended theories of gravity. These phenomena were explicitly shown in several different extensions of General Relativity, suggesting that a universal cause is behind them. We show that evaporation and antievaporation are originated from deformations of energy conditions on the Nariai horizon. Energy conditions get new contributions from the extra propagating degrees of freedom, which can provide extra focalizing or antifocalizing terms in the Raychaudhuri equation. We show the two explicit cases of f(R)-gravity and Gauss-Bonnet gravity.
Lu, Chao; Li, Xubin; Wu, Dongsheng; Zheng, Lianqing; Yang, Wei
2016-01-12
In aqueous solution, solute conformational transitions are governed by intimate interplays of the fluctuations of solute-solute, solute-water, and water-water interactions. To promote molecular fluctuations to enhance sampling of essential conformational changes, a common strategy is to construct an expanded Hamiltonian through a series of Hamiltonian perturbations and thereby broaden the distribution of certain interactions of focus. Due to a lack of active sampling of configuration response to Hamiltonian transitions, it is challenging for common expanded Hamiltonian methods to robustly explore solvent mediated rare conformational events. The orthogonal space sampling (OSS) scheme, as exemplified by the orthogonal space random walk and orthogonal space tempering methods, provides a general framework for synchronous acceleration of slow configuration responses. To more effectively sample conformational transitions in aqueous solution, in this work, we devised a generalized orthogonal space tempering (gOST) algorithm. Specifically, in the Hamiltonian perturbation part, a solvent-accessible-surface-area-dependent term is introduced to implicitly perturb near-solute water-water fluctuations; more importantly in the orthogonal space response part, the generalized force order parameter is generalized as a two-dimension order parameter set, in which essential solute-solvent and solute-solute components are separately treated. The gOST algorithm is evaluated through a molecular dynamics simulation study on the explicitly solvated deca-alanine (Ala10) peptide. On the basis of a fully automated sampling protocol, the gOST simulation enabled repetitive folding and unfolding of the solvated peptide within a single continuous trajectory and allowed for detailed constructions of Ala10 folding/unfolding free energy surfaces. The gOST result reveals that solvent cooperative fluctuations play a pivotal role in Ala10 folding/unfolding transitions. In addition, our assessment
On the stability of soliton solution in NLS-type general field model
International Nuclear Information System (INIS)
Chakrabarti, S.; Nayyar, A.H.
1982-08-01
A model incorporating the nonlinear Schroedinger equation and its generalizations is considered and the stability of its periodic-in-time solutions under the restriction of a fixed charge Q is analysed. It is shown that the necessary condition for the stability is given by the inequality deltaQ/deltaν<0, where ν is the parameter of periodicity of the solution in time. In particular, one specific class of Lagrangians is considered and, in addition, the sufficient conditions for the stability of the soliton solutions are also determined. This study thus examines both the necessary and the sufficient conditions for the stability of the solutions of nonlinear Schroedinger equation and some of its generalizations. (author)
Cosmology and modifications of gravity at large distances
International Nuclear Information System (INIS)
Ziour, R.
2010-01-01
In the framework of General Relativity, the observed current acceleration of the expansion of the Universe requires the presence of a Dark Energy component, whose nature is not well understood. In order to explain the acceleration of the Universe without introducing such a tantalizing source of energy, other gravitation theories have been designed. This thesis is devoted to the study of some of these modified gravity theories, as well as to the observation methods that could constrain them. The first part of this thesis presents a review of modified gravity theories and their motivations. The second part is devoted to the study of the massive gravity theories and of the so-called Vainshtein's mechanism, which allows some of the solutions of Massive Gravity to strongly differ from General Relativity at cosmological scales while satisfying the experimental constraints inside the solar system. For the first time, the validity of the Vainshtein's mechanism is demonstrated, through the study of specific spherically symmetric solutions. The third part deals with scalar modification of gravity; a new model of this sort is presented, inspired by the Vainshtein's mechanism in Massive Gravity. Finally, the fourth part discusses local, astrophysical and cosmological observations that might constrain modified gravity theories. (author)
Hsu, Jong-Ping
2013-01-01
Yang-Mills gravity is a new theory, consistent with experiments, that brings gravity back to the arena of gauge field theory and quantum mechanics in flat space-time. It provides solutions to long-standing difficulties in physics, such as the incompatibility between Einstein's principle of general coordinate invariance and modern schemes for a quantum mechanical description of nature, and Noether's 'Theorem II' which showed that the principle of general coordinate invariance in general relativity leads to the failure of the law of conservation of energy. Yang-Mills gravity in flat space-time a
N-Soliton Solutions of the Nonisospectral Generalized Sawada-Kotera Equation
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Jian Zhou
2014-01-01
Full Text Available The soliton interaction is investigated based on solving the nonisospectral generalized Sawada-Kotera (GSK equation. By using Hirota method, the analytic one-, two-, three-, and N-soliton solutions of this model are obtained. According to those solutions, the relevant properties and features of line-soliton and bright-soliton are illustrated. The results of this paper will be useful to the study of soliton resonance in the inhomogeneous media.
Fundamental solutions for Schrödinger operators with general inverse square potentials
Chen, Huyuan
2017-03-17
In this paper, we clarify the fundamental solutions for Schrödinger operators given as (Formula presented.), where the potential V is a general inverse square potential in (Formula presented.) with (Formula presented.). In particular, letting (Formula presented.),(Formula presented.) where (Formula presented.), we discuss the existence and nonexistence of positive fundamental solutions for Hardy operator (Formula presented.), which depend on the parameter t.
Directory of Open Access Journals (Sweden)
Qiying Wei
2009-01-01
Full Text Available By using the well-known Schauder fixed point theorem and upper and lower solution method, we present some existence criteria for positive solution of an -point singular -Laplacian dynamic equation on time scales with the sign changing nonlinearity. These results are new even for the corresponding differential (=ℝ and difference equations (=ℤ, as well as in general time scales setting. As an application, an example is given to illustrate the results.
Solutions of Riccati-Abel equation in terms of characteristics of general complex algebra
International Nuclear Information System (INIS)
Yamaleev, R.M.
2012-01-01
The Riccati-Abel differential equation defined as an equation between the first order derivative and the cubic polynomial is explored. In the case of constant coefficients this equation is reduced into an algebraic equation. A method of derivation of a summation formula for solutions of the Riccati-Abel equation is elaborated. The solutions of the Riccati-Abel equation are expressed in terms of the characteristic functions of general complex algebra of the third order
Existence of Generalized Homoclinic Solutions of Lotka-Volterra System under a Small Perturbation
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Yuzhen Mi
2016-01-01
Full Text Available This paper investigates Lotka-Volterra system under a small perturbation vxx=-μ(1-a2u-vv+ϵf(ϵ,v,vx,u,ux, uxx=-(1-u-a1vu+ϵg(ϵ,v,vx,u,ux. By the Fourier series expansion technique method, the fixed point theorem, the perturbation theorem, and the reversibility, we prove that near μ=0 the system has a generalized homoclinic solution exponentially approaching a periodic solution.
International Nuclear Information System (INIS)
Batcho, P.F.; Karniadakis, G.E.
1994-01-01
The present study focuses on the solution of the incompressible Navier-Stokes equations in general, non-separable domains, and employs a Galerkin projection of divergence-free vector functions as a trail basis. This basis is obtained from the solution of a generalized constrained Stokes eigen-problem in the domain of interest. Faster convergence can be achieved by constructing a singular Stokes eigen-problem in which the Stokes operator is modified to include a variable coefficient which vanishes at the domain boundaries. The convergence properties of such functions are advantageous in a least squares sense and are shown to produce significantly better approximations to the solution of the Navier-Stokes equations in post-critical states where unsteadiness characterizes the flowfield. Solutions for the eigen-systems are efficiently accomplished using a combined Lanczos-Uzawa algorithm and spectral element discretizations. Results are presented for different simulations using these global spectral trial basis on non-separable and multiply-connected domains. It is confirmed that faster convergence is obtained using the singular eigen-expansions in approximating stationary Navier-Stokes solutions in general domains. It is also shown that 100-mode expansions of time-dependent solutions based on the singular Stokes eigenfunctions are sufficient to accurately predict the dynamics of flows in such domains, including Hopf bifurcations, intermittency, and details of flow structures
General solution of the Dirac equation for quasi-two-dimensional electrons
Energy Technology Data Exchange (ETDEWEB)
Eremko, Alexander, E-mail: eremko@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Str., 14-b, Kyiv, 03680 (Ukraine); Brizhik, Larissa, E-mail: brizhik@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Str., 14-b, Kyiv, 03680 (Ukraine); Loktev, Vadim, E-mail: vloktev@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Str., 14-b, Kyiv, 03680 (Ukraine); National Technical University of Ukraine “KPI”, Peremohy av., 37, Kyiv, 03056 (Ukraine)
2016-06-15
The general solution of the Dirac equation for quasi-two-dimensional electrons confined in an asymmetric quantum well, is found. The energy spectrum of such a system is exactly calculated using special unitary operator and is shown to depend on the electron spin polarization. This solution contains free parameters, whose variation continuously transforms one known particular solution into another. As an example, two different cases are considered in detail: electron in a deep and in a strongly asymmetric shallow quantum well. The effective mass renormalized by relativistic corrections and Bychkov–Rashba coefficients are analytically obtained for both cases. It is demonstrated that the general solution transforms to the particular solutions, found previously (Eremko et al., 2015) with the use of spin invariants. The general solution allows to establish conditions at which a specific (accompanied or non-accompanied by Rashba splitting) spin state can be realized. These results can prompt the ways to control the spin degree of freedom via the synthesis of spintronic heterostructures with the required properties.
Directory of Open Access Journals (Sweden)
Rabounski D.
2007-07-01
Full Text Available We consider the Podkletnov effect — the weight loss of an object located over a superconducting disc in air due to support by an alternating magnetic field. We consider this problem using the mathematical methods of General Relativity. We show via Einstein’s equations and the geodesic equations in a space perturbed by a disc undergoing oscillatory bounces orthogonal to its own plane, that there is no r ˆ ole of superconductivity; the Podkletnov effect is due to the fact that the field of the background space non-holonomity (the basic non-othogonality of time lines to the spatial section, being perturbed by such an oscillating disc produces energy and momentum flow in order to compensate the perturbation in itself. Such a momentum flow is directed above the disc in Podkletnov’s experiment, so it works like negative gravity (anti-gravity. We propose a simple mechanical system which, simulating the Podkletnov effect, is an experimental test of the whole theory. The theory allows for other “anti-gravity devices”, which simulate the Podkletnov effect without use of very costly superconductor technology. Such devices could be applied to be used as a cheap source of new energy, and could have implications to air and space travel.
Breathers and Soliton Solutions for a Generalization of the Nonlinear Schrödinger Equation
Directory of Open Access Journals (Sweden)
Hai-Feng Zhang
2013-01-01
Full Text Available A generalized nonlinear Schrödinger equation, which describes the propagation of the femtosecond pulse in single mode optical silica fiber, is analytically investigated. By virtue of the Darboux transformation method, some new soliton solutions are generated: the bright one-soliton solution on the zero background, the dark one-soliton solution on the continuous wave background, the Akhmediev breather which delineates the modulation instability process, and the breather evolving periodically along the straight line with a certain angle of x-axis and t-axis. Those results might be useful in the study of the femtosecond pulse in single mode optical silica fiber.
Generalized dynamics of soft-matter quasicrystals mathematical models and solutions
Fan, Tian-You
2017-01-01
The book systematically introduces the mathematical models and solutions of generalized hydrodynamics of soft-matter quasicrystals (SMQ). It provides methods for solving the initial-boundary value problems in these systems. The solutions obtained demonstrate the distribution, deformation and motion of the soft-matter quasicrystals, and determine the stress, velocity and displacement fields. The interactions between phonons, phasons and fluid phonons are discussed in some fundamental materials samples. Mathematical solutions for solid and soft-matter quasicrystals are compared, to help readers to better understand the featured properties of SMQ.
The General Traveling Wave Solutions of the Fisher Equation with Degree Three
Directory of Open Access Journals (Sweden)
Wenjun Yuan
2013-01-01
degree three and the general meromorphic solutions of the integrable Fisher equations with degree three, which improves the corresponding results obtained by Feng and Li (2006, Guo and Chen (1991, and Ağırseven and Öziş (2010. Moreover, all wg,1(z are new general meromorphic solutions of the Fisher equations with degree three for c=±3/2. Our results show that the complex method provides a powerful mathematical tool for solving a large number of nonlinear partial differential equations in mathematical physics.
International Nuclear Information System (INIS)
Moussa, M.H.M.; El-Shiekh, Rehab M.
2010-01-01
In this paper, the symmetry method has been carried over to the generalized variable coefficients Zakharov-Kuznetsov equation. The infinitesimal symmetries and the optimal system are deduced and from this optimal system seven basic fields are determined, and for every vector field in the optimal system the admissible forms of the coefficients are found and this also leads us to transform the given equation into partial differential equations in two variables. After using some referenced transformations the mentioned partial differential equations eventually reduce to ordinary differential equations. The search for solutions to those equations has yielded many exact solutions in most cases. (general)
A Note about the General Meromorphic Solutions of the Fisher Equation
Directory of Open Access Journals (Sweden)
Jian-ming Qi
2014-01-01
Full Text Available We employ the complex method to obtain the general meromorphic solutions of the Fisher equation, which improves the corresponding results obtained by Ablowitz and Zeppetella and other authors (Ablowitz and Zeppetella, 1979; Feng and Li, 2006; Guo and Chen, 1991, and wg,i(z are new general meromorphic solutions of the Fisher equation for c=±5i/6. Our results show that the complex method provides a powerful mathematical tool for solving great many nonlinear partial differential equations in mathematical physics.
Ortín, Tomás
2015-01-01
Self-contained and comprehensive, this definitive new edition of Gravity and Strings is a unique resource for graduate students and researchers in theoretical physics. From basic differential geometry through to the construction and study of black-hole and black-brane solutions in quantum gravity - via all the intermediate stages - this book provides a complete overview of the intersection of gravity, supergravity, and superstrings. Now fully revised, this second edition covers an extensive array of topics, including new material on non-linear electric-magnetic duality, the electric-tensor formalism, matter-coupled supergravity, supersymmetric solutions, the geometries of scalar manifolds appearing in 4- and 5-dimensional supergravities, and much more. Covering reviews of important solutions and numerous solution-generating techniques, and accompanied by an exhaustive index and bibliography, this is an exceptional reference work.
Some aspects of reconstruction using a scalar field in f(T) gravity
Energy Technology Data Exchange (ETDEWEB)
Chakrabarti, Soumya [Indian Institute of Technology, Centre for Theoretical Studies, Kharagpur (India); Said, Jackson Levi [University of Malta, Institute of Space Sciences and Astronomy, Msida, MSD (Malta); Farrugia, Gabriel [University of Malta, Department of Physics, Msida, MSD (Malta)
2017-12-15
General relativity characterizes gravity as a geometric property exhibited on spacetime by massive objects, while teleparallel gravity achieves the same results at the level of equations, by taking a torsional perspective of gravity. Similar to the f(R) theory teleparallel gravity can also be generalized to f(T), with the resulting field equations being inherently distinct from f(R) gravity in that they are second order, while in the former case they turn out to be fourth order. In the present case, a minimally coupled scalar field is investigated in the f(T) gravity context for several forms of the scalar field potential. A number of new f(T) solutions are found for these potentials. Their respective state parameters are also being examined. (orig.)
CERN. Geneva
2007-01-01
Of the four fundamental forces, gravity has been studied the longest, yet gravitational physics is one of the most rapidly developing areas of science today. This talk will give a broad brush survey of the past achievements and future prospects of general relativistic gravitational physics. Gravity is a two frontier science being important on both the very largest and smallest length scales considered in contemporary physics. Recent advances and future prospects will be surveyed in precision tests of general relativity, gravitational waves, black holes, cosmology and quantum gravity. The aim will be an overview of a subject that is becoming increasingly integrated with experiment and other branches of physics.
A hierarchy of generalized Jaulent-Miodek equations and their explicit solutions
Geng, Xianguo; Guan, Liang; Xue, Bo
A hierarchy of generalized Jaulent-Miodek (JM) equations related to a new spectral problem with energy-dependent potentials is proposed. Depending on the Lax matrix and elliptic variables, the generalized JM hierarchy is decomposed into two systems of solvable ordinary differential equations. Explicit theta function representations of the meromorphic function and the Baker-Akhiezer function are constructed, the solutions of the hierarchy are obtained based on the theory of algebraic curves.
Directory of Open Access Journals (Sweden)
Xin Liang
2018-01-01
Full Text Available In this paper, an anomalous advection-dispersion model involving a new general Liouville–Caputo fractional-order derivative is addressed for the first time. The series solutions of the general fractional advection-dispersion equations are obtained with the aid of the Laplace transform. The results are given to demonstrate the efficiency of the proposed formulations to describe the anomalous advection dispersion processes.
Directory of Open Access Journals (Sweden)
Md. Nur Alam
2014-03-01
Full Text Available The new approach of generalized (G′/G-expansion method is significant, powerful and straightforward mathematical tool for finding exact traveling wave solutions of nonlinear evolution equations (NLEEs arise in the field of engineering, applied mathematics and physics. Dispersive effects due to microstructure of materials combined with nonlinearities give rise to solitary waves. In this article, the new approach of generalized (G′/G-expansion method has been applied to construct general traveling wave solutions of the strain wave equation in microstructured solids. Abundant exact traveling wave solutions including solitons, kink, periodic and rational solutions have been found. These solutions might play important role in engineering fields.
Exact solutions of (3â¯+â¯1-dimensional generalized KP equation arising in physics
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Syed Tauseef Mohyud-Din
Full Text Available In this work, we have obtained some exact solutions to (3â¯+â¯1-dimensional generalized KP Equation. The improved tanÏ(Î¾2-expansion method has been introduced to construct the exact solutions of nonlinear evolution equations. The obtained solutions include hyperbolic function solutions, trigonometric function solutions, exponential solutions, and rational solutions. Our study has added some new varieties of solutions to already available solutions. It is also worth mentioning that the computational work has been reduced significantly. Keywords: Improved tanÏ(Î¾2-expansion method, Hyperbolic function solution, Trigonometric function solution, Rational solution, (3â¯+â¯1-dimensional generalized KP equation
Schwartzkopf, Steven H.; Oleson, Mel W.; Cullingford, Hatice S.
1990-01-01
Described here are the results of a study to develop a conceptual design for an experimental closed loop fluid handling system capable of monitoring, controlling, and supplying nutrient solution to higher plants. The Plant Feeder Experiment (PFE) is designed to be flight tested in a microgravity environment. When flown, the PFX will provide information on both the generic problems of microgravity fluid handling and the specific problems associated with the delivery of the nutrient solution in a microgravity environment. The experimental hardware is designed to fit into two middeck lockers on the Space Shuttle, and incorporates several components that have previously been flight tested.
Cosmological dynamics of mimetic gravity
Dutta, Jibitesh; Khyllep, Wompherdeiki; Saridakis, Emmanuel N.; Tamanini, Nicola; Vagnozzi, Sunny
2018-02-01
We present a detailed investigation of the dynamical behavior of mimetic gravity with a general potential for the mimetic scalar field. Performing a phase-space and stability analysis, we show that the scenario at hand can successfully describe the thermal history of the universe, namely the successive sequence of radiation, matter, and dark-energy eras. Additionally, at late times the universe can either approach a de Sitter solution, or a scaling accelerated attractor where the dark-matter and dark-energy density parameters are of the same order, thus offering an alleviation of the cosmic coincidence problem. Applying our general analysis to various specific potential choices, including the power-law and the exponential ones, we show that mimetic gravity can be brought into good agreement with the observed behavior of the universe. Moreover, with an inverse square potential we find that mimetic gravity offers an appealing unified cosmological scenario where both dark energy and dark matter are characterized by a single scalar field, and where the cosmic coincidence problem is alleviated.
On the general solution to RC circuits: Green's function in prose form
Kelly, T. J.
2018-03-01
The general solution to the first-order resistor–capacitor (RC) circuit is often overlooked in many introductory and advanced electronics courses. In this article, I argue that one reason for this is a misalignment between the mathematical and conceptual representations. I then suggest a possible conceptual picture that serves as an introduction to Green’s functions and convolutions.
A generalized solution to a Cahn-Hilliard/Allen-Cahn system
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Jose Luiz Boldrini
2004-10-01
Full Text Available We study a system consisting of a Cahn-Hilliard and several Allen-Cahn type equations. This system was proposed by Fan, L.-Q. Chen, S. Chen and Voorhees for modelling Ostwald ripening in two-phase system. We prove the existence of a generalized solution whose concentration component is in $L^{infty}$.
Painlevé integrability and a new exact solution of a generalized Hirota-Satsuma equation
Ye, Yujian; di, Yanmei; Song, Junquan
2017-12-01
In this paper, Painlevé integrability of a generalized Hirota-Satsuma (gHS) equation is confirmed by using the Weiss-Tabor-Carnevale (WTC) test. Then, a new exact solution with two arbitrary functions is constructed. Some new soliton structures are illustrated analytically by selecting appropriate functions.
Directory of Open Access Journals (Sweden)
Maxim Olegovich Korpusov
2012-07-01
Full Text Available In this article the initial-boundary-value problem for generalized dissipative high-order equation of Klein-Gordon type is considered. We continue our study of nonlinear hyperbolic equations and systems with arbitrary positive energy. The modified concavity method by Levine is used for proving blow-up of solutions.
New and More General Rational Formal Solutions to (2+1)-Dimensional Toda System
International Nuclear Information System (INIS)
Bai Chenglin
2007-01-01
With the aid of computerized symbolic computation and Riccati equation rational expansion approach, some new and more general rational formal solutions to (2+1)-dimensional Toda system are obtained. The method used here can also be applied to solve other nonlinear differential-difference equation or equations.
Cosmic string in gravity's rainbow
Momeni, Davood; Upadhyay, Sudhaker; Myrzakulov, Yerlan; Myrzakulov, Ratbay
2017-09-01
In this paper, we study the various cylindrical solutions (cosmic strings) in gravity's rainbow scenario. In particular, we calculate the gravitational field equations corresponding to energy-dependent background. Further, we discuss the possible Kasner, quasi-Kasner and non-Kasner exact solutions of the field equations. In this framework, we find that quasi-Kasner solutions cannot be realized in gravity's rainbow. Assuming only time-dependent metric functions, we also analyse the time-dependent vacuum cosmic strings in gravity's rainbow, which are completely different than the other GR solutions.
Can chaos be observed in quantum gravity?
Energy Technology Data Exchange (ETDEWEB)
Dittrich, Bianca, E-mail: bdittrich@perimeterinstitute.ca [Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, ON N2L 2Y5 (Canada); Höhn, Philipp A., E-mail: p.hoehn@univie.ac.at [Vienna Center for Quantum Science and Technology, and Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna (Austria); Koslowski, Tim A., E-mail: koslowski@nucleares.unam.mx [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apartado Postal 70-543, México D.F. 04510 (Mexico); Nelson, Mike I., E-mail: mike@aims.edu.gh [African Institute for Mathematical Sciences, P.O Box LG 197, Legon, Accra (Ghana)
2017-06-10
Full general relativity is almost certainly ‘chaotic’. We argue that this entails a notion of non-integrability: a generic general relativistic model, at least when coupled to cosmologically interesting matter, likely possesses neither differentiable Dirac observables nor a reduced phase space. It follows that the standard notion of observable has to be extended to include non-differentiable or even discontinuous generalized observables. These cannot carry Poisson-algebraic structures and do not admit a standard quantization; one thus faces a quantum representation problem of gravitational observables. This has deep consequences for a quantum theory of gravity, which we investigate in a simple model for a system with Hamiltonian constraint that fails to be completely integrable. We show that basing the quantization on standard topology precludes a semiclassical limit and can even prohibit any solutions to the quantum constraints. Our proposed solution to this problem is to refine topology such that a complete set of Dirac observables becomes continuous. In the toy model, it turns out that a refinement to a polymer-type topology, as e.g. used in loop gravity, is sufficient. Basing quantization of the toy model on this finer topology, we find a complete set of quantum Dirac observables and a suitable semiclassical limit. This strategy is applicable to realistic candidate theories of quantum gravity and thereby suggests a solution to a long-standing problem which implies ramifications for the very concept of quantization. Our work reveals a qualitatively novel facet of chaos in physics and opens up a new avenue of research on chaos in gravity which hints at deep insights into the structure of quantum gravity.
Polar gravity fields from GOCE and airborne gravity
DEFF Research Database (Denmark)
Forsberg, René; Olesen, Arne Vestergaard; Yidiz, Hasan
2011-01-01
Airborne gravity, together with high-quality surface data and ocean satellite altimetric gravity, may supplement GOCE to make consistent, accurate high resolution global gravity field models. In the polar regions, the special challenge of the GOCE polar gap make the error characteristics...... of combination models especially sensitive to the correct merging of satellite and surface data. We outline comparisons of GOCE to recent airborne gravity surveys in both the Arctic and the Antarctic. The comparison is done to new 8-month GOCE solutions, as well as to a collocation prediction from GOCE gradients...... in Antarctica. It is shown how the enhanced gravity field solutions improve the determination of ocean dynamic topography in both the Arctic and in across the Drake Passage. For the interior of Antarctica, major airborne gravity programs are currently being carried out, and there is an urgent need...
Energy Technology Data Exchange (ETDEWEB)
Bejarano, Cecilia; Guzman, Maria Jose [Instituto de Astronomia y Fisica del Espacio (IAFE, CONICET-UBA), Buenos Aires (Argentina); Ferraro, Rafael [Instituto de Astronomia y Fisica del Espacio (IAFE, CONICET-UBA), Buenos Aires (Argentina); Universidad de Buenos Aires, Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Buenos Aires (Argentina)
2015-02-01
Null tetrads are shown to be a valuable tool in teleparallel theories of modified gravity. We use them to prove that Kerr geometry remains a solution for a wide family of f(T) theories of gravity. (orig.)
A general solution to the material performance index for bending strength design
International Nuclear Information System (INIS)
Burgess, S.C.; Pasini, D.; Smith, D.J.; Alemzadeh, K.
2006-01-01
This paper presents a general solution to the material performance index for the bending strength design of beams. In general, the performance index for strength design is ρ f q /ρ where σ f is the material strength, ρ is the material density and q is a function of the direction of scaling. Previous studies have only solved q for three particular cases: proportional scaling of width and height (q=2/3), constrained height (q=1) and constrained width (q=1/2). This paper presents a general solution to the exponent q for any arbitrary direction of scaling. The index is used to produce performance maps that rank relative material performance for particular design cases. The performance index and the performance maps are applied to a design case study
Lötstedt, Erik; Jentschura, Ulrich D
2009-02-01
In the relativistic and the nonrelativistic theoretical treatment of moderate and high-power laser-matter interaction, the generalized Bessel function occurs naturally when a Schrödinger-Volkov and Dirac-Volkov solution is expanded into plane waves. For the evaluation of cross sections of quantum electrodynamic processes in a linearly polarized laser field, it is often necessary to evaluate large arrays of generalized Bessel functions, of arbitrary index but with fixed arguments. We show that the generalized Bessel function can be evaluated, in a numerically stable way, by utilizing a recurrence relation and a normalization condition only, without having to compute any initial value. We demonstrate the utility of the method by illustrating the quantum-classical correspondence of the Dirac-Volkov solutions via numerical calculations.
Modified teleparallel gravity: Inflation without an inflaton
International Nuclear Information System (INIS)
Ferraro, Rafael; Fiorini, Franco
2007-01-01
The Born-Infeld strategy to smooth theories having divergent solutions is applied to the teleparallel equivalent of general relativity. Differing from other theories of modified gravity, modified teleparallelism leads to second order equations, since the teleparallel Lagrangian only contains first derivatives of the vierbein. We show that the Born-Infeld-modified teleparallelism solves the particle horizon problem in a spatially flat Friedmann-Robertson-Walker (FRW) universe by providing an initial exponential expansion without resorting to an inflaton field
Chen, Po-Chia; Chuang, Mo-Hsiung; Tan, Yih-Chi
2014-05-01
In recent years the urban and industrial developments near the coastal area are rapid and therefore the associated population grows dramatically. More and more water demand for human activities, agriculture irrigation, and aquaculture relies on heavy pumping in coastal area. The decline of groundwater table may result in the problems of seawater intrusion and/or land subsidence. Since the 1950s, numerous studies focused on the effect of tidal fluctuation on the groundwater flow in the coastal area. Many studies concentrated on the developments of one-dimensional (1D) and two-dimensional (2D) analytical solutions describing the tide-induced head fluctuations. For example, Jacob (1950) derived an analytical solution of 1D groundwater flow in a confined aquifer with a boundary condition subject to sinusoidal oscillation. Jiao and Tang (1999) derived a 1D analytical solution of a leaky confined aquifer by considered a constant groundwater head in the overlying unconfined aquifer. Jeng et al. (2002) studied the tidal propagation in a coupled unconfined and confined costal aquifer system. Sun (1997) presented a 2D solution for groundwater response to tidal loading in an estuary. Tang and Jiao (2001) derived a 2D analytical solution in a leaky confined aquifer system near open tidal water. This study aims at developing a general analytical solution describing the head fluctuations in a 2D estuarine aquifer system consisted of an unconfined aquifer, a confined aquifer, and an aquitard between them. Both the confined and unconfined aquifers are considered to be anisotropic. The predicted head fluctuations from this solution will compare with the simulation results from the MODFLOW program. In addition, the solutions mentioned above will be shown to be special cases of the present solution. Some hypothetical cases regarding the head fluctuation in costal aquifers will be made to investigate the dynamic effects of water table fluctuation, hydrogeological conditions, and
Generalized Langevin Theory Of The Brownian Motion And The Dynamics Of Polymers In Solution
International Nuclear Information System (INIS)
Tothova, J.; Lisy, V.
2015-01-01
The review deals with a generalization of the Rouse and Zimm bead-spring models of the dynamics of flexible polymers in dilute solutions. As distinct from these popular theories, the memory in the polymer motion is taken into account. The memory naturally arises as a consequence of the fluid and bead inertia within the linearized Navier-Stokes hydrodynamics. We begin with a generalization of the classical theory of the Brownian motion, which forms the basis of any theory of the polymer dynamics. The random force driving the Brownian particles is not the white one as in the Langevin theory, but “colored”, i.e., statistically correlated in time, and the friction force on the particles depends on the history of their motion. An efficient method of solving the resulting generalized Langevin equations is presented and applied to the solution of the equations of motion of polymer beads. The memory effects lead to several peculiarities in the time correlation functions used to describe the dynamics of polymer chains. So, the mean square displacement of the polymer coils contains algebraic long-time tails and at short times it is ballistic. It is shown how these features reveal in the experimentally observable quantities, such as the dynamic structure factors of the scattering or the viscosity of polymer solutions. A phenomenological theory is also presented that describes the dependence of these quantities on the polymer concentration in solution. (author)
General-purpose chemical analyzer for online analyses of radioactive solutions
International Nuclear Information System (INIS)
Spencer, W.A.; Kronberg, J.W.
1984-01-01
The Savannah River Laboratory is developing an automated analyzer to perform analytical measurements on radioactive solutions online in a hostile environment. This ''General Purpose Chemical Analyzer'' (GPCA) samples a process stream, adds reagents, measures solution absorbances or electrode potentials, and automatically calculates the results. The use of modular components, under microprocessor control, permits a single analyzer design to carry out many types of analyses. This paper discusses the more important design criteria for the GPCA, and describes the equipment being tested in a prototype unit
Travelling wave solutions in a class of generalized Korteweg-de Vries equation
International Nuclear Information System (INIS)
Shen Jianwei; Xu Wei
2007-01-01
In this paper, we consider a new generalization of KdV equation u t = u x u l-2 + α[2u xxx u p + 4pu p-1 u x u xx + p(p - 1)u p-2 (u x ) 3 ] and investigate its bifurcation of travelling wave solutions. From the above analysis, we know that there exists compacton and cusp waves in the system. We explain the reason that these non-smooth travelling wave solution arise by using the bifurcation theory
Scalar fields and higher-derivative gravity in brane worlds
International Nuclear Information System (INIS)
Pichler, S.
2004-01-01
We consider the brane world picture in the context of higher-derivative theories of gravity and tackle the problematic issues fine-tuning and brane-embedding. First, we give an overview of extra-dimensional physics, from the Kaluza-Klein picture up to modern brane worlds with large extra dimensions. We describe the different models and their physical impact on future experiments. We work within the framework of Randall-Sundrum models in which the brane is a gravitating object, which warps the background metric. We add scalar fields to the original model and find new and self-consistent solutions for quadratic potentials of the fields. This gives us the tools to investigate higher-derivative gravity theories in brane world models. Specifically, we take gravitational Lagrangians that depend on an arbitrary function of the Ricci scalar only, so-called f(R)-gravity. We make use of the conformal equivalence between f(R)-gravity and Einstein-Hilbert gravity with an auxiliary scalar field. We find that the solutions in the higher-derivative gravity framework behave very differently from the original Randall-Sundrum model: the metric functions do not have the typical kink across the brane. Furthermore, we present solutions that do not rely on a cosmological constant in the bulk and so avoid the fine-tuning problem. We address the issue of brane-embedding, which is important in perturbative analyses. We consider the embedding of codimension one hypersurfaces in general and derive a new equation of motion with which the choice for the embedding has to comply. In particular, this allows for a consistent consideration of brane world perturbations in the case of higher-derivative gravity. We use the newly found background solutions for quadratic potentials and find that gravity is still effectively localized on the brane, i.e that the Newtonian limit holds
On weak solutions to the 2D Savage-Hutter model of the motion of a gravity driven avalanche flow
Czech Academy of Sciences Publication Activity Database
Feireisl, Eduard; Gwiazda, P.; Swierczewska-Gwiazda, A.
2016-01-01
Roč. 41, č. 5 (2016), s. 759-773 ISSN 0360-5302 EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : avalanche flow * convex integration * Savage-Hutter system Subject RIV: BA - General Mathematics Impact factor: 1.608, year: 2016 http://www.tandfonline.com/doi/full/10.1080/03605302.2015.1127968
Violation of causality in f( T) gravity
Otalora, G.; Rebouças, M. J.
2017-11-01
In the standard formulation, the f( T) field equations are not invariant under local Lorentz transformations, and thus the theory does not inherit the causal structure of special relativity. Actually, even locally violation of causality can occur in this formulation of f( T) gravity. A locally Lorentz covariant f( T) gravity theory has been devised recently, and this local causality problem seems to have been overcome. The non-locality question, however, is left open. If gravitation is to be described by this covariant f( T) gravity theory there are a number of issues that ought to be examined in its context, including the question as to whether its field equations allow homogeneous Gödel-type solutions, which necessarily leads to violation of causality on non-local scale. Here, to look into the potentialities and difficulties of the covariant f( T) theories, we examine whether they admit Gödel-type solutions. We take a combination of a perfect fluid with electromagnetic plus a scalar field as source, and determine a general Gödel-type solution, which contains special solutions in which the essential parameter of Gödel-type geometries, m^2, defines any class of homogeneous Gödel-type geometries. We show that solutions of the trigonometric and linear classes (m^2 electromagnetic field matter component. We extended to the context of covariant f( T) gravity a theorem which ensures that any perfect-fluid homogeneous Gödel-type solution defines the same set of Gödel tetrads h_A^{ μ } up to a Lorentz transformation. We also showed that the single massless scalar field generates Gödel-type solution with no closed time-like curves. Even though the covariant f( T) gravity restores Lorentz covariance of the field equations and the local validity of the causality principle, the bare existence of the Gödel-type solutions makes apparent that the covariant formulation of f( T) gravity does not preclude non-local violation of causality in the form of closed time
Generalized conditional symmetries and related solutions of the Grad-Shafranov equation
Energy Technology Data Exchange (ETDEWEB)
Cimpoiasu, Rodica, E-mail: rodicimp@yahoo.com [University of Craiova, 13 A.I.Cuza, 200585 Craiova (Romania)
2014-04-15
The generalized conditional symmetry (GCS) method is applied to a specific case of the Grad–Shafranov (GS) equation, in cylindrical geometry assuming the existence of an axial symmetry. We investigate the conditions that yield the GS equation admitting a special class of second-order GCSs. The determining system for the unknown arbitrary functions is solved in several special cases and new exact solutions, including solitary waves, different in form and structure from the ones obtained using other nonclassical symmetry methods, are pointed out. Several plots of the level sets or flux surfaces of the new solutions as well as surfaces with vanishing flow are displayed. The obtained solutions can be useful for studying plasma equilibrium, transport phenomena, and magnetohydrodynamic stability.
O, Hyong-Chol; Jo, Jong-Jun; Kim, Ji-Sok
2016-02-01
We provide representations of solutions to terminal value problems of inhomogeneous Black-Scholes equations and study such general properties as min-max estimates, gradient estimates, monotonicity and convexity of the solutions with respect to the stock price variable, which are important for financial security pricing. In particular, we focus on finding representation of the gradient (with respect to the stock price variable) of solutions to the terminal value problems with discontinuous terminal payoffs or inhomogeneous terms. Such terminal value problems are often encountered in pricing problems of compound-like options such as Bermudan options or defaultable bonds with discrete default barrier, default intensity and endogenous default recovery. Our results can be used in pricing real defaultable bonds under consideration of existence of discrete coupons or taxes on coupons.
Junction conditions in extended Teleparallel gravities
Energy Technology Data Exchange (ETDEWEB)
De la Cruz-Dombriz, Álvaro [Departamento de Física Teórica I, Ciudad Universitaria, Universidad Complutense de Madrid, E-28040 Madrid (Spain); Dunsby, Peter K.S.; Sáez-Gómez, Diego, E-mail: dombriz@fis.ucm.es, E-mail: peter.dunsby@uct.ac.za, E-mail: diego.saezgomez@uct.ac.za [Astrophysics, Cosmology and Gravity Centre (ACGC), Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7701, Cape Town (South Africa)
2014-12-01
In the context of extended Teleparallel gravity theories, we address the issue of junction conditions required to guarantee the correct matching of different regions of spacetime. In the absence of shells/branes, these conditions turn out to be more restrictive than their counterparts in General Relativity as in other extended theories of gravity. In fact, the general junction conditions on the matching hypersurfaces depend on the underlying theory and a new condition on the induced tetrads in order to avoid delta-like distributions in the field equations. This result imposes strict consequences on the viability of standard solutions such as the Einstein-Straus-like construction. We find that the continuity of the scalar torsion is required in order to recover the usual General Relativity results.
Directory of Open Access Journals (Sweden)
Sukjung Hwang
2015-11-01
Full Text Available Here we generalize quasilinear parabolic p-Laplacian type equations to obtain the prototype equation $$ u_t - \\hbox{div} \\Big(\\frac{g(|Du|}{|Du|} Du\\Big = 0, $$ where g is a nonnegative, increasing, and continuous function trapped in between two power functions $|Du|^{g_0 -1}$ and $|Du|^{g_1 -1}$ with $1
Numerical solution of shock and ramp compression for general material properties
Energy Technology Data Exchange (ETDEWEB)
Swift, D C
2009-01-28
A general formulation was developed to represent material models for applications in dynamic loading. Numerical methods were devised to calculate response to shock and ramp compression, and ramp decompression, generalizing previous solutions for scalar equations of state. The numerical methods were found to be flexible and robust, and matched analytic results to a high accuracy. The basic ramp and shock solution methods were coupled to solve for composite deformation paths, such as shock-induced impacts, and shock interactions with a planar interface between different materials. These calculations capture much of the physics of typical material dynamics experiments, without requiring spatially-resolving simulations. Example calculations were made of loading histories in metals, illustrating the effects of plastic work on the temperatures induced in quasi-isentropic and shock-release experiments, and the effect of a phase transition.
Nodal soliton solutions for generalized quasilinear Schrödinger equations
Energy Technology Data Exchange (ETDEWEB)
Deng, Yinbin, E-mail: ybdeng@mail.ccnu.edu.cn; Peng, Shuangjie, E-mail: sjpeng@mail.ccnu.edu.cn [School of Mathematics and Statistics, Huazhong Normal University, Wuhan 430079 (China); Wang, Jixiu, E-mail: wangjixiu127@aliyun.com [School of Mathematics and Computer Science, Hubei University of Arts and Science, Xiangyang 441053 (China)
2014-05-15
This paper is concerned with constructing nodal radial solutions for generalized quasilinear Schrödinger equations in R{sup N} which arise from plasma physics, fluid mechanics, as well as high-power ultashort laser in matter. For any given integer k ⩾ 0, by using a change of variables and minimization argument, we obtain a sign-changing minimizer with k nodes of a minimization problem.
General Solutions of Two Quadratic Functional Equations of Pexider Type on Orthogonal Vectors
Fochi, Margherita
2012-01-01
Based on the studies on the Hyers-Ulam stability and the orthogonal stability of some Pexider-quadratic functional equations, in this paper we find the general solutions of two quadratic functional equations of Pexider type. Both equations are studied in restricted domains: the first equation is studied on the restricted domain of the orthogonal vectors in the sense of Rätz, and the second equation is considered on the orthogonal vectors in the inner product spaces with the usual orthogonality.
Solution of the General Helmholtz Equation Starting from Laplace’s Equation
2002-11-01
Salazar Palma Grupo de Microondas y Radar, Dpto. Senales, Sistemas y Radiocomunicaciones ETSI Telecomunicacion, Universidad Politecnica de Madrid Ciudad...updated at each step of the iteration. excitation. A new boundary integral method for Further, the BIM formulations are in most cases solving the...Hankel functions as it is commonly done in BIM element solutions of the same problem. Application of [10]. Besides its generality to solve Laplace’s
Wang, Yu-Zhu; Wei, Changhua
2018-04-01
In this paper, we investigate the initial value problem for the generalized double dispersion equation in R^n. Weighted decay estimate and asymptotic profile of global solutions are established for n≥3 . The global existence result was already proved by Kawashima and the first author in Kawashima and Wang (Anal Appl 13:233-254, 2015). Here, we show that the nonlinear term plays an important role in this asymptotic profile.
A General Construction of Linear Differential Equations with Solutions of Prescribed Properties
Czech Academy of Sciences Publication Activity Database
Neuman, František
2004-01-01
Roč. 17, č. 1 (2004), s. 71-76 ISSN 0893-9659 R&D Projects: GA AV ČR IAA1019902; GA ČR GA201/99/0295 Institutional research plan: CEZ:AV0Z1019905 Keywords : construction of linear differential equations * prescribed qualitative properties of solutions Subject RIV: BA - General Mathematics Impact factor: 0.414, year: 2004
Introduction to general relativity
Parthasarthy, R
2016-01-01
INTRODUCTION TO GENERAL RELATIVITY begins with a description of the geometry of curved space, explaining geodesics, parallel transport, covariant differentiation, geodesic deviation and spacetime symmetry by killing vectors. It then introduces Einstein's theory of gravitation followed by Schwarzschild solution with its relevance to Positive Mass theorem. The three tests for Einstein's gravity are explained. Other exact solutions such as Vaidya, Kerr and Reisner - Nordstrom metric are included. In the Chapter on cosmological solutions, a detailed description of Godel metric is provided. It then introduces five dimensional spacetime of Kaluza showing the unification of gravity with electromagnetism. This is extended to include non-Abelian gauge theory by invoking compact extra dimensions. Explicit expressions in this case for Christoffel connections and ricci tensor are derived and the higher dimensional gravity action is shown to compactification are given.
Geometric flows in Horava-Lifshitz gravity
Bakas, Ioannis; Lust, Dieter; Petropoulos, Marios
2010-01-01
We consider instanton solutions of Euclidean Horava-Lifshitz gravity in four dimensions satisfying the detailed balance condition. They are described by geometric flows in three dimensions driven by certain combinations of the Cotton and Ricci tensors as well as the cosmological-constant term. The deformation curvature terms can have competing behavior leading to a variety of fixed points. The instantons interpolate between any two fixed points, which are vacua of topologically massive gravity with Lambda > 0, and their action is finite. Special emphasis is placed on configurations with SU(2) isometry associated with homogeneous but generally non-isotropic Bianchi IX model geometries. In this case, the combined Ricci-Cotton flow reduces to an autonomous system of ordinary differential equations whose properties are studied in detail for different couplings. The occurrence and stability of isotropic and anisotropic fixed points are investigated analytically and some exact solutions are obtained. The correspond...
Geometric actions for three-dimensional gravity
Barnich, G.; González, H. A.; Salgado-Rebolledo, P.
2018-01-01
The solution space of three-dimensional asymptotically anti-de Sitter or flat Einstein gravity is given by the coadjoint representation of two copies of the Virasoro group in the former and the centrally extended BMS3 group in the latter case. Dynamical actions that control these solution spaces are usually constructed by starting from the Chern–Simons formulation and imposing all boundary conditions. In this note, an alternative route is followed. We study in detail how to derive these actions from a group-theoretical viewpoint by constructing geometric actions for each of the coadjoint orbits, including the appropriate Hamiltonians. We briefly sketch relevant generalizations and potential applications beyond three-dimensional gravity.
Zhao, Qile; Guo, Jing; Hu, Zhigang; Shi, Chuang; Liu, Jingnan; Cai, Hua; Liu, Xianglin
2011-05-01
The GRACE (Gravity Recovery And Climate Experiment) monthly gravity models have been independently produced and published by several research institutions, such as Center for Space Research (CSR), GeoForschungsZentrum (GFZ), Jet Propulsion Laboratory (JPL), Centre National d’Etudes Spatiales (CNES) and Delft Institute of Earth Observation and Space Systems (DEOS). According to their processing standards, above institutions use the traditional variational approach except that the DEOS exploits the acceleration approach. The background force models employed are rather similar. The produced gravity field models generally agree with one another in the spatial pattern. However, there are some discrepancies in the gravity signal amplitude between solutions produced by different institutions. In particular, 10%-30% signal amplitude differences in some river basins can be observed. In this paper, we implemented a variant of the traditional variational approach and computed two sets of monthly gravity field solutions using the data from January 2005 to December 2006. The input data are K-band range-rates (KBRR) and kinematic orbits of GRACE satellites. The main difference in the production of our two types of models is how to deal with nuisance parameters. This type of parameters is necessary to absorb low-frequency errors in the data, which are mainly the aliasing and instrument errors. One way is to remove the nuisance parameters before estimating the geopotential coefficients, called NPARB approach in the paper. The other way is to estimate the nuisance parameters and geopotential coefficients simultaneously, called NPESS approach. These two types of solutions mainly differ in geopotential coefficients from degree 2 to 5. This can be explained by the fact that the nuisance parameters and the gravity field coefficients are highly correlated, particularly at low degrees. We compare these solutions with the official and published ones by means of spectral analysis. It is
International Nuclear Information System (INIS)
Deser, S.
1987-01-01
We obtain the Einstein action plus quadratic curvature corrections generated by closed bosonic, heterotic and supersymmetric strings by matching the four-graviton amplitude (to first order in the slope parameter and fourth power of momenta) with an effective local gravitational action. The resulting corrections are first shown to be of the Gauss-Bonnet form. It is then noted that, by the very nature of the slope expansion, the field-redefinition theorem applies. Consequently, only the curvature-squared term is determined, while squares of its contractions are explicitly seen not to contribute. This latter property has a generalization to all orders which implies that the effective gravitational action is unavoidably ghost-free. The properties of solutions to these corrected theories are then examined. First neglecting dilatons, we find the explicit 'Schwarzschild' metrics. Both asymptotically flat and de Sitter solutions are present. The latter are however shown to be unstable. The former have horizons and singularities which are respectively smaller and less violent than in Einstein gravity; the correct sign of the slope parameter also ensures absence of naked singularities. When dilatons are included, the cosmological vacua are gratifyingly excluded. (orig.)
Dipole magnetic field of neutron stars in f(R) gravity
Bakirova, Elizat; Folomeev, Vladimir
2016-10-01
The structure of an interior dipole magnetic field of neutron stars in f( R) gravity is considered. For this purpose, the perturbative approaches are used when both the deviations from general relativity and the deformations of spherically symmetric configurations associated with the presence of the magnetic field are assumed to be small. Solutions are constructed which describe relativistic, spherically symmetric configurations consisting of a gravitating magnetized perfect fluid modeled by a realistic equation of state. Comparing configurations from general relativity and modified gravity, we reveal possible differences in the structure of the magnetic field which occur in considering neutron stars in modified gravity.
Rajabi, Fateme; Nozari, Kourosh
2017-10-01
We extend the idea of unimodular gravity to the modified f (R ,T ) theories. A new class of cosmological solutions, that the unimodular constraint on the metric imposes on the f (R ,T ) theories, is studied. This extension is done in both Jordan and Einstein frames. We show that while the Lagrange multiplier (that imposes the unimodular constraint on the action) depends on the cosmic time in Jordan frame and therefore, can act as an evolving scalar field in the universe history, in the Einstein frame it acts as a cosmological constant. Then a general reconstruction method is used to realize an explicit form of the unimodular f (R ,T ) corresponding to a given cosmological solution. By adopting a specific form of f (R ,T ), the issue of cosmological inflation is studied in this setup. To see the observational viability of this model, a numerical analysis on the model parameter space is done in the background of Planck2015 observational data.
Carroll versus Galilei gravity
Energy Technology Data Exchange (ETDEWEB)
Bergshoeff, Eric [Centre for Theoretical Physics, University of Groningen,Nijenborgh 4, 9747 AG Groningen (Netherlands); Gomis, Joaquim [Departament de Física Cuàntica i Astrofísica and Institut de Ciències del Cosmos,Universitat de Barcelona,Martí i Franquès 1, E-08028 Barcelona (Spain); Rollier, Blaise [Centre for Theoretical Physics, University of Groningen,Nijenborgh 4, 9747 AG Groningen (Netherlands); Rosseel, Jan [Faculty of Physics, University of Vienna,Boltzmanngasse 5, A-1090 Vienna (Austria); Veldhuis, Tonnis ter [Centre for Theoretical Physics, University of Groningen,Nijenborgh 4, 9747 AG Groningen (Netherlands)
2017-03-30
We consider two distinct limits of General Relativity that in contrast to the standard non-relativistic limit can be taken at the level of the Einstein-Hilbert action instead of the equations of motion. One is a non-relativistic limit and leads to a so-called Galilei gravity theory, the other is an ultra-relativistic limit yielding a so-called Carroll gravity theory. We present both gravity theories in a first-order formalism and show that in both cases the equations of motion (i) lead to constraints on the geometry and (ii) are not sufficient to solve for all of the components of the connection fields in terms of the other fields. Using a second-order formalism we show that these independent components serve as Lagrange multipliers for the geometric constraints we found earlier. We point out a few noteworthy differences between Carroll and Galilei gravity and give some examples of matter couplings.
Cosmological Chaplygin gas as modified gravity
Elmardi, Maye; Abebe, Amare
2017-10-01
In the scramble for the understanding of the nature of dark matter and dark energy, it has recently been suggested that the change of behavior of the missing energy density might be regulated by the change in the equation of state of the background uid. The Chaplygin Gas (CG) model in cosmology is one of the most profound candidates for this suggestion. This work aims to bring to light a geometric interpretation of the model by re-writing the difierent toy models in terms of exact f(R) gravity solutions that are generally quadratic in the Ricci scalar with appropriate ΛCDM limiting solutions.
Emergent Abelian Gauge Fields from Noncommutative Gravity
Directory of Open Access Journals (Sweden)
Allen Stern
2010-02-01
Full Text Available We construct exact solutions to noncommutative gravity following the formulation of Chamseddine and show that they are in general accompanied by Abelian gauge fields which are first order in the noncommutative scale. This provides a mechanism for generating cosmological electromagnetic fields in an expanding space-time background, and also leads to multipole-like fields surrounding black holes. Exact solutions to noncommutative Einstein-Maxwell theory can give rise to first order corrections to the metric tensor, as well as to the electromagnetic fields. This leads to first order shifts in the horizons of charged black holes.
Bergshoeff, Eric A.; Hohm, Olaf; Rosseel, Jan; Townsend, Paul K.
2011-01-01
The physical modes of a recently proposed D-dimensional "critical gravity'', linearized about its anti-de Sitter vacuum, are investigated. All "log mode'' solutions, which we categorize as "spin-2'' or "Proca'', arise as limits of the massive spin-2 modes of the noncritical theory. The linearized
International Nuclear Information System (INIS)
Gregory, Ruth
2007-01-01
only for starting researchers in this area, but also any researcher interested in the details of computing more general brane propagators. However, the book must be used with some caution as a guide to Randall-Sundrum theory, as it has a rather unusual perspective on the subject, and does not set it in a broader context. For example, it is well known in brane cosmology that the most general bulk solution contains a black hole, which is not discussed, the book preferring to immediately focus on the case of a pure AdS bulk. There is also no real discussion of how Randall-Sundrum links into string theory or phenomenology. One other problem with the book is that it does not reference the literature appropriately, I woould have expected a more comprehensive and accurate set of references accompanying a book which appears to be aimed at starting researchers in a subject. The later stages of the book, in which the author deals in detail with the normalization of the graviton propagator, are rather involved and technical. A student would find this material rather heavy-going; however, the fine points of the discussion of Green's functions will be of use to those dealing with perturbations around more general branes. In summary, the book is a tightly focused discussion of gravity in maximally symmetric Randall-Sundrum braneworlds. It will be useful as a companion text to starting researchers in the area, and other researchers should also find the more technical discussions of some use. However, one should note that the perspective of the book is somewhat narrow. (book review)
Energy Technology Data Exchange (ETDEWEB)
Gregory, Ruth [Department of Mathematical Sciences Science Laboratory, South Road, Durham DH1 3LE (United Kingdom)
2007-06-18
only for starting researchers in this area, but also any researcher interested in the details of computing more general brane propagators. However, the book must be used with some caution as a guide to Randall-Sundrum theory, as it has a rather unusual perspective on the subject, and does not set it in a broader context. For example, it is well known in brane cosmology that the most general bulk solution contains a black hole, which is not discussed, the book preferring to immediately focus on the case of a pure AdS bulk. There is also no real discussion of how Randall-Sundrum links into string theory or phenomenology. One other problem with the book is that it does not reference the literature appropriately, I woould have expected a more comprehensive and accurate set of references accompanying a book which appears to be aimed at starting researchers in a subject. The later stages of the book, in which the author deals in detail with the normalization of the graviton propagator, are rather involved and technical. A student would find this material rather heavy-going; however, the fine points of the discussion of Green's functions will be of use to those dealing with perturbations around more general branes. In summary, the book is a tightly focused discussion of gravity in maximally symmetric Randall-Sundrum braneworlds. It will be useful as a companion text to starting researchers in the area, and other researchers should also find the more technical discussions of some use. However, one should note that the perspective of the book is somewhat narrow. (book review)
Gao, Ning; Zhou, Wei; Jiang, Xiaocheng; Hong, Guosong; Fu, Tian-Ming; Lieber, Charles M
2015-03-11
Transistor-based nanoelectronic sensors are capable of label-free real-time chemical and biological detection with high sensitivity and spatial resolution, although the short Debye screening length in high ionic strength solutions has made difficult applications relevant to physiological conditions. Here, we describe a new and general strategy to overcome this challenge for field-effect transistor (FET) sensors that involves incorporating a porous and biomolecule permeable polymer layer on the FET sensor. This polymer layer increases the effective screening length in the region immediately adjacent to the device surface and thereby enables detection of biomolecules in high ionic strength solutions in real-time. Studies of silicon nanowire field-effect transistors with additional polyethylene glycol (PEG) modification show that prostate specific antigen (PSA) can be readily detected in solutions with phosphate buffer (PB) concentrations as high as 150 mM, while similar devices without PEG modification only exhibit detectable signals for concentrations ≤10 mM. Concentration-dependent measurements exhibited real-time detection of PSA with a sensitivity of at least 10 nM in 100 mM PB with linear response up to the highest (1000 nM) PSA concentrations tested. The current work represents an important step toward general application of transistor-based nanoelectronic detectors for biochemical sensing in physiological environments and is expected to open up exciting opportunities for in vitro and in vivo biological sensing relevant to basic biology research through medicine.
International Nuclear Information System (INIS)
Rosenfeld, M.; Kwak, D.; Vinokur, M.
1988-01-01
A solution method based on a fractional step approach is developed for obtaining time-dependent solutions of the three-dimensional, incompressible Navier-Stokes equations in generalized coordinate systems. The governing equations are discretized conservatively by finite volumes using a staggered mesh system. The primitive variable formulation uses the volume fluxes across the faces of each computational cell as dependent variables. This procedure, combined with accurate and consistent approximations of geometric parameters, is done to satisfy the discretized mass conservation equation to machine accuracy as well as to gain favorable convergence properties of the Poisson solver. The discretized equations are second-order-accurate in time and space and no smoothing terms are added. An approximate-factorization scheme is implemented in solving the momentum equations. A novel ZEBRA scheme with four-color ordering is devised for the efficient solution of the Poisson equation. Several two and three-dimensional solutions are compared with other numerical and experimental results to validate the present method. 23 references
On generalized Melvin solution for the Lie algebra E{sub 6}
Energy Technology Data Exchange (ETDEWEB)
Bolokhov, S.V. [Peoples' Friendship University of Russia (RUDN University), Moscow (Russian Federation); Ivashchuk, V.D. [VNIIMS, Center for Gravitation and Fundamental Metrology, Moscow (Russian Federation); Peoples' Friendship University of Russia (RUDN University), Moscow (Russian Federation)
2017-10-15
A multidimensional generalization of Melvin's solution for an arbitrary simple Lie algebra G is considered. The gravitational model in D dimensions, D ≥ 4, contains n 2-forms and l ≥ n scalar fields, where n is the rank of G. The solution is governed by a set of n functions H{sub s}(z) obeying n ordinary differential equations with certain boundary conditions imposed. It was conjectured earlier that these functions should be polynomials (the so-called fluxbrane polynomials). The polynomials H{sub s}(z), s = 1,.., 6, for the Lie algebra E{sub 6} are obtained and a corresponding solution for l = n = 6 is presented. The polynomials depend upon integration constants Q{sub s}, s = 1,.., 6. They obey symmetry and duality identities. The latter ones are used in deriving asymptotic relations for solutions at large distances. The power-law asymptotic relations for E{sub 6}-polynomials at large z are governed by the integer-valued matrix ν = A{sup -1}(I + P), where A{sup -1} is the inverse Cartan matrix, I is the identity matrix and P is a permutation matrix, corresponding to a generator of the Z{sub 2}-group of symmetry of the Dynkin diagram. The 2-form fluxes Φ{sup s}, s = 1,.., 6, are calculated. (orig.)
Inverse planning for x-ray rotation therapy: a general solution of the inverse problem
International Nuclear Information System (INIS)
Oelfke, U.; Bortfeld, T.
1999-01-01
Rotation therapy with photons is currently under investigation for the delivery of intensity modulated radiotherapy (IMRT). An analytical approach for inverse treatment planning of this radiotherapy technique is described. The inverse problem for the delivery of arbitrary 2D dose profiles is first formulated and then solved analytically. In contrast to previously applied strategies for solving the inverse problem, it is shown that the most general solution for the fluence profiles consists of two independent solutions of different parity. A first analytical expression for both fluence profiles is derived. The mathematical derivation includes two different strategies, an elementary expansion of fluence and dose into polynomials and a more practical approach in terms of Fourier transforms. The obtained results are discussed in the context of previous work on this problem. (author)
Data collapse, scaling functions, and analytical solutions of generalized growth models.
Cabella, Brenno Caetano Troca; Martinez, Alexandre Souto; Ribeiro, Fabiano
2011-06-01
We consider a nontrivial one-species population dynamics model with finite and infinite carrying capacities. Time-dependent intrinsic and extrinsic growth rates are considered in these models. Through the model per capita growth rate we obtain a heuristic general procedure to generate scaling functions to collapse data into a simple linear behavior even if an extrinsic growth rate is included. With this data collapse, all the models studied become independent from the parameters and initial condition. Analytical solutions are found when time-dependent coefficients are considered. These solutions allow us to perceive nontrivial transitions between species extinction and survival and to calculate the transition's critical exponents. Considering an extrinsic growth rate as a cancer treatment, we show that the relevant quantity depends not only on the intensity of the treatment, but also on when the cancerous cell growth is maximum.
Steady and Unsteady Numerical Solution of Generalized Newtonian Fluids Flow by Runge-Kutta method
Keslerová, R.; Kozel, K.; Prokop, V.
2010-09-01
In this paper the laminar viscous incompressible flow for generalized Newtonian (Newtonian and non-Newtonian) fluids is considered. The governing system of equations is the system of Navier-Stokes equations and the continuity equation. The steady and unsteady numerical solution for this system is computed by finite volume method combined with an artificial compressibility method. For time discretization the explicit multistage Runge-Kutta numerical scheme is considered. Steady state solution is achieved for t→∞ using steady boundary conditions and followed by steady residual behavior. The dual time-stepping method is considered for unsteady computation. The high artificial compressibility coefficient is used in the artificial compressibility method applied in the dual time τ. The steady and unsteady numerical results of Newtonian and non-Newtonian (shear thickening and shear thinning) fluids flow in the branching channel are presented.
A gauge-theoretic approach to gravity.
Krasnov, Kirill
2012-08-08
Einstein's general relativity (GR) is a dynamical theory of the space-time metric. We describe an approach in which GR becomes an SU(2) gauge theory. We start at the linearized level and show how a gauge-theoretic Lagrangian for non-interacting massless spin two particles (gravitons) takes a much more simple and compact form than in the standard metric description. Moreover, in contrast to the GR situation, the gauge theory Lagrangian is convex. We then proceed with a formulation of the full nonlinear theory. The equivalence to the metric-based GR holds only at the level of solutions of the field equations, that is, on-shell. The gauge-theoretic approach also makes it clear that GR is not the only interacting theory of massless spin two particles, in spite of the GR uniqueness theorems available in the metric description. Thus, there is an infinite-parameter class of gravity theories all describing just two propagating polarizations of the graviton. We describe how matter can be coupled to gravity in this formulation and, in particular, how both the gravity and Yang-Mills arise as sectors of a general diffeomorphism-invariant gauge theory. We finish by outlining a possible scenario of the ultraviolet completion of quantum gravity within this approach.
A gauge-theoretic approach to gravity
Krasnov, Kirill
2012-01-01
Einstein's general relativity (GR) is a dynamical theory of the space–time metric. We describe an approach in which GR becomes an SU(2) gauge theory. We start at the linearized level and show how a gauge-theoretic Lagrangian for non-interacting massless spin two particles (gravitons) takes a much more simple and compact form than in the standard metric description. Moreover, in contrast to the GR situation, the gauge theory Lagrangian is convex. We then proceed with a formulation of the full nonlinear theory. The equivalence to the metric-based GR holds only at the level of solutions of the field equations, that is, on-shell. The gauge-theoretic approach also makes it clear that GR is not the only interacting theory of massless spin two particles, in spite of the GR uniqueness theorems available in the metric description. Thus, there is an infinite-parameter class of gravity theories all describing just two propagating polarizations of the graviton. We describe how matter can be coupled to gravity in this formulation and, in particular, how both the gravity and Yang–Mills arise as sectors of a general diffeomorphism-invariant gauge theory. We finish by outlining a possible scenario of the ultraviolet completion of quantum gravity within this approach. PMID:22792040
Directory of Open Access Journals (Sweden)
S. C. Oukouomi Noutchie
2014-01-01
Full Text Available We make use of Laplace transform techniques and the method of characteristics to solve fragmentation equations explicitly. Our result is a breakthrough in the analysis of pure fragmentation equations as this is the first instance where an exact solution is provided for the fragmentation evolution equation with general fragmentation rates. This paper is the key for resolving most of the open problems in fragmentation theory including “shattering” and the sudden appearance of infinitely many particles in some systems with initial finite particles number.
Global weak solutions for a gas liquid model with external forces and general pressure law
Evje, Steinar; Friis, Helmer André
2011-01-01
This is a copy of an article previously published in; SIAM journal on applied mathematics, which has been made available here with permission. Original article; http://dx.doi.org/10.1137/100813336. In this work we show existence of global weak solutions for a two-phase gas-liquid model where the gas phase is represented by a general isothermal pressure law, whereas the liquid is assumed to be incompressible. To make the model relevant for pipe and well-flow applications we have included ex...
N=1 domain wall solutions of massive type II supergravity as generalized geometries
International Nuclear Information System (INIS)
Louis, J.
2006-05-01
We study N=1 domain wall solutions of type IIB supergravity compactified on a Calabi-Yau manifold in the presence of RR and NS electric and magnetic fluxes. We show that the dynamics of the scalar fields along the direction transverse to the domain wall is described by gradient flow equations controlled by a superpotential W. We then provide a geometrical interpretation of the gradient flow equations in terms of the mirror symmetric compactification of type IIA. They correspond to a set of generalized Hitchin flow equations of a manifold with SU(3) x SU(3)structure which is fibered over the direction transverse to the domain wall. (Orig.)
General Solutions of Two Quadratic Functional Equations of Pexider Type on Orthogonal Vectors
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Margherita Fochi
2012-01-01
Full Text Available Based on the studies on the Hyers-Ulam stability and the orthogonal stability of some Pexider-quadratic functional equations, in this paper we find the general solutions of two quadratic functional equations of Pexider type. Both equations are studied in restricted domains: the first equation is studied on the restricted domain of the orthogonal vectors in the sense of Rätz, and the second equation is considered on the orthogonal vectors in the inner product spaces with the usual orthogonality.
Classic tests of General Relativity described by brane-based spherically symmetric solutions
Energy Technology Data Exchange (ETDEWEB)
Cuzinatto, R.R. [Universidade Federal de Alfenas, Instituto de Ciencia e Tecnologia, Pocos de Caldas, MG (Brazil); Pompeia, P.J. [Departamento de Ciencia e Tecnologia Aeroespacial, Instituto de Fomento e Coordenacao Industrial, Sao Jose dos Campos, SP (Brazil); Departamento de Ciencia e Tecnologia Aeroespacial, Instituto Tecnologico de Aeronautica, Sao Jose dos Campos, SP (Brazil); De Montigny, M. [University of Alberta, Theoretical Physics Institute, Edmonton, AB (Canada); University of Alberta, Campus Saint-Jean, Edmonton, AB (Canada); Khanna, F.C. [University of Alberta, Theoretical Physics Institute, Edmonton, AB (Canada); TRIUMF, Vancouver, BC (Canada); University of Victoria, Department of Physics and Astronomy, PO box 1700, Victoria, BC (Canada); Silva, J.M.H. da [Universidade Estadual Paulista, Departamento de Fisica e Quimica, Guaratingueta, SP (Brazil)
2014-08-15
We discuss a way to obtain information about higher dimensions from observations by studying a brane-based spherically symmetric solution. The three classic tests of General Relativity are analyzed in detail: the perihelion shift of the planet Mercury, the deflection of light by the Sun, and the gravitational redshift of atomic spectral lines. The braneworld version of these tests exhibits an additional parameter b related to the fifth-coordinate. This constant b can be constrained by comparison with observational data for massive and massless particles. (orig.)
Directory of Open Access Journals (Sweden)
Maartens Roy
2004-01-01
Full Text Available The observable universe could be a 1+3-surface (the "brane" embedded in a 1+3+$d$-dimensional spacetime (the "bulk", with Standard Model particles and fields trapped on the brane while gravity is free to access the bulk. At least one of the $d$ extra spatial dimensions could be very large relative to the Planck scale, which lowers the fundamental gravity scale, possibly even down to the electroweak ($sim$TeV level. This revolutionary picture arises in the framework of recent developments in M theory. The 1+10-dimensional M theory encompasses the known 1+9-dimensional superstring theories, and is widely considered to be a promising potential route to quantum gravity. General relativity cannot describe gravity at high enough energies and must be replaced by a quantum gravity theory, picking up significant corrections as the fundamental energy scale is approached. At low energies, gravity is localized at the brane and general relativity is recovered, but at high energies gravity "leaks" into the bulk, behaving in a truly higher-dimensional way. This introduces significant changes to gravitational dynamics and perturbations, with interesting and potentially testable implications for high-energy astrophysics, black holes and cosmology. Brane-world models offer a phenomenological way to test some of the novel predictions and corrections to general relativity that are implied by M theory. This review discusses the geometry, dynamics and perturbations of simple brane-world models for cosmology and astrophysics, mainly focusing on warped 5-dimensional brane-worlds based on the Randall-Sundrum models.
The general Klein-Gordon-Schroedinger system: modulational instability and exact solutions
International Nuclear Information System (INIS)
Tang Xiaoyan; Ding Wei
2008-01-01
The general Klein-Gordon-Schroedinger (gKGS) system is studied where the cubic auto-interactions are introduced in both the nonlinear Schroedinger and the nonlinear Klein-Gordon fields. We first investigate the modulational instability (MI) of the system, and thus derive the general dispersion relation between the frequency and wavenumber of the modulating perturbations, which demonstrates many possibilities for the MI regions. Using the travelling wave reduction, the gKGS system is greatly simplified. Via a simple function expansion method, we obtain some exact travelling wave solutions. Under some special parameter values, some representative wave structures are graphically displayed including the kink, anti-kink, bright, dark, grey and periodic solitons
Brane Solutions of Gravity–Dilaton–Axion Systems
Bergshoeff, E.; Collinucci, A.; Gran, U.; Roest, D.; Vandoren, S.; Lukierski, J.; Sorokin, D.
2005-01-01
We consider general properties of brane solutions of gravity-dilaton-axion systems. We focus on the case of 7-branes and instantons. In both cases we show that besides the standard solutions there are new deformed solutions whose charges take value in any of the three conjugacy classes of SL(2,R).
On flux integrals for generalized Melvin solution related to simple finite-dimensional Lie algebra
International Nuclear Information System (INIS)
Ivashchuk, V.D.
2017-01-01
A generalized Melvin solution for an arbitrary simple finite-dimensional Lie algebra G is considered. The solution contains a metric, n Abelian 2-forms and n scalar fields, where n is the rank of G. It is governed by a set of n moduli functions H s (z) obeying n ordinary differential equations with certain boundary conditions imposed. It was conjectured earlier that these functions should be polynomials - the so-called fluxbrane polynomials. These polynomials depend upon integration constants q s , s = 1,.., n. In the case when the conjecture on the polynomial structure for the Lie algebra G is satisfied, it is proved that 2-form flux integrals Φ s over a proper 2d submanifold are finite and obey the relations q s Φ s = 4πn s h s , where the h s > 0 are certain constants (related to dilatonic coupling vectors) and the n s are powers of the polynomials, which are components of a twice dual Weyl vector in the basis of simple (co-)roots, s = 1,.., n. The main relations of the paper are valid for a solution corresponding to a finite-dimensional semi-simple Lie algebra G. Examples of polynomials and fluxes for the Lie algebras A 1 , A 2 , A 3 , C 2 , G 2 and A 1 + A 1 are presented. (orig.)
M, S. CHU; Yemin, HU; Wenfeng, GUO
2018-03-01
Solovev’s approach of finding equilibrium solutions was found to be extremely useful for generating a library of linear-superposable equilibria for the purpose of shaping studies. This set of solutions was subsequently expanded to include the vacuum solutions of Zheng, Wootton and Solano, resulting in a set of functions {SOLOVEV_ZWS} that were usually used for all toroidally symmetric plasmas, commonly recognized as being able to accommodate any desired plasma shapes (complete-shaping capability). The possibility of extending the Solovev approach to toroidal equilibria with a general plasma flow is examined theoretically. We found that the only meaningful extension is to plasmas with a pure toroidal rotation and with a constant Mach number. We also show that the simplification ansatz made to the current profiles, which was the basis of the Solovev approach, should be applied more systematically to include an internal boundary condition at the magnetic axis; resulting in a modified and more useful set {SOLOVEV_ZWSm}. Explicit expressions of functions in this set are given for equilibria with a quasi-constant current density profile, with a toroidal flow at a constant Mach number and with specific heat capacity 1. The properties of {SOLOVEV_ZWSm} are studied analytically. Numerical examples of achievable equilibria are demonstrated. Although the shaping capability of the set {SOLOVE_ZWSm} is quite extensive, it nevertheless still does not have complete shaping capability, particularly for plasmas with negative curvature points on the plasma boundary such as the doublets or indented bean shaped tokamaks.
General analytical solutions for DC/AC circuit-network analysis
Rubido, Nicolás; Grebogi, Celso; Baptista, Murilo S.
2017-06-01
In this work, we present novel general analytical solutions for the currents that are developed in the edges of network-like circuits when some nodes of the network act as sources/sinks of DC or AC current. We assume that Ohm's law is valid at every edge and that charge at every node is conserved (with the exception of the source/sink nodes). The resistive, capacitive, and/or inductive properties of the lines in the circuit define a complex network structure with given impedances for each edge. Our solution for the currents at each edge is derived in terms of the eigenvalues and eigenvectors of the Laplacian matrix of the network defined from the impedances. This derivation also allows us to compute the equivalent impedance between any two nodes of the circuit and relate it to currents in a closed circuit which has a single voltage generator instead of many input/output source/sink nodes. This simplifies the treatment that could be done via Thévenin's theorem. Contrary to solving Kirchhoff's equations, our derivation allows to easily calculate the redistribution of currents that occurs when the location of sources and sinks changes within the network. Finally, we show that our solutions are identical to the ones found from Circuit Theory nodal analysis.
Lujan, Richard E.
2001-01-01
A mechanical gravity brake that prevents hoisted loads within a shaft from free-falling when a loss of hoisting force occurs. A loss of hoist lifting force may occur in a number of situations, for example if a hoist cable were to break, the brakes were to fail on a winch, or the hoist mechanism itself were to fail. Under normal hoisting conditions, the gravity brake of the invention is subject to an upward lifting force from the hoist and a downward pulling force from a suspended load. If the lifting force should suddenly cease, the loss of differential forces on the gravity brake in free-fall is translated to extend a set of brakes against the walls of the shaft to stop the free fall descent of the gravity brake and attached load.
Bragg reflection in mosaic crystals. I. General solution of the Darwin equations
International Nuclear Information System (INIS)
Sears, V.F.
1996-01-01
The Darwin equations, which describe the multiple Bragg reflection of X-rays or neutrons in a mosaic crystal slab, have previously been solved only for special cases. Here, the complete and exact analytical solution of these equations is obtained for both the Bragg case (reflection geometry) and the Laue case (transmission geometry) with the help of a computer algebra program and it is shown that the resulting general expressions for both the reflectivity R and the transmissivity T can each be expressed in a compact form. It is found, for example, that for a mosaic crystal anomalous absorption occurs only in the Bragg case and not in the Laue case. This is in contrast to the dynamical theory of diffraction, which applies to an ideally perfect crystal, where anomalous absorption (due to the Borrmann effect) is found in both Laue and Bragg cases. With this new general expression for R, the Fankuchen gain is calculated for a crystal of finite thickness, taking correctly into account the effects of both absorption and secondary extinction. General expressions for the optimum crystal thickness are also obtained for both Bragg and Laue cases. In a companion paper, these general results are applied to a detailed numerical calculation of the reflecting properties of various neutron monochromator crystals. (author)
Cusping, transport and variance of solutions to generalized Fokker-Planck equations
Carnaffan, Sean; Kawai, Reiichiro
2017-06-01
We study properties of solutions to generalized Fokker-Planck equations through the lens of the probability density functions of anomalous diffusion processes. In particular, we examine solutions in terms of their cusping, travelling wave behaviours, and variance, within the framework of stochastic representations of generalized Fokker-Planck equations. We give our analysis in the cases of anomalous diffusion driven by the inverses of the stable, tempered stable and gamma subordinators, demonstrating the impact of changing the distribution of waiting times in the underlying anomalous diffusion model. We also analyse the cases where the underlying anomalous diffusion contains a Lévy jump component in the parent process, and when a diffusion process is time changed by an uninverted Lévy subordinator. On the whole, we present a combination of four criteria which serve as a theoretical basis for model selection, statistical inference and predictions for physical experiments on anomalously diffusing systems. We discuss possible applications in physical experiments, including, with reference to specific examples, the potential for model misclassification and how combinations of our four criteria may be used to overcome this issue.
Energy Technology Data Exchange (ETDEWEB)
Tornabene, F.; Viola, E. [Bologna Univ., DISTART-Dept., Faculty of Engineering (Italy)
2008-11-15
The Generalized Differential Quadrature (GDQ) procedure is developed for the free vibration analysis of complete parabolic shells of revolution and parabolic shell panels. The First-order Shear Deformation Theory (FSDT) is used to analyze the above moderately thick structural elements. The treatment is conducted within the theory of linear elasticity, when the material behaviour is assumed to be homogeneous and isotropic. The governing equations of motion, written in terms of internal resultants, are expressed as functions of five kinematic parameters, by using the constitutive and kinematic relationships. The solution is given in terms of generalized displacement components of the points lying on the middle surface of the shell. The discretization of the system by means of the Differential Quadrature (DQ) technique leads to a standard linear eigenvalue problem, where two independent variables are involved. The results are obtained taking the meridional and circumferential co-ordinates into account, without using the Fourier modal expansion methodology. Several examples of parabolic shell elements are presented to illustrate the validity and the accuracy of GDQ method. Numerical solutions are compared with the ones obtained using commercial programs such as Abaqus, Ansys, Femap/Nastran, Straus, Pro/Mechanica. Very good agreement is observed. Furthermore, the convergence rate of natural frequencies is shown to be very fast and the stability of the numerical methodology is very good. The accuracy of the method is sensitive to the number of sampling points used, to their distribution and to the boundary conditions. Different typologies of non-uniform grid point distributions are considered. The effect of the distribution choice of sampling points on the accuracy of GDQ solution is investigated. New numerical results are presented. (authors)
International Nuclear Information System (INIS)
Tornabene, F.; Viola, E.
2008-01-01
The Generalized Differential Quadrature (GDQ) procedure is developed for the free vibration analysis of complete parabolic shells of revolution and parabolic shell panels. The First-order Shear Deformation Theory (FSDT) is used to analyze the above moderately thick structural elements. The treatment is conducted within the theory of linear elasticity, when the material behaviour is assumed to be homogeneous and isotropic. The governing equations of motion, written in terms of internal resultants, are expressed as functions of five kinematic parameters, by using the constitutive and kinematic relationships. The solution is given in terms of generalized displacement components of the points lying on the middle surface of the shell. The discretization of the system by means of the Differential Quadrature (DQ) technique leads to a standard linear eigenvalue problem, where two independent variables are involved. The results are obtained taking the meridional and circumferential co-ordinates into account, without using the Fourier modal expansion methodology. Several examples of parabolic shell elements are presented to illustrate the validity and the accuracy of GDQ method. Numerical solutions are compared with the ones obtained using commercial programs such as Abaqus, Ansys, Femap/Nastran, Straus, Pro/Mechanica. Very good agreement is observed. Furthermore, the convergence rate of natural frequencies is shown to be very fast and the stability of the numerical methodology is very good. The accuracy of the method is sensitive to the number of sampling points used, to their distribution and to the boundary conditions. Different typologies of non-uniform grid point distributions are considered. The effect of the distribution choice of sampling points on the accuracy of GDQ solution is investigated. New numerical results are presented. (authors)
Gravitation. [consideration of black holes in gravity theories
Fennelly, A. J.
1978-01-01
Investigations of several problems of gravitation are discussed. The question of the existence of black holes is considered. While black holes like those in Einstein's theory may not exist in other gravity theories, trapped surfaces implying such black holes certainly do. The theories include those of Brans-Dicke, Lightman-Lee, Rosen, and Yang. A similar two-tensor theory of Yilmaz is investigated and found inconsistent and nonviable. The Newman-Penrose formalism for Riemannian geometries is adapted to general gravity theories and used to implement a search for twisting solutions of the gravity theories for empty and nonempty spaces. The method can be used to find the gravitational fields for all viable gravity theories. The rotating solutions are of particular importance for strong field interpretation of the Stanford/Marshall gyroscope experiment. Inhomogeneous cosmologies are examined in Einstein's theory as generalizations of homogeneous ones by raising the dimension of the invariance groups by one more parameter. The nine Bianchi classifications are extended to Rosen's theory of gravity for homogeneous cosmological models.
Davidson, Matthew G.; Snaith, Ronald; Stalke, Dietmar; Wright, Dominic S.
1993-01-01
A simple way by which equilibrium species can be identified with reasonable certainty, and equilibrium constants and thermodynamic data can be thereby extracted, from variable-concentration cryoscopic molecular mass measurements in solution is reported. The method relies on the assumption that the individual molecular species involved in such solution equilibria exert independent and additive contributions to the depression in freezing point from that of the pure solvent. Given this assumptio...
Directory of Open Access Journals (Sweden)
Marwan Fahs
2018-02-01
Full Text Available The Henry problem (HP continues to play a useful role in theoretical and practical studies related to seawater intrusion (SWI into coastal aquifers. The popularity of this problem is attributed to its simplicity and precision to the existence of semi-analytical (SA solutions. The first SA solution has been developed for a high uniform diffusion coefficient. Several further studies have contributed more realistic solutions with lower diffusion coefficients or velocity-dependent dispersion. All the existing SA solutions are limited to homogenous and isotropic domains. This work attempts to improve the realism of the SA solution of the dispersive HP by extending it to heterogeneous and anisotropic coastal aquifers. The solution is obtained using the Fourier series method. A special hydraulic conductivity–depth model describing stratified heterogeneity is used for mathematical convenience. An efficient technique is developed to solve the flow and transport equations in the spectral space. With this technique, we show that the HP can be solved in the spectral space with the salt concentration as primary unknown. Several examples are generated, and the SA solutions are compared against an in-house finite element code. The results provide high-quality data assessed by quantitative indicators that can be effectively used for code verification in realistic configurations of heterogeneity and anisotropy. The SA solution is used to explain contradictory results stated in the previous works about the effect of anisotropy on the saltwater wedge. It is also used to investigate the combined influence of stratification and anisotropy on relevant metrics characterizing SWI. At a constant gravity number, anisotropy leads to landward migration of the saltwater wedge, more intense saltwater flux, a wider mixing zone and shallower groundwater discharge zone to the sea. The influence of stratified heterogeneity is more pronounced in highly anisotropic aquifers. The
Black holes a laboratory for testing strong gravity
Bambi, Cosimo
2017-01-01
This textbook introduces the current astrophysical observations of black holes, and discusses the leading techniques to study the strong gravity region around these objects with electromagnetic radiation. More importantly, it provides the basic tools for writing an astrophysical code and testing the Kerr paradigm. Astrophysical black holes are an ideal laboratory for testing strong gravity. According to general relativity, the spacetime geometry around these objects should be well described by the Kerr solution. The electromagnetic radiation emitted by the gas in the inner part of the accretion disk can probe the metric of the strong gravity region and test the Kerr black hole hypothesis. With exercises and examples in each chapter, as well as calculations and analytical details in the appendix, the book is especially useful to the beginners or graduate students who are familiar with general relativity while they do not have any background in astronomy or astrophysics.
Shabani, Hamid; Ziaie, Amir Hadi
2017-08-01
In this work, we study the late-time cosmological solutions of f(R,T)=g(R)+h(-T) models assuming that the conservation of the energy-momentum tensor ( EMT) is violated. We perform our analysis through constructing an autonomous dynamical system for the equations of motion. We study the stability properties of solutions via considering linear perturbations about the related equilibrium points. Moreover, we parameterize the Lagrangian by introducing the parameters m( r) and n( s). These parameters which are constructed out of the functions g(R) and h(-T) play the main role in finding the late-time behavior of the solutions. We find that there exist, in general, three classes of solutions; all models with n>0 include a proper transition from a prolonged matter era to a de Sitter solution. Models with -0.51, for at least a root of equation n(s)=s-1, include an unphysical dark energy solution preceding an improper matter era. Finally, for nmotivating for m→ 0+ and -0.024<α <0.02 and therefore could provide a suitable setting for later investigations.
Scalar geons in Born-Infeld gravity
Afonso, V. I.; Olmo, Gonzalo J.; Rubiera-Garcia, D.
2017-08-01
The existence of static, spherically symmetric, self-gravitating scalar field solutions in the context of Born-Infeld gravity is explored. Upon a combination of analytical approximations and numerical methods, the equations for a free scalar field (without a potential term) are solved, verifying that the solutions recover the predictions of General Relativity far from the center but finding important new effects in the central regions. We find two classes of objects depending on the ratio between the Schwarzschild radius and a length scale associated to the Born-Infeld theory: massive solutions have a wormhole structure, with their throat at r≈ 2M, while for the lighter configurations the topology is Euclidean. The total energy density of these solutions exhibits a solitonic profile with a maximum peaked away from the center, and located at the throat whenever a wormhole exists. The geodesic structure and curvature invariants are analyzed for the various configurations considered.
Scalar geons in Born-Infeld gravity
Energy Technology Data Exchange (ETDEWEB)
Afonso, V.I. [Unidade Acadêmica de Física, Universidade Federal de Campina Grande, 58109-970 Campina Grande, PB (Brazil); Olmo, Gonzalo J. [Departamento de Física Teórica and IFIC, Centro Mixto Universidad de Valencia—CSIC, Universidad de Valencia, Burjassot-46100, Valencia (Spain); Rubiera-Garcia, D., E-mail: viafonso@df.ufcg.edu.br, E-mail: gonzalo.olmo@uv.es, E-mail: drgarcia@fc.ul.pt [Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências da Universidade de Lisboa, Edifício C8, Campo Grande, P-1749-016 Lisbon (Portugal)
2017-08-01
The existence of static, spherically symmetric, self-gravitating scalar field solutions in the context of Born-Infeld gravity is explored. Upon a combination of analytical approximations and numerical methods, the equations for a free scalar field (without a potential term) are solved, verifying that the solutions recover the predictions of General Relativity far from the center but finding important new effects in the central regions. We find two classes of objects depending on the ratio between the Schwarzschild radius and a length scale associated to the Born-Infeld theory: massive solutions have a wormhole structure, with their throat at r ≈ 2 M , while for the lighter configurations the topology is Euclidean. The total energy density of these solutions exhibits a solitonic profile with a maximum peaked away from the center, and located at the throat whenever a wormhole exists. The geodesic structure and curvature invariants are analyzed for the various configurations considered.
Non Newtonian gravity creeping flow
International Nuclear Information System (INIS)
Gratton, J.; Mahajan, S.M.; Minotti, F.
1988-11-01
We derive the governing equations for creeping gravity currents of non Newtonian liquids having a power law rheology, using a lubrication approximation. We consider unidirectional and axisymmetric currents. The equations differ from those for Newtonian liquids, being nonlinear in the spatial derivative of the thickness of the current. However, many solutions are closely analogous to those for Newtonian rheology; in particular the spreading relations can also be expressed as power laws of time, with exponents that depend on the rheological index. Similarity solutions for currents whose volume varies as a power of time are obtained. For the spread of a constant volume of liquid, analytic solutions are found. We also derive solutions of the waiting-time type, as well as the ones describing steady flows from a constant source to a sink. General travelling wave solutions are given, and analytic formulae for a simple case are derived. A phase plane formalism, that allows the systematic derivation of self similar solutions, is introduced. The application of the Boltzmann transform is briefly discussed. Present results are closely analogous to those for Newtonian liquids; all the solutions obtained here have their counterparts in Newtonian flows. This happens because the power law rheology, like the Newtonian constitutive relation, involves a single dimensional parameter. Thus one finds similarity solutions whenever the analogous Newtonian problem is self similar. Although the spreading relations are rheology-dependent, in most cases the dependence is rather weak. The present results may be of interest for geophysics since the lithosphere deforms according to an average power law rheology. (author). 17 refs
International Nuclear Information System (INIS)
Banerjee, Rabin; Majhi, Bibhas Ranjan
2010-01-01
Starting from the definition of entropy used in statistical mechanics we show that it is proportional to the gravity action. For a stationary black hole this entropy is expressed as S=E/2T, where T is the Hawking temperature and E is shown to be the Komar energy. This relation is also compatible with the generalized Smarr formula for mass.
Bergmann, P. G.; de Sabbata, V.; Treder, H.-J.
The following topics were dealt with: relativistic heat theories; unified field theory; mixed field theories; de Sitter gauges; black hole entropy; null hypersurface canonical formalism; gauge aspects; superluminal behavior; general relativity; twistor theory; quantum geometry and gravity; strings; Poincaré gauge theory and spacetime quantization.
Stochastic Gravity: Theory and Applications
Directory of Open Access Journals (Sweden)
Hu Bei Lok
2004-01-01
Full Text Available Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin equation, which has in addition sources due to the noise kernel. The noise kernel is the vacuum expectation value of the (operator-valued stress-energy bi-tensor which describes the fluctuations of quantum matter fields in curved spacetimes. In the first part, we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. The axiomatic approach is useful to see the structure of the theory from the framework of semiclassical gravity, showing the link from the mean value of the stress-energy tensor to their correlation functions. The functional approach uses the Feynman-Vernon influence functional and the Schwinger-Keldysh closed-time-path effective action methods which are convenient for computations. It also brings out the open systems concepts and the statistical and stochastic contents of the theory such as dissipation, fluctuations, noise, and decoherence. We then focus on the properties of the stress-energy bi-tensor. We obtain a general expression for the noise kernel of a quantum field defined at two distinct points in an arbitrary curved spacetime as products of covariant derivatives of the quantum field's Green function. In the second part, we describe three applications of stochastic gravity theory. First, we consider metric perturbations in a Minkowski spacetime. We offer an analytical solution of the Einstein-Langevin equation and compute the two-point correlation functions for the linearized Einstein tensor and for the metric perturbations. Second, we discuss structure formation from the stochastic gravity viewpoint, which can go beyond the standard treatment by incorporating the full quantum effect of the inflaton fluctuations. Third, we discuss the backreaction
Directory of Open Access Journals (Sweden)
Mohamed Abdalla Darwish
2014-01-01
Full Text Available We study a generalized fractional quadratic functional-integral equation of Erdélyi-Kober type in the Banach space BC(ℝ+. We show that this equation has at least one asymptotically stable solution.
Darwish, Mohamed Abdalla; Rzepka, Beata
2014-01-01
We study a generalized fractional quadratic functional-integral equation of Erdélyi-Kober type in the Banach space BC(ℝ+). We show that this equation has at least one asymptotically stable solution.
A Generalized Measure for the Optimal Portfolio Selection Problem and its Explicit Solution
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Zinoviy Landsman
2018-03-01
Full Text Available In this paper, we offer a novel class of utility functions applied to optimal portfolio selection. This class incorporates as special cases important measures such as the mean-variance, Sharpe ratio, mean-standard deviation and others. We provide an explicit solution to the problem of optimal portfolio selection based on this class. Furthermore, we show that each measure in this class generally reduces to the efficient frontier that coincides or belongs to the classical mean-variance efficient frontier. In addition, a condition is provided for the existence of the a one-to-one correspondence between the parameter of this class of utility functions and the trade-off parameter λ in the mean-variance utility function. This correspondence essentially provides insight into the choice of this parameter. We illustrate our results by taking a portfolio of stocks from National Association of Securities Dealers Automated Quotation (NASDAQ.
International Nuclear Information System (INIS)
Buchelnikov, Anatoly S.; Evstigneev, Vladyslav P.; Evstigneev, Maxim P.
2013-01-01
Highlights: • Multicomponent non-covalent molecular hetero-association has been modeled. • The equations obtained have an exclusive link to experimental observable. • The matrix form of key equations distinguishes the present model from other known. - Abstract: A general treatment has been developed for the multicomponent one-dimensional non-covalent molecular hetero-assembly in solution using transfer matrix and sequence generating function approaches. The main result is set of equations, which allows one to obtain any thermodynamical quantities of the multicomponent system and, in particular, experimental observable enabling one to get all equilibrium parameters of molecular interaction. The matrix form of presentation of the key equations allows their direct incorporation into matrix-oriented mathematical software, which leads to a two orders of magnitude increase in speed of calculation of as compared to other known approaches
Analytical Solution of Relativistic Few-Body Bound Systems with a Generalized Yukawa Potential
Aslanzadeh, M.; Rajabi, A. A.
2016-03-01
We have investigated in this paper the few-body bound systems in a simple semi-relativistic scheme. For this aim, we introduced a spin independent relativistic description for a few-identical body system by presenting the analytical solution of few-particle Klein-Gordon equation. Performing calculations in D-dimensional configuration on the basis of the hypercentral approach, we reduced the few-body Klein-Gordon equation to a Schrödinger-like form. This equation is solved by using the Nikiforov-Uvarov method, through which the energy equations and eigenfunctions for a few-body bound system are obtained. We used the spin- and isospin-independent generalized Yukawa potential in our calculations, and the dependence of the few-body binding energies on the potential parameters has been investigated.
Multigrid method applied to the solution of an elliptic, generalized eigenvalue problem
Energy Technology Data Exchange (ETDEWEB)
Alchalabi, R.M. [BOC Group, Murray Hill, NJ (United States); Turinsky, P.J. [North Carolina State Univ., Raleigh, NC (United States)
1996-12-31
The work presented in this paper is concerned with the development of an efficient MG algorithm for the solution of an elliptic, generalized eigenvalue problem. The application is specifically applied to the multigroup neutron diffusion equation which is discretized by utilizing the Nodal Expansion Method (NEM). The underlying relaxation method is the Power Method, also known as the (Outer-Inner Method). The inner iterations are completed using Multi-color Line SOR, and the outer iterations are accelerated using Chebyshev Semi-iterative Method. Furthermore, the MG algorithm utilizes the consistent homogenization concept to construct the restriction operator, and a form function as a prolongation operator. The MG algorithm was integrated into the reactor neutronic analysis code NESTLE, and numerical results were obtained from solving production type benchmark problems.
On flux integrals for generalized Melvin solution related to simple finite-dimensional Lie algebra
Energy Technology Data Exchange (ETDEWEB)
Ivashchuk, V.D. [VNIIMS, Center for Gravitation and Fundamental Metrology, Moscow (Russian Federation); Peoples' Friendship University of Russia (RUDN University), Institute of Gravitation and Cosmology, Moscow (Russian Federation)
2017-10-15
A generalized Melvin solution for an arbitrary simple finite-dimensional Lie algebra G is considered. The solution contains a metric, n Abelian 2-forms and n scalar fields, where n is the rank of G. It is governed by a set of n moduli functions H{sub s}(z) obeying n ordinary differential equations with certain boundary conditions imposed. It was conjectured earlier that these functions should be polynomials - the so-called fluxbrane polynomials. These polynomials depend upon integration constants q{sub s}, s = 1,.., n. In the case when the conjecture on the polynomial structure for the Lie algebra G is satisfied, it is proved that 2-form flux integrals Φ{sup s} over a proper 2d submanifold are finite and obey the relations q{sub s} Φ{sup s} = 4πn{sub s}h{sub s}, where the h{sub s} > 0 are certain constants (related to dilatonic coupling vectors) and the n{sub s} are powers of the polynomials, which are components of a twice dual Weyl vector in the basis of simple (co-)roots, s = 1,.., n. The main relations of the paper are valid for a solution corresponding to a finite-dimensional semi-simple Lie algebra G. Examples of polynomials and fluxes for the Lie algebras A{sub 1}, A{sub 2}, A{sub 3}, C{sub 2}, G{sub 2} and A{sub 1} + A{sub 1} are presented. (orig.)
General Quantum Meet-in-the-Middle Search Algorithm Based on Target Solution of Fixed Weight
Fu, Xiang-Qun; Bao, Wan-Su; Wang, Xiang; Shi, Jian-Hong
2016-10-01
Similar to the classical meet-in-the-middle algorithm, the storage and computation complexity are the key factors that decide the efficiency of the quantum meet-in-the-middle algorithm. Aiming at the target vector of fixed weight, based on the quantum meet-in-the-middle algorithm, the algorithm for searching all n-product vectors with the same weight is presented, whose complexity is better than the exhaustive search algorithm. And the algorithm can reduce the storage complexity of the quantum meet-in-the-middle search algorithm. Then based on the algorithm and the knapsack vector of the Chor-Rivest public-key crypto of fixed weight d, we present a general quantum meet-in-the-middle search algorithm based on the target solution of fixed weight, whose computational complexity is \\sumj = 0d {(O(\\sqrt {Cn - k + 1d - j }) + O(C_kj log C_k^j))} with Σd i =0 Ck i memory cost. And the optimal value of k is given. Compared to the quantum meet-in-the-middle search algorithm for knapsack problem and the quantum algorithm for searching a target solution of fixed weight, the computational complexity of the algorithm is lower. And its storage complexity is smaller than the quantum meet-in-the-middle-algorithm. Supported by the National Basic Research Program of China under Grant No. 2013CB338002 and the National Natural Science Foundation of China under Grant No. 61502526
Carter, Gillian; van der Steen, Jenny T; Galway, Karen; Brazil, Kevin
2015-04-16
The general practitioner (GP) is in a pivotal position to initiate and adapt care for their patients living with dementia. This study aimed to elicit GPs' perceptions of the potential barriers and solutions to the provision of good-quality palliative care in dementia in their practices. A postal survey of GPs across Northern Ireland was conducted with open-ended items soliciting for barriers in their practices and possible solutions; 40.6% (138/340) were returned completed. Barriers to palliative care in dementia were perceived to be a dementia knowledge deficit for healthcare staff and the public, a resource shortfall within the GP practice and community, poor team coordination alongside inappropriate dementia care provision, and disagreements from and within families. These findings have significant implications for educators and clinicians as enhanced dementia education and training were highlighted as a strong agenda for GPs with the suggestions of dementia awareness programmes for the public. © The Author(s) 2015 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav.
Directory of Open Access Journals (Sweden)
Milena Netka
2009-01-01
Full Text Available The paper is concerned with weak solutions of a generalized Cauchy problem for a nonlinear system of first order differential functional equations. A theorem on the uniqueness of a solution is proved. Nonlinear estimates of the Perron type are assumed. A method of integral functional inequalities is used.
Directory of Open Access Journals (Sweden)
V. Rukavishnikov
2014-01-01
Full Text Available The existence and uniqueness of the Rv-generalized solution for the first boundary value problem and a second order elliptic equation with coordinated and uncoordinated degeneracy of input data and with strong singularity solution on all boundary of a two-dimensional domain are established.
Born-Infeld inspired modifications of gravity
Beltrán Jiménez, Jose; Heisenberg, Lavinia; Olmo, Gonzalo J.; Rubiera-Garcia, Diego
2018-01-01
General Relativity has shown an outstanding observational success in the scales where it has been directly tested. However, modifications have been intensively explored in the regimes where it seems either incomplete or signals its own limit of validity. In particular, the breakdown of unitarity near the Planck scale strongly suggests that General Relativity needs to be modified at high energies and quantum gravity effects are expected to be important. This is related to the existence of spacetime singularities when the solutions of General Relativity are extrapolated to regimes where curvatures are large. In this sense, Born-Infeld inspired modifications of gravity have shown an extraordinary ability to regularise the gravitational dynamics, leading to non-singular cosmologies and regular black hole spacetimes in a very robust manner and without resorting to quantum gravity effects. This has boosted the interest in these theories in applications to stellar structure, compact objects, inflationary scenarios, cosmological singularities, and black hole and wormhole physics, among others. We review the motivations, various formulations, and main results achieved within these theories, including their observational viability, and provide an overview of current open problems and future research opportunities.
Energy Technology Data Exchange (ETDEWEB)
Houndjo, M.J.S. [Faculte des Sciences et Techniques de Natitingou, Natitingou (Benin); Institut de Mathematiques et de Sciences Physiques, Porto-Novo (Benin)
2017-09-15
In this paper we study a modified version of unimodular general relativity in the context of f(G), G denoting the Gauss-Bonnet invariant. We focus on Bianchi-type I and Friendmann-Robertson-Walker universes and search for unimodular f(G) models according to the de Sitter and power-law solutions. Assuming unimodular f(G) gravity as a perfect fluid and making use of the slow-roll parameters, the inflationary model has been reconstructed in concordance with the Planck observational data. Moreover, we investigate the realization of the bounce and loop quantum cosmological ekpyrotic paradigms. Assuming suitable and appropriate scale factors, unimodular f(G) models able to reproduce superbounce and ekpyrotic scenarios have been reconstructed. (orig.)
International Nuclear Information System (INIS)
Rumpf, H.
1987-01-01
We begin with a naive application of the Parisi-Wu scheme to linearized gravity. This will lead into trouble as one peculiarity of the full theory, the indefiniteness of the Euclidean action, shows up already at this level. After discussing some proposals to overcome this problem, Minkowski space stochastic quantization will be introduced. This will still not result in an acceptable quantum theory of linearized gravity, as the Feynman propagator turns out to be non-causal. This defect will be remedied only after a careful analysis of general covariance in stochastic quantization has been performed. The analysis requires the notion of a metric on the manifold of metrics, and a natural candidate for this is singled out. With this a consistent stochastic quantization of Einstein gravity becomes possible. It is even possible, at least perturbatively, to return to the Euclidean regime. 25 refs. (Author)
Shah, Jayna J; Gaitan, Michael; Geist, Jon
2009-10-01
Temperature mapping based on fluorescent signal intensity ratios is a widely used noncontact approach for investigating temperature distributions in various systems. This noninvasive method is especially useful for applications, such as microfluidics, where accurate temperature measurements are difficult with conventional physical probes. However, the application of a calibration equation to relate fluorescence intensity ratio to temperature is not straightforward when the reference temperature in a given application is different than the one used to derive the calibration equation. In this report, we develop and validate generalized calibration equations that can be applied for any value of reference temperature. Our analysis shows that a simple linear correction for a 40 degrees C reference temperature produces errors in measured temperatures between -3 to 8 degrees C for three previously published sets of cubic calibration equations. On the other hand, corrections based on an exact solution of these equations restrict the errors to those inherent in the calibration equations. The methods described here are demonstrated for cubic calibration equations derived by three different groups, but the general method can be applied to other dyes and calibration equations.
Spherically-symmetric solutions in general relativity using a tetrad-based approach
Kim, Do Young; Lasenby, Anthony N.; Hobson, Michael P.
2018-03-01
We present a tetrad-based method for solving the Einstein field equations for spherically-symmetric systems and compare it with the widely-used Lemaître-Tolman-Bondi (LTB) model. In particular, we focus on the issues of gauge ambiguity and the use of comoving versus `physical' coordinate systems. We also clarify the correspondences between the two approaches, and illustrate their differences by applying them to the classic examples of the Schwarzschild and Friedmann-Lemaître-Robertson-Walker spacetimes. We demonstrate that the tetrad-based method does not suffer from the gauge freedoms inherent to the LTB model, naturally accommodates non-uniform pressure and has a more transparent physical interpretation. We further apply our tetrad-based method to a generalised form of `Swiss cheese' model, which consists of an interior spherical region surrounded by a spherical shell of vacuum that is embedded in an exterior background universe. In general, we allow the fluid in the interior and exterior regions to support pressure, and do not demand that the interior region be compensated. We pay particular attention to the form of the solution in the intervening vacuum region and illustrate the validity of Birkhoff's theorem at both the metric and tetrad level. We then reconsider critically the original theoretical arguments underlying the so-called Rh = ct cosmological model, which has recently received considerable attention. These considerations in turn illustrate the interesting behaviour of a number of `horizons' in general cosmological models.
The relativistic gravity train
Seel, Max
2018-05-01
The gravity train that takes 42.2 min from any point A to any other point B that is connected by a straight-line tunnel through Earth has captured the imagination more than most other applications in calculus or introductory physics courses. Brachystochron and, most recently, nonlinear density solutions have been discussed. Here relativistic corrections are presented. It is discussed how the corrections affect the time to fall through Earth, the Sun, a white dwarf, a neutron star, and—the ultimate limit—the difference in time measured by a moving, a stationary and the fiducial observer at infinity if the density of the sphere approaches the density of a black hole. The relativistic gravity train can serve as a problem with approximate and exact analytic solutions and as numerical exercise in any introductory course on relativity.
Zhao, J.; Wang, S.
2017-12-01
Gravity wave drag (GWD) is among the drivers of meridional overturning in the middle atmosphere, also known as the Brewer-Dobson Circulation, and of the quasi-biennial oscillation (QBO). The small spatial scales and complications due to wave breaking require their effects to be parameterised. GWD parameterizations are usually divided into two parts, orographic and non-orographic. The basic dynamical and physical processes of the middle atmosphere and the mechanism of the interactions between the troposphere and the middle atmosphere were studied in the frame of a general circulation model. The model for the troposphere was expanded to a global model considering middle atmosphere with the capability of describing the basic processes in the middle atmosphere and the troposphere-middle atmosphere interactions. Currently, it is too costly to include full non-hydrostatic and rotational wave dynamics in an operational parameterization. The hydrostatic non-rotational wave dynamics which allow an efficient implementation that is suitably fast for operation. The simplified parameterization of non-orographic GWD follows from the WM96 scheme in which a framework is developed using conservative propagation of gravity waves, critical level filtering, and non-linear dissipation. In order to simulate and analysis the influence of non-orographic GWD on the stratospheric wind and temperature fields, experiments using Stratospheric Sudden Warming (SSW) event case occurred in January 2013 were carried out, and results of objective weather forecast verifications of the two months period were compared in detail. The verification of monthly mean of forecast anomaly correlation (ACC) and root mean square (RMS) errors shows consistently positive impact of non-orographic GWD on skill score of forecasting for the three to eight days, both in the stratosphere and troposphere, and visible positive impact on prediction of the stratospheric wind and temperature fields. Numerical simulation
Cosmological tests of modified gravity.
Koyama, Kazuya
2016-04-01
We review recent progress in the construction of modified gravity models as alternatives to dark energy as well as the development of cosmological tests of gravity. Einstein's theory of general relativity (GR) has been tested accurately within the local universe i.e. the Solar System, but this leaves the possibility open that it is not a good description of gravity at the largest scales in the Universe. This being said, the standard model of cosmology assumes GR on all scales. In 1998, astronomers made the surprising discovery that the expansion of the Universe is accelerating, not slowing down. This late-time acceleration of the Universe has become the most challenging problem in theoretical physics. Within the framework of GR, the acceleration would originate from an unknown dark energy. Alternatively, it could be that there is no dark energy and GR itself is in error on cosmological scales. In this review, we first give an overview of recent developments in modified gravity theories including f(R) gravity, braneworld gravity, Horndeski theory and massive/bigravity theory. We then focus on common properties these models share, such as screening mechanisms they use to evade the stringent Solar System tests. Once armed with a theoretical knowledge of modified gravity models, we move on to discuss how we can test modifications of gravity on cosmological scales. We present tests of gravity using linear cosmological perturbations and review the latest constraints on deviations from the standard [Formula: see text]CDM model. Since screening mechanisms leave distinct signatures in the non-linear structure formation, we also review novel astrophysical tests of gravity using clusters, dwarf galaxies and stars. The last decade has seen a number of new constraints placed on gravity from astrophysical to cosmological scales. Thanks to on-going and future surveys, cosmological tests of gravity will enjoy another, possibly even more, exciting ten years.
[Burnout of general practitioners in Belgium: societal consequences and paths to solutions].
Kacenelenbogen, N; Offermans, A M; Roland, M
2011-09-01
corollary a questioning of the viability of the health care system as we know it. At the time of writing this article, the Belgian Health Care Knowledge Centre (KCE) is completing, at the request of the Belgian Ministry (SPF) of Health a study entitled "Burn Out of General Practitioners: which prevention, which solutions" whose goal is to make recommendations for the prevention and support of this issue. To measure the real impact of the solutions eventually implemented, we need to create a tool for a regular assessment of the prevalence of this problem in our country.
Directory of Open Access Journals (Sweden)
Huanhe Dong
2014-01-01
Full Text Available We introduce how to obtain the bilinear form and the exact periodic wave solutions of a class of (2+1-dimensional nonlinear integrable differential equations directly and quickly with the help of the generalized Dp-operators, binary Bell polynomials, and a general Riemann theta function in terms of the Hirota method. As applications, we solve the periodic wave solution of BLMP equation and it can be reduced to soliton solution via asymptotic analysis when the value of p is 5.
Path integral of unimodular gravity
de León Ardón, R.; Ohta, N.; Percacci, R.
2018-01-01
We compute the one-loop effective action in unimodular gravity, starting from two different classical formulations of the theory. We find that the effective action is the same in both cases, and agrees with the one of general relativity.
Directory of Open Access Journals (Sweden)
Roy Maartens
2010-09-01
Full Text Available The observable universe could be a 1+3-surface (the “brane” embedded in a 1+3+d-dimensional spacetime (the “bulk”, with Standard Model particles and fields trapped on the brane while gravity is free to access the bulk. At least one of the d extra spatial dimensions could be very large relative to the Planck scale, which lowers the fundamental gravity scale, possibly even down to the electroweak (∼ TeV level. This revolutionary picture arises in the framework of recent developments in M theory. The 1+10-dimensional M theory encompasses the known 1+9-dimensional superstring theories, and is widely considered to be a promising potential route to quantum gravity. At low energies, gravity is localized at the brane and general relativity is recovered, but at high energies gravity “leaks” into the bulk, behaving in a truly higher-dimensional way. This introduces significant changes to gravitational dynamics and perturbations, with interesting and potentially testable implications for high-energy astrophysics, black holes, and cosmology. Brane-world models offer a phenomenological way to test some of the novel predictions and corrections to general relativity that are implied by M theory. This review analyzes the geometry, dynamics and perturbations of simple brane-world models for cosmology and astrophysics, mainly focusing on warped 5-dimensional brane-worlds based on the Randall–Sundrum models. We also cover the simplest brane-world models in which 4-dimensional gravity on the brane is modified at low energies – the 5-dimensional Dvali–Gabadadze–Porrati models. Then we discuss co-dimension two branes in 6-dimensional models.
Nonlinear electrodynamics coupled to teleparallel theory of gravity
Gamal, G. L. Nashed
2011-02-01
Using nonlinear electrodynamics coupled to teleparallel theory of gravity, regular charged spherically symmetric solutions are obtained. The nonlinear theory is reduced to the Maxwell one in the weak limit and the solutions correspond to charged spacetimes. One of the obtained solutions contains an arbitrary function which we call general solution since we can generate from it the other solutions. The metric associated with these spacetimes is the same, i.e., regular charged static spherically symmetric black hole. In calculating the energy content of the general solution using the gravitational energy—momentum within the framework of the teleparallel geometry, we find that the resulting form depends on the arbitrary function. Using the regularized expression of the gravitational energy—momentum we obtain the value of energy.
International Nuclear Information System (INIS)
Konopleva, N.P.
1996-01-01
The problems of application of nonperturbative quantization methods in the theories of the gauge fields and gravity are discussed. Unification of interactions is considered in the framework of the geometrical gauge fields theory. Vacuum conception in the unified theory of interactions and instantons role in the vacuum structure are analyzed. The role of vacuum solutions of Einstein equations in definition of the gauge field vacuum is demonstrated
Directory of Open Access Journals (Sweden)
Yingwei Li
2013-01-01
Full Text Available The global exponential stability issues are considered for almost periodic solution of the neural networks with mixed time-varying delays and discontinuous neuron activations. Some sufficient conditions for the existence, uniqueness, and global exponential stability of almost periodic solution are achieved in terms of certain linear matrix inequalities (LMIs, by applying differential inclusions theory, matrix inequality analysis technique, and generalized Lyapunov functional approach. In addition, the existence and asymptotically almost periodic behavior of the solution of the neural networks are also investigated under the framework of the solution in the sense of Filippov. Two simulation examples are given to illustrate the validity of the theoretical results.
Ribeiro, F B
1999-01-01
Solutions of the diffusion equation in cylindrical coordinates are presented for a radionuclide produced by the decay of a not diffusing parent isotope with arbitrary activity distribution. General initial and Dirichlet boundary conditions are considered and the diffusion equation is solved for a finite cylinder. Solutions corresponding to two particular boundary conditions that can be imposed in laboratory diffusion coefficient measurements are presented. An analysis of the speed of convergence and of the series truncation error is done for these particular solutions. An example of the escape to production ratio derived from one of the solutions is also presented.
Compact objects in Horndeski gravity
Silva, Hector O.; Maselli, Andrea; Minamitsuji, Masato; Berti, Emanuele
2016-04-01
Horndeski gravity holds a special position as the most general extension of Einstein’s theory of general relativity (GR) with a single scalar degree of freedom and second-order field equations. Because of these features, Horndeski gravity is an attractive phenomenological playground to investigate the consequences of modifications of GR in cosmology and astrophysics. We present a review of the progress made so far in the study of compact objects (black holes (BHs) and neutron stars (NSs)) within Horndeski gravity. In particular, we review our recent work on slowly rotating BHs and present some new results on slowly rotating NSs.
Vaidya spacetime in massive gravity's rainbow
Heydarzade, Yaghoub; Rudra, Prabir; Darabi, Farhad; Ali, Ahmed Farag; Faizal, Mir
2017-11-01
In this paper, we will analyze the energy dependent deformation of massive gravity using the formalism of massive gravity's rainbow. So, we will use the Vainshtein mechanism and the dRGT mechanism for the energy dependent massive gravity, and thus analyze a ghost free theory of massive gravity's rainbow. We study the energy dependence of a time-dependent geometry, by analyzing the radiating Vaidya solution in this theory of massive gravity's rainbow. The energy dependent deformation of this Vaidya metric will be performed using suitable rainbow functions.
Vaidya spacetime in massive gravity's rainbow
Directory of Open Access Journals (Sweden)
Yaghoub Heydarzade
2017-11-01
Full Text Available In this paper, we will analyze the energy dependent deformation of massive gravity using the formalism of massive gravity's rainbow. So, we will use the Vainshtein mechanism and the dRGT mechanism for the energy dependent massive gravity, and thus analyze a ghost free theory of massive gravity's rainbow. We study the energy dependence of a time-dependent geometry, by analyzing the radiating Vaidya solution in this theory of massive gravity's rainbow. The energy dependent deformation of this Vaidya metric will be performed using suitable rainbow functions.
Astrophysical Tests of Modified Gravity
Sakstein, Jeremy
2015-01-01
Einstein's theory of general relativity has been the accepted theory of gravity for nearly a century but how well have we really tested it? The laws of gravity have been probed in our solar system to extremely high precision using several different tests and general relativity has passed each one with flying colours. Despite this, there are still some mysteries it cannot account for, one of which being the recently discovered acceleration of the universe and this has prompted a theoretical st...
Energy Technology Data Exchange (ETDEWEB)
Shabani, Hamid [University of Sistan and Baluchestan, Physics Department, Faculty of Sciences, Zahedan (Iran, Islamic Republic of); Ziaie, Amir Hadi [Islamic Azad University, Department of Physics, Kahnooj Branch, Kerman (Iran, Islamic Republic of)
2017-08-15
In this work, we study the late-time cosmological solutions of f(R, T) = g(R) + h(-T) models assuming that the conservation of the energy-momentum tensor (EMT) is violated. We perform our analysis through constructing an autonomous dynamical system for the equations of motion. We study the stability properties of solutions via considering linear perturbations about the related equilibrium points. Moreover, we parameterize the Lagrangian by introducing the parameters m(r) and n(s). These parameters which are constructed out of the functions g(R) and h(-T) play the main role in finding the late-time behavior of the solutions. We find that there exist, in general, three classes of solutions; all models with n > 0 include a proper transition from a prolonged matter era to a de Sitter solution. Models with -0.5 < n < 0 and n{sup '} > 1, for at least a root of equation n(s) = s - 1, include an unphysical dark energy solution preceding an improper matter era. Finally, for n < -1/2 there is a transient accelerated expansion era with -1/2 < w{sup (eff)} < -1/3 before a de Sitter phase. For all cases, in order to have a long enough matter dominated epoch, the condition m{sup '} → 0{sup +} for r
Pipinos, Savas
2010-01-01
This article describes one classroom activity in which the author simulates the Newtonian gravity, and employs the Euclidean Geometry with the use of new technologies (NT). The prerequisites for this activity were some knowledge of the formulae for a particle free fall in Physics and most certainly, a good understanding of the notion of similarity…
Amm, O.; Fujii, R.; VanhamäKi, H.; Yoshikawa, A.; Ieda, A.
2013-05-01
We devise an approach to calculate the polarization electric field in the ionosphere, when the ionospheric conductances, the primary (modeled) or the total (measured) electric field, and the Cowling efficiency are given. In contrast to previous studies, our approach is a general solution which is not limited to specific geometrical setups, and all parameters may have any kind of spatial dependence. The solution technique is based on spherical elementary current (vector) systems (SECS). This way, we avoid the need to specify explicit boundary conditions for the searched polarization electric field of its potential which would be required if the problem was solved in a differential equation approach. Instead, we solve an algebraic matrix equation, and the implicit boundary condition that the divergence of the polarization electric field vanishes outside our analysis area is sufficient. In order to illustrate our theory, we then apply it to two simple models of auroral electrodynamic situations, the first being a mesoscale strong conductance enhancement in the early morning sector within a relatively weak southward primary electric field, and a morning sector auroral arc with only a weak conductance enhancement, but a large southward primary electric field at the poleward flank of the arc. While the significance of the polarization electric field for maximum Cowling efficiency is large for the first case, it is rather minor for the second one. Both models show that the polarization electric field effect may not only change the magnitude of the current systems but also their overall geometry. Furthermore, the polarization electric field may extend into regions where the primary electric field is small, thus even dominating the total electric field in these regions. For the first model case, the total Joule heating integrated over the analysis area decreases by a factor of about 4 for maximum Cowling efficiency as compared to the case of vanishing Cowling efficiency
Black holes in six-dimensional conformal gravity
Lü, H.; Pang, Yi; Pope, C. N.
2013-05-01
We study conformally invariant theories of gravity in six dimensions. In four dimensions, there is a unique such theory that is polynomial in the curvature and its derivatives, namely, Weyl-squared, and furthermore all solutions of Einstein gravity are also solutions of the conformal theory. By contrast, in six dimensions there are three independent conformally invariant polynomial terms one could consider. There is a unique linear combination (up to overall scale) for which Einstein metrics are also solutions, and this specific theory forms the focus of our attention in this paper. We reduce the equations of motion for the most general spherically symmetric black hole to a single fifth-order differential equation. We obtain the general solution in the form of an infinite series, characterized by five independent parameters, and we show how a finite three-parameter truncation reduces to the already known Schwarzschild-AdS metric and its conformal scaling. We derive general results for the thermodynamics and the first law for the full five-parameter solutions. We also investigate solutions in extended theories coupled to conformally invariant matter, and in addition we derive some general results for conserved charges in cubic-curvature theories in arbitrary dimensions.
Directory of Open Access Journals (Sweden)
Rovelli Carlo
1998-01-01
Full Text Available The problem of finding the quantum theory of the gravitational field, and thus understanding what is quantum spacetime, is still open. One of the most active of the current approaches is loop quantum gravity. Loop quantum gravity is a mathematically well-defined, non-perturbative and background independent quantization of general relativity, with its conventional matter couplings. Research in loop quantum gravity today forms a vast area, ranging from mathematical foundations to physical applications. Among the most significant results obtained are: (i The computation of the physical spectra of geometrical quantities such as area and volume, which yields quantitative predictions on Planck-scale physics. (ii A derivation of the Bekenstein-Hawking black hole entropy formula. (iii An intriguing physical picture of the microstructure of quantum physical space, characterized by a polymer-like Planck scale discreteness. This discreteness emerges naturally from the quantum theory and provides a mathematically well-defined realization of Wheeler's intuition of a spacetime ``foam''. Long standing open problems within the approach (lack of a scalar product, over-completeness of the loop basis, implementation of reality conditions have been fully solved. The weak part of the approach is the treatment of the dynamics: at present there exist several proposals, which are intensely debated. Here, I provide a general overview of ideas, techniques, results and open problems of this candidate theory of quantum gravity, and a guide to the relevant literature.
Burla, Santoshkumar; Mueller, Vitali; Flury, Jakob; Jovanovic, Nemanja
2016-04-01
CHAMP, GRACE and GOCE missions have been successful in the field of satellite geodesy (especially to improve Earth's gravity field models) and have established the necessity towards the next generation gravity field missions. Especially, GRACE has shown its capabilities beyond any other gravity field missions. GRACE Follow-On mission is going to continue GRACE's legacy which is almost identical to GRACE mission with addition of laser interferometry. But these missions are not only quite expensive but also takes quite an effort to plan and to execute. Still there are few drawbacks such as under-sampling and incapability of exploring new ideas within a single mission (ex: to perform different orbit configurations with multi satellite mission(s) at different altitudes). The budget is the major limiting factor to build multi satellite mission(s). Here, we offer a solution to overcome these drawbacks using cubesat/ nanosatellite mission. Cubesats are widely used in research because they are cheaper, smaller in size and building them is easy and faster than bigger satellites. Here, we design a 3D model of GRACE like mission with available sensors and explain how the Attitude and Orbit Control System (AOCS) works. The expected accuracies on final results of gravity field are also explained here.
An approximate solution for a generalized Hirota-Satsom coupled (Kdv equation
Directory of Open Access Journals (Sweden)
H.A. Wahab
2017-03-01
Full Text Available In this paper the Homotopy Analysis Method (HAM, is applied to find the approximate solution of Hirota-Satsuma coupled (KdV equations, which don't need a small parameter for solution. The results obtained by HAM is compared with exact solution, the results divulge that the Homotopy Analysis Method are most accurate, closed and suitable to exact solution of the equation, as compare to Homotopy Perturbation Method. It is predicated that the HAM can be found usually.
Neutron stars in Horndeski gravity
Maselli, Andrea; Silva, Hector O.; Minamitsuji, Masato; Berti, Emanuele
2016-06-01
Horndeski's theory of gravity is the most general scalar-tensor theory with a single scalar whose equations of motion contain at most second-order derivatives. A subsector of Horndeski's theory known as "Fab Four" gravity allows for dynamical self-tuning of the quantum vacuum energy, and therefore it has received particular attention in cosmology as a possible alternative to the Λ CDM model. Here we study compact stars in Fab Four gravity, which includes as special cases general relativity ("George"), Einstein-dilaton-Gauss-Bonnet gravity ("Ringo"), theories with a nonminimal coupling with the Einstein tensor ("John"), and theories involving the double-dual of the Riemann tensor ("Paul"). We generalize and extend previous results in theories of the John class and were not able to find realistic compact stars in theories involving the Paul class.
International Nuclear Information System (INIS)
Jarsjoe, Jerker; Destouni, Georgia; Persson, Klas; Prieto, Carmen
2007-12-01
We formulate a general theoretical conceptualisation of solute transport from inland sources to downstream recipients, considering main recipient load contributions from all different nutrient and pollutant sources that may exist within any catchment. Since the conceptualisation is model independent, its main hydrological factors and mass delivery factors can be quantified on the basis of inputs to and outputs from any considered analytical or numerical model. Some of the conceptually considered source contribution and transport pathway combinations are however commonly neglected in catchment-scale solute transport and attenuation modelling, in particular those related to subsurface sources, diffuse sources at the land surface and direct groundwater transport into the recipient. The conceptual framework provides a possible tool for clarification of underlying and often implicit model assumptions, which can be useful for e.g. inter-model comparisons. In order to further clarify and explain research questions that may be of particular importance for transport pathways from deep groundwater surrounding a repository, we concretise and interpret some selected transport scenarios for model conditions in the Forsmark area. Possible uncertainties in coastal discharge predictions, related to uncertain spatial variation of evapotranspiration within the catchment, were shown to be small for the relatively large, focused surface water discharges from land to sea, because local differences were averaged out along the length of the main water flow paths. In contrast, local flux values within the diffuse groundwater flow field from land to sea are more uncertain, although estimates of mean values and total sums of submarine groundwater discharge (SGD) along some considerable coastline length may be robust. The present results show that 80% to 90% of the total coastal discharge of Forsmark occurred through focused flows in visible streams, whereas the remaining 10% to 20% was
No hair theorem in quasi-dilaton massive gravity
Energy Technology Data Exchange (ETDEWEB)
Wu, De-Jun, E-mail: wudejun10@mails.ucas.ac.cn [School of Physics, University of Chinese Academy of Sciences, Beijing 100049 (China); Zhou, Shuang-Yong, E-mail: sxz353@case.edu [Department of Physics, Case Western Reserve University, 10900 Euclid Ave, Cleveland, OH 44106 (United States)
2016-06-10
We investigate the static, spherically symmetric black hole solutions in the quasi-dilaton model and its generalizations, which are scalar extended dRGT massive gravity with a shift symmetry. We show that, unlike generic scalar extended massive gravity models, these theories do not admit static, spherically symmetric black hole solutions until the theory parameters in the dRGT potential are fine-tuned. When fine-tuned, the geometry of the static, spherically symmetric black hole is necessarily that of general relativity and the quasi-dilaton field is constant across the spacetime. The fine-tuning and the no hair theorem apply to black holes with flat, anti-de Sitter or de Sitter asymptotics.
Constraining f(T) gravity in the Solar System
Energy Technology Data Exchange (ETDEWEB)
Iorio, Lorenzo [Ministero dell' Istruzione dell' Università e della Ricerca (M.I.U.R), Viale Unità di Italia 68, 70125 Bari (Italy); Radicella, Ninfa [Dipartimento di Fisica E.R. Caianiello, Università di Salerno, Via Giovanni Paolo II 132, Fisciano (Italy); Ruggiero, Matteo Luca, E-mail: lorenzo.iorio@libero.it, E-mail: ninfa.radicella@sa.infn.it, E-mail: matteo.ruggiero@polito.it [DISAT, Politecnico di Torino, Corso Duca degli Abruzzi 24, Torino (Italy)
2015-08-01
In the framework of f(T) theories of gravity, we solve the field equations for f(T)=T+α T{sup n} in the weak-field approximation and for spherical symmetry spacetime. Since f(T)=T corresponds to Teleparallel Gravity, which is equivalent to General Relativity, the non linearity of the Lagrangian are expected to produce perturbations of the general relativistic solutions, parameterized by α. Hence, we use the f(T) solutions to model the gravitational field of the Sun and exploit data from accurate radio-tracking of spacecrafts orbiting Mercury and Saturn to infer preliminary bounds on the model parameter α and on the cosmological constant Λ.
Positive global solutions for a general model of size-dependent population dynamics
Directory of Open Access Journals (Sweden)
Nobuyuki Kato
2000-01-01
have the growth rate depending on the size and time. The local existence and uniqueness of the solution have been shown by Kato and Torikata (1997. Here, we discuss the positivity of the solution and global existence as well as L ∞ solutions.
Stealth configurations in vector-tensor theories of gravity
Chagoya, Javier; Tasinato, Gianmassimo
2018-01-01
Studying the physics of compact objects in modified theories of gravity is important for understanding how future observations can test alternatives to General Relativity. We consider a subset of vector-tensor Galileon theories of gravity characterized by new symmetries, which can prevent the propagation of the vector longitudinal polarization, even in absence of Abelian gauge invariance. We investigate new spherically symmetric and slowly rotating solutions for these systems, including an arbitrary matter Lagrangian. We show that, under certain conditions, there always exist stealth configurations whose geometry coincides with solutions of Einstein gravity coupled with the additional matter. Such solutions have a non-trivial profile for the vector field, characterized by independent integration constants, which extends to asymptotic infinity. We interpret our findings in terms of the symmetries and features of the original vector-tensor action, and on the number of degrees of freedom that it propagates. These results are important to eventually describe gravitationally bound configurations in modified theories of gravity, such as black holes and neutron stars, including realistic matter fields forming or surrounding the object.
Energy Technology Data Exchange (ETDEWEB)
Jarsjoe, Jerker; Destouni, Georgia; Persson, Klas; Prieto, Carmen (Dept. of Physical Geography, Quaternary Geology, Stockholm Univ., Stockholm (Sweden))
2007-12-15
We formulate a general theoretical conceptualisation of solute transport from inland sources to downstream recipients, considering main recipient load contributions from all different nutrient and pollutant sources that may exist within any catchment. Since the conceptualisation is model independent, its main hydrological factors and mass delivery factors can be quantified on the basis of inputs to and outputs from any considered analytical or numerical model. Some of the conceptually considered source contribution and transport pathway combinations are however commonly neglected in catchment-scale solute transport and attenuation modelling, in particular those related to subsurface sources, diffuse sources at the land surface and direct groundwater transport into the recipient. The conceptual framework provides a possible tool for clarification of underlying and often implicit model assumptions, which can be useful for e.g. inter-model comparisons. In order to further clarify and explain research questions that may be of particular importance for transport pathways from deep groundwater surrounding a repository, we concretise and interpret some selected transport scenarios for model conditions in the Forsmark area. Possible uncertainties in coastal discharge predictions, related to uncertain spatial variation of evapotranspiration within the catchment, were shown to be small for the relatively large, focused surface water discharges from land to sea, because local differences were averaged out along the length of the main water flow paths. In contrast, local flux values within the diffuse groundwater flow field from land to sea are more uncertain, although estimates of mean values and total sums of submarine groundwater discharge (SGD) along some considerable coastline length may be robust. The present results show that 80% to 90% of the total coastal discharge of Forsmark occurred through focused flows in visible streams, whereas the remaining 10% to 20% was
14 CFR 27.27 - Center of gravity limits.
2010-01-01
... 14 Aeronautics and Space 1 2010-01-01 2010-01-01 false Center of gravity limits. 27.27 Section 27... AIRWORTHINESS STANDARDS: NORMAL CATEGORY ROTORCRAFT Flight General § 27.27 Center of gravity limits. The extreme forward and aft centers of gravity and, where critical, the extreme lateral centers of gravity must be...
14 CFR 29.27 - Center of gravity limits.
2010-01-01
... 14 Aeronautics and Space 1 2010-01-01 2010-01-01 false Center of gravity limits. 29.27 Section 29... AIRWORTHINESS STANDARDS: TRANSPORT CATEGORY ROTORCRAFT Flight General § 29.27 Center of gravity limits. The extreme forward and aft centers of gravity and, where critical, the extreme lateral centers of gravity...
Ikhdair, Sameer M.; Sever, Ramazan
2006-01-01
The analytical solutions of the N-dimensional Schrodinger equation with position-dependent mass for a general class of central potentials is obtained via the series expansion method. The position-dependent mass is expanded in series about origin. As a special case, the analytical bound-state series solutions and the recursion relation of the linear-plus-Coulomb (Cornell) potential with the decaying position-dependent mass m=m_{0}e^{-\\lambda r} are also found.
International Nuclear Information System (INIS)
Fernandes, L.; Friedlander, A.; Guedes, M.; Judice, J.
2001-01-01
This paper addresses a General Linear Complementarity Problem (GLCP) that has found applications in global optimization. It is shown that a solution of the GLCP can be computed by finding a stationary point of a differentiable function over a set defined by simple bounds on the variables. The application of this result to the solution of bilinear programs and LCPs is discussed. Some computational evidence of its usefulness is included in the last part of the paper
Topics in string theory and quantum gravity
Alvarez-Gaume, Luis
1992-01-01
These are the lecture notes for the Les Houches Summer School on Quantum Gravity held in July 1992. The notes present some general critical assessment of other (non-string) approaches to quantum gravity, and a selected set of topics concerning what we have learned so far about the subject from string theory. Since these lectures are long (133 A4 pages), we include in this abstract the table of contents, which should help the user of the bulletin board in deciding whether to latex and print the full file. 1-FIELD THEORETICAL APPROACH TO QUANTUM GRAVITY: Linearized gravity; Supergravity; Kaluza-Klein theories; Quantum field theory and classical gravity; Euclidean approach to Quantum Gravity; Canonical quantization of gravity; Gravitational Instantons. 2-CONSISTENCY CONDITIONS: ANOMALIES: Generalities about anomalies; Spinors in 2n dimensions; When can we expect to find anomalies?; The Atiyah-Singer Index Theorem and the computation of anomalies; Examples: Green-Schwarz cancellation mechanism and Witten's SU(2) ...
Directory of Open Access Journals (Sweden)
C. Bossuet
1998-02-01
Full Text Available Systematic westerly biases in the southern hemisphere wintertime flow and easterly equatorial biases are experienced in the Météo-France climate model. These biases are found to be much reduced when a simple parameterization is introduced to take into account the vertical momentum transfer through the gravity waves excited by deep convection. These waves are quasi-stationary in the frame of reference moving with convection and they propagate vertically to higher levels in the atmosphere, where they may exert a significant deceleration of the mean flow at levels where dissipation occurs. Sixty-day experiments have been performed from a multiyear simulation with the standard 31 levels for a summer and a winter month, and with a T42 horizontal resolution. The impact of this parameterization on the integration of the model is found to be generally positive, with a significant deceleration in the westerly stratospheric jet and with a reduction of the easterly equatorial bias. The sensitivity of the Météo-France climate model to vertical resolution is also investigated by increasing the number of vertical levels, without moving the top of the model. The vertical resolution is increased up to 41 levels, using two kinds of level distribution. For the first, the increase in vertical resolution concerns especially the troposphere (with 22 levels in the troposphere, and the second treats the whole atmosphere in a homogeneous way (with 15 levels in the troposphere; the standard version of 31 levels has 10 levels in the troposphere. A comparison is made between the dynamical aspects of the simulations. The zonal wind and precipitation are presented and compared for each resolution. A positive impact is found with the finer tropospheric resolution on the precipitation in the mid-latitudes and on the westerly stratospheric jet, but the general impact on the model climate is weak, the physical parameterizations used appear to be mostly independent to the
Directory of Open Access Journals (Sweden)
C. Bossuet
Full Text Available Systematic westerly biases in the southern hemisphere wintertime flow and easterly equatorial biases are experienced in the Météo-France climate model. These biases are found to be much reduced when a simple parameterization is introduced to take into account the vertical momentum transfer through the gravity waves excited by deep convection. These waves are quasi-stationary in the frame of reference moving with convection and they propagate vertically to higher levels in the atmosphere, where they may exert a significant deceleration of the mean flow at levels where dissipation occurs. Sixty-day experiments have been performed from a multiyear simulation with the standard 31 levels for a summer and a winter month, and with a T42 horizontal resolution. The impact of this parameterization on the integration of the model is found to be generally positive, with a significant deceleration in the westerly stratospheric jet and with a reduction of the easterly equatorial bias. The sensitivity of the Météo-France climate model to vertical resolution is also investigated by increasing the number of vertical levels, without moving the top of the model. The vertical resolution is increased up to 41 levels, using two kinds of level distribution. For the first, the increase in vertical resolution concerns especially the troposphere (with 22 levels in the troposphere, and the second treats the whole atmosphere in a homogeneous way (with 15 levels in the troposphere; the standard version of 31 levels has 10 levels in the troposphere. A comparison is made between the dynamical aspects of the simulations. The zonal wind and precipitation are presented and compared for each resolution. A positive impact is found with the finer tropospheric resolution on the precipitation in the mid-latitudes and on the westerly stratospheric jet, but the general impact on the model climate is weak, the physical parameterizations used appear to be mostly independent to the
Euler-Chern-Simons gravity from Lovelock-Born-Infeld gravity
International Nuclear Information System (INIS)
Izaurieta, F.; Rodriguez, E.; Salgado, P.
2004-01-01
In the context of a gauge theoretical formulation, higher-dimensional gravity invariant under the AdS group is dimensionally reduced to Euler-Chern-Simons gravity. The dimensional reduction procedure of Grignani-Nardelli [Phys. Lett. B 300 (1993) 38] is generalized so as to permit reducing D-dimensional Lanczos-Lovelock gravity to d=D-1 dimensions
Euler–Chern–Simons gravity from Lovelock–Born–Infeld gravity
Izaurieta, F.; Rodriguez, E.; Salgado, P.
2004-01-01
In the context of a gauge theoretical formulation, higher dimensional gravity invariant under the AdS group is dimensionally reduced to Euler-Chern-Simons gravity. The dimensional reduction procedure of Grignani-Nardelli [Phys. Lett. B 300, 38 (1993)] is generalized so as to permit reducing D-dimensional Lanczos Lovelock gravity to d=D-1 dimensions.
Directory of Open Access Journals (Sweden)
Shaw-Yang Yang Hund-Der Yeh
2012-01-01
Full Text Available This note develops a general mathematical model for describing the transient hydraulic head response for constant-head test, constant-flux test, and slug test in a radial confined aquifer system with a partially penetrating well. The Laplace-domain solution for the model is derived by applying the Laplace transform with respect to time and finite Fourier cosine transform with respect to the z-direction. This new solution has been shown to reduce to the constant-head test when discounting the wellbore storage and maintaining a constant well water level. This solution can also be reduced to the constant-flux test solution when discounting the wellbore storage and keeping a constant pumping rate in the well. Moreover, the solution becomes the slug test solution when there is no pumping in the well. This general solution can be used to develop a single computer code to estimate aquifer parameters if coupled with an optimization algorithm or to assess the effect of well partial penetration on hydraulic head distribution for three types of aquifer tests.
Energy Technology Data Exchange (ETDEWEB)
Mehta, M; Dancer, K A; Gould, M D; Links, J [Centre for Mathematical Physics, School of Physical Sciences, University of Queensland, Brisbane 4072 (Australia)
2006-01-06
The Perk-Schultz model may be expressed in terms of the solution of the Yang-Baxter equation associated with the fundamental representation of the untwisted affine extension of the general linear quantum superalgebra U{sub q}[gl(m vertical bar n)], with a multiparametric coproduct action as given by Reshetikhin. Here, we present analogous explicit expressions for solutions of the Yang-Baxter equation associated with the fundamental representations of the twisted and untwisted affine extensions of the orthosymplectic quantum superalgebras U{sub q}[osp(m vertical bar n)]. In this manner, we obtain generalizations of the Perk-Schultz model. (letter to the editor)
Classical aspects of higher spin topologically massive gravity
International Nuclear Information System (INIS)
Chen Bin; Long Jiang; Zhang Jiandong
2012-01-01
We study the classical solutions of three-dimensional topologically massive gravity (TMG) and its higher spin generalization, in the first-order formulation. The action of higher spin TMG has been proposed by Chen and Long (2011 J. High Energy Phys. JHEP12(2011)114) to be of a Chern–Simons-like form. The equations of motion are more complicated than the ones in pure higher spin AdS 3 gravity, but are still tractable. As all the solutions in higher spin gravity are automatically the solutions of higher spin TMG, we focus on other solutions. We manage to find the AdS pp-wave solutions with higher spin hair and find that the non-vanishing higher spin fields may or may not modify the pp-wave geometry. In order to discuss the warped spacetime, we introduce the notion of a special Killing vector, which is defined to be the symmetry on the frame-like fields. We reproduce various warped spacetimes of TMG in our framework, with the help of special Killing vectors. (paper)