Generalized equations of gravitational field
Stanyukovich, K.P.; Borisova, L.B.
1985-01-01
Equations for gravitational fields are obtained on the basis of a generalized Lagrangian Z=f(R) (R is the scalar curvature). Such an approach permits to take into account the evolution of a gravitation ''constant''. An expression for the force Fsub(i) versus the field variability is obtained. Conservation laws are formulated differing from the standard ones by the fact that in the right part of new equations the value Fsub(i) is present that goes to zero at an ultimate passage to the standard Einstein theory. An equation of state is derived for cosmological metrics for a particular case, f=bRsup(1+α) (b=const, α=const)
Generalization of Einstein's gravitational field equations
Moulin, Frédéric
2017-12-01
The Riemann tensor is the cornerstone of general relativity, but as is well known it does not appear explicitly in Einstein's equation of gravitation. This suggests that the latter may not be the most general equation. We propose here for the first time, following a rigorous mathematical treatment based on the variational principle, that there exists a generalized 4-index gravitational field equation containing the Riemann curvature tensor linearly, and thus the Weyl tensor as well. We show that this equation, written in n dimensions, contains the energy-momentum tensor for matter and that of the gravitational field itself. This new 4-index equation remains completely within the framework of general relativity and emerges as a natural generalization of the familiar 2-index Einstein equation. Due to the presence of the Weyl tensor, we show that this equation contains much more information, which fully justifies the use of a fourth-order theory.
Gravitational closure of matter field equations
Düll, Maximilian; Schuller, Frederic P.; Stritzelberger, Nadine; Wolz, Florian
2018-04-01
The requirement that both the matter and the geometry of a spacetime canonically evolve together, starting and ending on shared Cauchy surfaces and independently of the intermediate foliation, leaves one with little choice for diffeomorphism-invariant gravitational dynamics that can equip the coefficients of a given system of matter field equations with causally compatible canonical dynamics. Concretely, we show how starting from any linear local matter field equations whose principal polynomial satisfies three physicality conditions, one may calculate coefficient functions which then enter an otherwise immutable set of countably many linear homogeneous partial differential equations. Any solution of these so-called gravitational closure equations then provides a Lagrangian density for any type of tensorial geometry that features ultralocally in the initially specified matter Lagrangian density. Thus the given system of matter field equations is indeed closed by the so obtained gravitational equations. In contrast to previous work, we build the theory on a suitable associated bundle encoding the canonical configuration degrees of freedom, which allows one to include necessary constraints on the geometry in practically tractable fashion. By virtue of the presented mechanism, one thus can practically calculate, rather than having to postulate, the gravitational theory that is required by specific matter field dynamics. For the special case of standard model matter one obtains general relativity.
Dyons in presence of gravitation and symmetrized field equations
Rawat, A.S.; Negi, O.P.S.
1999-01-01
Combined theory of gravitation and electromagnetism associated with particles carrying electric and magnetic charges has been established from an invariant action principle. Corresponding field equations, equation of motion and Einstein Maxwell's equations are obtained in unique and consistent way. It is shown that weak field approximation of slowly moving particle in gravitational field leads the symmetry between electromagnetic and linear gravitational fields. Postulation of the existence of gravimagnetic monopole leads structural symmetry between generalized electromagnetic and gravielectromagnetic fields. Corresponding quantization conditions and angular momentum are also analysed. (author)
Generalization of Einstein's gravitational field equations
Moulin, Frederic
2017-01-01
The Riemann tensor is the cornerstone of general relativity, but as is well known it does not appear explicitly in Einstein's equation of gravitation. This suggests that the latter may not be the most general equation. We propose here for the first time, following a rigorous mathematical treatment based on the variational principle, that there exists a generalized 4-index gravitational field equation containing the Riemann curvature tensor linearly, and thus the Weyl tensor as well. We show that this equation, written in n dimensions, contains the energy-momentum tensor for matter and that of the gravitational field itself. This new 4-index equation remains completely within the framework of general relativity and emerges as a natural generalization of the familiar 2-index Einstein equation. Due to the presence of the Weyl tensor, we show that this equation contains much more information, which fully justifies the use of a fourth-order theory. (orig.)
Generalization of Einstein's gravitational field equations
Moulin, Frederic [Ecole Normale Superieure Paris-Saclay, Departement de Physique, Cachan (France)
2017-12-15
The Riemann tensor is the cornerstone of general relativity, but as is well known it does not appear explicitly in Einstein's equation of gravitation. This suggests that the latter may not be the most general equation. We propose here for the first time, following a rigorous mathematical treatment based on the variational principle, that there exists a generalized 4-index gravitational field equation containing the Riemann curvature tensor linearly, and thus the Weyl tensor as well. We show that this equation, written in n dimensions, contains the energy-momentum tensor for matter and that of the gravitational field itself. This new 4-index equation remains completely within the framework of general relativity and emerges as a natural generalization of the familiar 2-index Einstein equation. Due to the presence of the Weyl tensor, we show that this equation contains much more information, which fully justifies the use of a fourth-order theory. (orig.)
Equations of motion derived from a generalization of Einstein's equation for the gravitational field
Mociutchi, C.
1980-01-01
The extended Einstein's equation, combined with a vectorial theory of maxwellian type of the gravitational field, leads to: a) the equation of motion; b) the equation of the trajectory for the static case of spherical symmetry, the test particle having a rest mass other than zero, and c) the propagation of light on null geodesics. All the basic tests of the theory given by Einstein's extended equation. Thus, the new theory of gravitation suggested by us is competitive. (author)
Gravitational field equations on and off a 3-brane world
Aliev, A N; Guemruekcueoglu, A E
2004-01-01
The effective gravitational field equations on and off a 3-brane world possessing a Z 2 mirror symmetry and embedded in a five-dimensional bulk spacetime with cosmological constant were derived by Shiromizu, Maeda and Sasaki (SMS) in the framework of the Gauss-Codazzi projective approach with the subsequent specialization to the Gaussian normal coordinates in the neighbourhood of the brane. However, the Gaussian normal coordinates imply a very special slicing of spacetime and clearly, the consistent analysis of the brane dynamics would benefit from complete freedom in the slicing of spacetime, pushing the layer surfaces in the fifth dimension at any rates of evolution and in arbitrary positions. We rederive the SMS effective gravitational field equations on a 3-brane and generalize the off-brane equations to the case where there is an arbitrary energy-momentum tensor in the bulk. We use a more general setting to allow for acceleration of the normals to the brane surface through the lapse function and the shift vector in the spirit of Arnowitt, Deser and Misner. We show that the gravitational influence of the bulk spacetime on the brane may be described by a traceless second-rank tensor W ij , constructed from the 'electric' part of the bulk Riemann tensor. We also present the evolution equations for the tensor W ij , as well as for the corresponding 'magnetic' part of the bulk curvature. These equations involve terms determined by both the nonvanishing acceleration of normals in the nongeodesic slicing of spacetime and the presence of other fields in the bulk
Einstein's equations of motion in the gravitational field of an oblate ...
In an earlier paper we derived Einstein's geometrical gravitational field equations for the metric tensor due to an oblate spheroidal massive body. In this paper we derive the corresponding Einstein's equations of motion for a test particle of nonzero rest mass in the gravitational field exterior to a homogeneous oblate ...
Alternative equations of gravitation
Pinto Neto, N.
1983-01-01
It is shown, trough a new formalism, that the quantum fluctuation effects of the gravitational field in Einstein's equations are analogs to the effects of a continuum medium in Maxwell's Electrodynamics. Following, a real example of the applications of these equations is studied. Qunatum fluctuations effects as perturbation sources in Minkowski and Friedmann Universes are examined. (L.C.) [pt
Manoff, S.
1979-07-01
By utilization of the method of Lagrangians with covariant derivatives (MLCD) the different energy-momentum tensors (canonical, generalized canonical, symmetrical) and the relations between them are considered. On this basis, Einstein's theory of gravitation is studied as a field theory with a Lagrangian density of the type Lsub(g)=√-g.Lsub(g)(gsub(ij),Rsub(A)), (Rsub(A)=Rsub(ijkl)). It is shown that the energy-momentum tensors of the gravitational field can be defined for this theory. The symmetrical energy-momentum tensor of the gravitational field sub(gs)Tsub(k)sup(i), which in the general case is not a local conserved quantity (sub(gs)Tsub(k)sup(i)sub(;i) unequal 0) (in contrast to the material fields satisfying condition sub(Ms)Tsub(k)sup(i)sub(;i) = 0), is equal to zero for the gravitational field in vacuum (cosmological constant Λ = 0). Equations of the gravitational field of a new type are suggested, leading to equations of motion (sub(Ms)Tsub(k)sup(i) + sub(gs)Tsub(k)sup(i))sub(;i) = 0. The equations corresponding to the Lagrangian density Lsub(g)=(√-g/kappasub(o)) (R - lambda approximately), lambda approximately = const., are considered. The equations of Einstein Rsub(ij) = 0 are obtained in the case of gravitational field in vacuum. Some particular cases are examined as an illustration to material fields and the corresponding gravitational equations. (author)
Parametrized post-Newtonian approximation and Rastall's gravitational field equations
Smalley, L.L.
1978-01-01
The parametrized post-Newtonian (PPN) approximation is generalized to accomodate Rastall's modification of Einstein's theory of gravity, which allows nonzero divergence of the energy-momentum tensor. Rastall's theory is then shown to have consistent field equations, gauge conditions, and the correct Newtonian limit of the equations of motion. The PPN parameters are obtained and shown to agree experimentally with those for the Einstein theory. In light of the nonzero divergence condition, integral conservation laws are investigated and shown to yield conserved energy-momentum and angular-momentum. We conclude that the above generalization of metric theories, within the PPN framework, is a natural extension of the concept of metric theories
New exact solutions of Einstein's field equations: gravitational force can also be repulsive!
Dietz, W.
1988-01-01
This article has not been written for specialists of exact solutions of Einstein's field equations but for physicists who are interested in nontrivial information on this topic. We recall the history and some basic properties of exact solutions of Einstein's vacuum equations. We show that the field equations for stationary axisymmetric vacuum gravitational fields can be expressed by only one nonlinear differential equation for a complex function. This compact form of the field equations allows the generation of almost all stationary axisymmetric vacuum gravitational fields. We present a new stationary two-body solution of Einstein's equations as an application of this generation technique. This new solution proves the existence of a macroscopic, repulsive spin-spin interaction in general relativity. Some estimates that are related to this new two-body solution are given
Radiation tails of the scalar wave equation in a weak gravitational field
Mankin, R.; Piir, I.
1974-01-01
A class of solutions of the linearized Einstein equations is found making use of the Newman-Penrose spin coefficient formalism. These solutions describe a weak retarded gravitational field with an arbitrary multipole structure. The study of the radial propagation of the scalar waves in this gravitational field shows that in the first approximation the tails of the scalar outgoing radiation appear either in the presence of a gravitational mass or in the case of a nonzero linear momentum of the gravitational source. The quadrupole moment and the higher multipole moments of the gravitational field as well as the constant dipole moment and the angular moment of the source do not contribute to the tail
Newton\\'s equation of motion in the gravitational field of an oblate ...
In this paper, we derived Newton's equation of motion for a satellite in the gravitational scalar field of a uniformly rotating, oblate spheriodal Earth using spheriodal coordinates. The resulting equation is solved for the corresponding precession and the result compared with similar ones. JONAMP Vol. 11 2007: pp. 279-286 ...
On the discovery of the gravitational field equations by Einstein and Hilbert: new materials
Vizgin, Vladimir P
2001-01-01
This article describes the history of discovery of the equations of gravitational field by Albert Einstein and David Hilbert in November 1915. The proof sheet of Hilbert's lecture report, made on 20 November 1915 and published in March 1916, rediscovered in 1997 in the archive of the university of Goettingen, throws new light on the history of this discovery. We also discuss the early history of the general theory of relativity that led to the expression of the general covariant equations of gravitational field. (from the history of physics)
Equations of motion for anisotropic nonlinear elastic continuum in gravitational field
Sokolov, S.N.
1994-01-01
Equations of motion for anisotropic nonlinear elastic continuum in the gravitational field are written in the form convenient for numerical calculations. The energy-stress tensor is expressed through scalar and tensor products of three vectors frozen in the continuum. Examples of expansion of the energy-stress tensor into scalar and tensor invariants corresponding to some crystal classes are given. 47 refs
Bleyer, U.; Muecket, J.P.
1980-01-01
In general the Birkhoff theorem is violated in non-Einsteinian theories of gravitation. We show for theories in which the dynamical equations do not follow from the field equations that time-dependent vacuum solutions are needed in order to join nonstatic spherically symmetric incoherent matter distributions. It is shown for Treder's tetrad theories that such vacuum solutions exist and a continuous and unique junction is possible. In generalization of these results we consider the problem in what theories of gravitation the dynamical equations do not follow from the field equations. This consideration leads to non-Einsteinian theories like bimetric theories or Treder's tetrad theories containing supplementary geometrical quantities which are not dynamical variables of the theory. (author)
Tevikyan, R.V.
1986-01-01
This paper presents equations that describe particles with spins s = 0, 1/2, 1 completely and which also describe 2s + 2 limiting fields as E → ∞. It is shown that the ordinary Hilbert-Einstein action for the gravitation field must be augmented by the action for the Bose vacuum field. This means that one must introduce in the gravitational equations a cosmological term proportional to the square of the strength of the Bose vacuum field. It is shown that the theory of gravitation describes three realities: matter, field, and vacuum field. A new form of matter--the vacuum field--is introduced into field theory
Horizon thermodynamics and gravitational field equations in Horava-Lifshitz gravity
Cai Ronggen; Ohta, Nobuyoshi
2010-01-01
We explore the relationship between the first law of thermodynamics and gravitational field equation at a static, spherically symmetric black hole horizon in Horava-Lifshitz theory with/without detailed balance. It turns out that as in the cases of Einstein gravity and Lovelock gravity, the gravitational field equation can be cast to a form of the first law of thermodynamics at the black hole horizon. This way we obtain the expressions for entropy and mass in terms of black hole horizon, consistent with those from other approaches. We also define a generalized Misner-Sharp energy for static, spherically symmetric spacetimes in Horava-Lifshitz theory. The generalized Misner-Sharp energy is conserved in the case without matter field, and its variation gives the first law of black hole thermodynamics at the black hole horizon.
Wu Ning; Zhang Dahua
2007-01-01
A systematic method is developed to study the classical motion of a mass point in gravitational gauge field. First, by using Mathematica, a spherical symmetric solution of the field equation of gravitational gauge field is obtained, which is just the traditional Schwarzschild solution. Combining the principle of gauge covariance and Newton's second law of motion, the equation of motion of a mass point in gravitational field is deduced. Based on the spherical symmetric solution of the field equation and the equation of motion of a mass point in gravitational field, we can discuss classical tests of gauge theory of gravity, including the deflection of light by the sun, the precession of the perihelia of the orbits of the inner planets and the time delay of radar echoes passing the sun. It is found that the theoretical predictions of these classical tests given by gauge theory of gravity are completely the same as those given by general relativity.
Stachel, J.
1977-01-01
A first-order Lagrangian is given, from which follow the definitions of the fully covariant form of the Riemann tensor Rsub(μνkappalambda) in terms of the affine connection and metric; the definition of the affine connection in terms of the metric; the Einstein field equations; and the definition of a set of gravitational 'superpotentials' closely connected with the Komar conservation laws (Phys. Rev.; 113:934 (1959)). Substitution of the definition of the affine connection into this Lagrangian results in a second-order Lagrangian, from which follow the definition of the fully covariant Riemann tensor in terms of the metric, the Einstein equations, and the definition of the gravitational 'superpotentials'. (author)
Gogala, B.
1983-01-01
The equations of the gauge theory of gravitation are derived from a complex quadratic Lagrangian with torsion. The derivation is performed in a coordinate basis in a completely covariant way. (author)
Baxter, Mathew; Van Gorder, Robert A
2013-01-01
We obtain solutions to a transformation of the axially symmetric Ernst equation, which governs a class of exact solutions of Einstein's field equations. Physically, the equation serves as a model of axially symmetric stationary vacuum gravitational fields. By an application of the method of homotopy analysis, we are able to construct approximate analytic solutions to the relevant boundary value problem in the case where exact solutions are not possible. The results presented constitute a solution for a complicated nonlinear and singular initial value problem. Through appropriate selection of the auxiliary linear operator and convergence control parameter, we are able to obtain low order approximations which minimize residual error over the problem domain. The benefit to such approach is that we obtain very accurate approximations after computing very few terms, hence the computational efficiency is high. Finally, an exact solution is provided in a special case, and this corresponds to the analytical solutions obtained in the more general case. The approximate solutions agree qualitatively with the exact solutions. (paper)
Chifu E. N.
2009-10-01
Full Text Available In this article, we formulate solutions to Einstein's geometrical field equations derived using our new approach. Our field equations exterior and interior to the mass distribution have only one unknown function determined by the mass or pressure distribution. Our obtained solutions yield the unknown function as generalizations of Newton's gravitational scalar potential. Thus, our solution puts Einstein's geometrical theory of gravity on same footing with Newton's dynamical theory; with the dependence of the field on one and only one unknown function comparable to Newton's gravitational scalar potential. Our results in this article are of much significance as the Sun and planets in the solar system are known to be more precisely oblate spheroidal in geometry. The oblate spheroidal geometries of these bodies have effects on their gravitational fields and the motions of test particles and photons in these fields.
The Theory of Vortical Gravitational Fields
Rabounski D.
2007-04-01
Full Text Available This paper treats of vortical gravitational fields, a tensor of which is the rotor of the general covariant gravitational inertial force. The field equations for a vortical gravitational field (the Lorentz condition, the Maxwell-like equations, and the continuity equation are deduced in an analogous fashion to electrodynamics. From the equations it is concluded that the main kind of vortical gravitational fields is “electric”, determined by the non-stationarity of the acting gravitational inertial force. Such a field is a medium for traveling waves of the force (they are different to the weak deformation waves of the space metric considered in the theory of gravitational waves. Standing waves of the gravitational inertial force and their medium, a vortical gravitational field of the “magnetic” kind, are exotic, since a non-stationary rotation of a space body (the source of such a field is a very rare phenomenon in the Universe.
Chifu E. N.
2009-07-01
Full Text Available Here, we present a profound and complete analytical solution to Einstein’s gravitational field equations exterior to astrophysically real or hypothetical time varying distribu- tions of mass or pressure within regions of spherical geometry. The single arbitrary function f in our proposed exterior metric tensor and constructed field equations makes our method unique, mathematically less combersome and astrophysically satisfactory. The obtained solution of Einstein’s gravitational field equations tends out to be a gen- eralization of Newton’s gravitational scalar potential exterior to the spherical mass or pressure distribution under consideration
Fiedler, B.; Schimming, R.
1983-01-01
The fourth order field equations proposed by TREDER with a linear combination of BACH's tensor and EINSTEIN's tensor on the left-hand side admit static centrally symmetric solutions which are analytical and non-flat in some neighborhood of the centre of symmetry. (author)
Exact Solutions of the Field Equations for Empty Space in the Nash Gravitational Theory
Matthew T. Aadne
2017-02-01
Full Text Available John Nash has proposed a new theory of gravity. We define a Nash-tensor equal to the curvature tensor appearing in the Nash field equations for empty space, and calculate its components for two cases: 1. A static, spherically symmetric space; and 2. The expanding, homogeneous and isotropic space of the Friedmann-Lemaitre-Robertson-Walker (FLRW universe models. We find the general, exact solution of Nash’s field equations for empty space in the static case. The line element turns out to represent the Schwarzschild-de Sitter spacetime. Also we find the simplest non-trivial solution of the field equations in the cosmological case, which gives the scale factor corresponding to the de Sitter spacetime. Hence empty space in the Nash theory corresponds to a space with Lorentz Invariant Vacuum Energy (LIVE in the Einstein theory. This suggests that dark energy may be superfluous according to the Nash theory. We also consider a radiation filled universe model in an effort to find out how energy and matter may be incorporated into the Nash theory. A tentative interpretation of the Nash theory as a unified theory of gravity and electromagnetism leads to a very simple form of the field equations in the presence of matter. It should be noted, however, that the Nash theory is still unfinished. A satisfying way of including energy momentum into the theory has yet to be found.
Gravitational and electromagnetic potentials of the stationary Einstein-Maxwell field equations
Jones, T.C.
1979-01-01
Associated with the stationary Einstein-Maxwell field equations is an infinite hierarchy of potentials. The basic characteristics of these potentials are examined in general and then in greater detail for the particular case of the Reissner-Nordstrom metric. Thier essential utility in the process of solution generation is elucidated, and the necessary equations for solution generation are developed. Appropriate generating functions, which contain the complete infinite hierarchy of potentials, are developed and analyzed. Particular attention is paid to the inherent gauge freedom of these generating functions. Two methods of solution generation, which yield asymptotically flat solutions in vacuum, are generalized to include electromagnetism. One method, using potentials consistent with the Harrison transformation and the Reissner-Nordstrom metric, is discussed in detail, and its resultant difficulties are explored
Poisson equation for weak gravitational lensing
Kling, Thomas P.; Campbell, Bryan
2008-01-01
Using the Newman and Penrose [E. T. Newman and R. Penrose, J. Math. Phys. (N.Y.) 3, 566 (1962).] spin-coefficient formalism, we examine the full Bianchi identities of general relativity in the context of gravitational lensing, where the matter and space-time curvature are projected into a lens plane perpendicular to the line of sight. From one component of the Bianchi identity, we provide a rigorous, new derivation of a Poisson equation for the projected matter density where the source term involves second derivatives of the observed weak gravitational lensing shear. We also show that the other components of the Bianchi identity reveal no new results. Numerical integration of the Poisson equation in test cases shows an accurate mass map can be constructed from the combination of a ground-based, wide-field image and a Hubble Space Telescope image of the same system
Budinich, Paolo
2009-03-01
In a previous paper we proposed a purely mathematical way to quantum mechanics based on Cartan's simple spinors in their most elementary form of 2 components spinors. Here we proceed along that path proposing, this time, a symmetric tensor, quadrilinear in simple spinors, as a candidate for the symmetric tensor of general relativity. The procedure resembles closely that in which one builds bilinearly from simple spinors an asymmetric electromagnetic tensor, from which easily descend Maxwell's equations and the photon can be seen as a bilinear combination of neutrinos. Here Lorentzian spaces result compact, building up spheres, where hopefully the problems of the Standard Model could be solved. (author)
Topological quantization of gravitational fields
Patino, Leonardo; Quevedo, Hernando
2005-01-01
We introduce the method of topological quantization for gravitational fields in a systematic manner. First we show that any vacuum solution of Einstein's equations can be represented in a principal fiber bundle with a connection that takes values in the Lie algebra of the Lorentz group. This result is generalized to include the case of gauge matter fields in multiple principal fiber bundles. We present several examples of gravitational configurations that include a gravitomagnetic monopole in linearized gravity, the C-energy of cylindrically symmetric fields, the Reissner-Nordstroem and the Kerr-Newman black holes. As a result of the application of the topological quantization procedure, in all the analyzed examples we obtain conditions implying that the parameters entering the metric in each case satisfy certain discretization relationships
Superconductor in a weak static gravitational field
Ummarino, Giovanni Alberto [Dipartimento DISAT, Politecnico di Torino, Turin (Italy); National Research Nuclear University MEPhI-Moscow Engineering Physics Institute, Moscow (Russian Federation); Gallerati, Antonio [Dipartimento DISAT, Politecnico di Torino, Turin (Italy)
2017-08-15
We provide the detailed calculation of a general form for Maxwell and London equations that takes into account gravitational corrections in linear approximation. We determine the possible alteration of a static gravitational field in a superconductor making use of the time-dependent Ginzburg-Landau equations, providing also an analytic solution in the weak field condition. Finally, we compare the behavior of a high-T{sub c} superconductor with a classical low-T{sub c} superconductor, analyzing the values of the parameters that can enhance the reduction of the gravitational field. (orig.)
On the field theoretic description of gravitation
Nieuwenhuizen, T.M.; Kleinert, H.; Jantzen, R.T.; Ruffini, R.
2008-01-01
Maxwell started to describe gravitation as a field in Minkowski space. Such an approach brought Babak and Grishchuk in 1999 the gravitational energy-momentum tensor. Simple manipulations allow the Einstein equations to take the form Aµν = (8πG/c4)Θµν, where A is the acceleration tensor and Θ, the
Gao, Xian; Kobayashi, Tsutomu; Yamaguchi, Masahide; Yokoyama, Jun'ichi
2011-11-18
We completely clarify the feature of primordial non-Gaussianities of tensor perturbations in the most general single-field inflation model with second-order field equations. It is shown that the most general cubic action for the tensor perturbation h(ij) is composed only of two contributions, one with two spacial derivatives and the other with one time derivative on each h(ij). The former is essentially identical to the cubic term that appears in Einstein gravity and predicts a squeezed shape, while the latter newly appears in the presence of the kinetic coupling to the Einstein tensor and predicts an equilateral shape. Thus, only two shapes appear in the graviton bispectrum of the most general single-field inflation model, which could open a new clue to the identification of inflationary gravitational waves in observations of cosmic microwave background anisotropies as well as direct detection experiments.
The earth's gravitational field
Ramprasad, T.
. But to say that gravity acts downwards is not correct. Gravity acts down, no matter where you stand on the Earth. It is better to say that on Earth gravity pulls objects towards the centre of the Earth. So no matter where you are on Earth all objects fall... pull than objects at the poles. In combination, the equatorial bulge and the effects of centrifugal force mean that sea-level gravitational acceleration increases from about 9.780 m/s² at the equator to about 9.832 m/s² at the poles, so an object...
Gravitational effects in field gravitation theory
Denisov, V.I.; Logunov, A.A.; Mestvirishvili, M.A.; Vlasov, A.A.
1979-01-01
The possibilities to describe various gravitation effects of field gravitation theory (FGT) are considered. Past-Newtonian approximation of the FGT has been constructed and on the basis of this approximation it has been shown that the field theory allows one to describe the whole set of experimental facts. The comparison of post-Newtonian parameters in FGT with those in the Einstein's theory makes it clear that these two; theories are undistinguishable from the viewpoint of any experiments, realized with post-Newtonian accuracy. Gravitational field of an island type source with spherically symmetrical distribution of matter and unstationary homogeneous model of Universe, which allows to describe the effect of cosmological red shift, are considered
The Rainich problem for coupled gravitational and scalar meson fields
Hyde, J.M.
1975-01-01
The equations of the coupled gravitational and scalar meson fields in general relativity are considered. It is shown that the wave equation for the scalar meson field which is usually specified explicitly in addition to the Einstein field equations is implied by Einstein's equations. Using this result it is then shown how the scalar field may be eliminated explicitly from the field equations, thus solving the Rainich problem for the coupled gravitational and scalar meson fields. (author) [fr
Gravitational field of relativistic gyratons
Frolov, Valeri P [Theoretical Physics Institute, Department of Physics, University of Alberta, Edmonton, AB, T6G 2J1 (Canada)
2007-05-15
A gyraton is an object moving with the speed of light and having finite energy and internal angular momentum (spin). First we derive the gravitational field of a gyraton in the linear approximation. After this we study solutions of the vacuum Einstein equations for gyratons. We demonstrate that these solutions in 4 and higher dimensions reduce to two linear problems in a Euclidean space. A similar reduction is also valid for gyraton solutions of the Einstein-Maxwell gravity and in supergravity. Namely, we demonstrate that in the both cases the solutions in 4 and higher dimensions reduce to linear problems in a Euclidean space.
Loop equations in the theory of gravitation
Makeenko, Yu.M.; Voronov, N.A.
1981-01-01
Loop-space variables (matrices of parallel transport) for the theory of gravitation are described. Loop equations, which are equivalent to the Einstein equations, are derived in the classical case. Loop equations are derived for gravity with cosmological constant as well. An analogy with the loop-space approach in Yang-Mills theory is discussed [ru
Schubert, G.; Anderson, J. D.
2013-12-01
Titan's gravitational field is inferred from an analysis of archived radio Doppler data for six Cassini flybys. The analysis considers each flyby separately in contrast to the approach of lumping all the data together in a massive inversion. In this way it is possible to gain an improved understanding of the character of each flyby and its usefulness in constraining the gravitational coefficient C22 . Though our analysis is not yet complete and our final determination of C22 could differ from the result we report here by 1 or 2 sigma, we find a best-fit value of C22 equal to (13.21 × 0.17) × 10-6, significantly larger than the value of 10.0 × 10-6 obtained from an inversion of the lumped Cassini data. We also find no determination of the tidal Love number k2. The larger value of C22 implies a moment of inertia factor equal to 0.3819 × 0.0020 and a less differentiated Titan than is suggested by the smaller value. The larger value of C22 is consistent with an undifferentiated model of the satellite. While it is not possible to rule out either value of C22 , we prefer the larger value because its derivation results from a more hands on analysis of the data that extracts the weak hydrostatic signal while revealing the effects of gravity anomalies and unmodeled spacecraft accelerations on each of the six flybys.
Equation of motion for the axial gravitational superfield
Ogievetsky, V.; Sokatchev, E.
1980-01-01
Transformation properties of the axial supergravitational field variants are investigated. The equation of motion for the axial gravitational superfield is derived by direct variation of the N = 1 supergravity action. The left-hand side of this equation is a component of the torsion tensor, and the right-hand side is the supercurrent. The question about the cosmological term in supergravity is discussed
Einstein equation and Yang-Mills theory of gravitation
Stedile, E.
1988-01-01
The possibility of Yang Mills theory of gravitation being a candidate as a gauge model for the Poincare group is pointed out. If the arguments favoring this theory are accepted then Einstein's equations can be derived by a different method in which they arise from a dynamical equation for the torsion field, in a particular case. (author) [pt
Gravitational peculiarities of a scalar field
Kleber, A.; Fonseca Teixeira, A.F. da
1979-11-01
The zero-adjoint of a time-static Ricci-flat solution to Einstein's field equations is investigated. It represents a spacetime curved solely by a massless scalar field. The cylindrical symmetry is assumed to permit both planar and non-planar geodetic motions. Unusual, velocity-dependent gravitational features are encountered from these geodesics. (Author) [pt
Quantum phenomena in gravitational field
Bourdel, Th.; Doser, M.; Ernest, A. D.; Voronin, A. Yu.; Voronin, V. V.
2011-10-01
The subjects presented here are very different. Their common feature is that they all involve quantum phenomena in a gravitational field: gravitational quantum states of ultracold antihydrogen above a material surface and measuring a gravitational interaction of antihydrogen in AEGIS, a quantum trampoline for ultracold atoms, and a hypothesis on naturally occurring gravitational quantum states, an Eötvös-type experiment with cold neutrons and others. Considering them together, however, we could learn that they have many common points both in physics and in methodology.
Quantum phenomena in gravitational field
Bourdel, Th.; Doser, M.; Ernest, A.D.; Voronin, A.Y.; Voronin, V.V.
2010-01-01
The subjects presented here are very different. Their common feature is that they all involve quantum phenomena in a gravitational field: gravitational quantum states of ultracold anti-hydrogen above a material surface and measuring a gravitational interaction of anti-hydrogen in AEGIS, a quantum trampoline for ultracold atoms, and a hypothesis on naturally occurring gravitational quantum states, an Eoetvoes-type experiment with cold neutrons and others. Considering them together, however, we could learn that they have many common points both in physics and in methodology. (authors)
Quantum gravitational corrections to the functional Schroedinger equation
Kiefer, C.; Singh, T.P.
1990-10-01
We derive corrections to the Schroedinger equation which arise from the quantization of the gravitational field. This is achieved through an expansion of the full functional Wheeler-DeWitt equation with respect to powers of the Planck mass. We demonstrate that the corrections terms are independent of the factor ordering which is chosen for the gravitational kinetic term. Although the corrections are numerically extremely tiny, we show how they lead, at least in principle, to shift in the spectral lines of hydrogen type atoms. We discuss the significance of these corrections for quantum field theory near the Planck scale. (author). 35 refs
An electric field in a gravitational field
Harpaz, Amos
2005-01-01
The behaviour of an electric field in a gravitational field is analysed. It is found that due to the mass (energy) of the electric field, it is subjected to gravity and it falls in the gravitational field. This fall curves the electric field, a stress force (a reaction force) is created, and the interaction of this reaction force with the static charge gives rise to the creation of radiation
R. Vlokh; M. Kostyrko
2006-01-01
Nonlinear effect of the gravitation field of spherically symmetric mass on the gravitational coefficient G has been analysed. In frame of the approaches of parametric optics and gravitation nonlinearity we have shown that the gravitation field of spherically symmetric mass can lead to changes in the gravitational coefficient G.
Relativistic equations for axisymmetric gravitational collapse with escaping neutrinos
Patel, M.D.
1979-01-01
Einstein's field equations for the dynamics of a self-gravitating axially symmetric source of a perfect fluid, presented by Chandrasekhar and Friedman (1964), are modified to allow emission of neutrinos. The boundary conditions at the outer surface of the radiating axisymmetric source are obtained by matching to an exterior solution of an axisymmetric rotating, radiating core. (auth.)
Penrose, R.
1986-01-01
The author's definition for the mass-momentum/angular momentum surrounded by a spacelike 2-surface with S/sup 2/ topology is presented. This definition is motivated by some ideas from twistor theory in relation to linearized gravitational theory. The status of this definition is examined in relation to many examples which have been worked out. The reason for introducing a slight modification of the original definition is also presented
On the relativistic particle dynamics in external gravitational fields
Kuz'menkov, L.S.; Naumov, N.D.
1977-01-01
On the base of the Riemann metrics of an event space, leading to the Newton mechanics at nonrelativistic velocities and not obligatory weak gravitational fields relativistic particle dynamics in external gravitation fields has been considered. Found are trajectories, motion laws and light ray equations for the homogeneous and Newton fields
A distinguishing gravitational property for gravitational equation in higher dimensions
Dadhich, Naresh
2016-01-01
It is well known that Einstein gravity is kinematic (meaning that there is no non-trivial vacuum solution; i.e. the Riemann tensor vanishes whenever the Ricci tensor does so) in 3 dimension because the Riemann tensor is entirely given in terms of the Ricci tensor. Could this property be universalized for all odd dimensions in a generalized theory? The answer is yes, and this property uniquely singles out pure Lovelock (it has only one Nth order term in the action) gravity for which the Nth order Lovelock-Riemann tensor is indeed given in terms of the corresponding Ricci tensor for all odd, d = 2N + 1, dimensions. This feature of gravity is realized only in higher dimensions and it uniquely picks out pure Lovelock gravity from all other generalizations of Einstein gravity. It serves as a good distinguishing and guiding criterion for the gravitational equation in higher dimensions. (orig.)
A distinguishing gravitational property for gravitational equation in higher dimensions
Dadhich, Naresh
2016-03-01
It is well known that Einstein gravity is kinematic (meaning that there is no non-trivial vacuum solution; i.e. the Riemann tensor vanishes whenever the Ricci tensor does so) in 3 dimension because the Riemann tensor is entirely given in terms of the Ricci tensor. Could this property be universalized for all odd dimensions in a generalized theory? The answer is yes, and this property uniquely singles out pure Lovelock (it has only one Nth order term in the action) gravity for which the Nth order Lovelock-Riemann tensor is indeed given in terms of the corresponding Ricci tensor for all odd, d=2N+1, dimensions. This feature of gravity is realized only in higher dimensions and it uniquely picks out pure Lovelock gravity from all other generalizations of Einstein gravity. It serves as a good distinguishing and guiding criterion for the gravitational equation in higher dimensions.
Field theory approach to gravitation
Yilmaz, H.
1978-01-01
A number of authors considered the possibility of formulating a field-theory approach to gravitation with the claim that such an approach would uniquely lead to Einstein's theory of general relativity. In this article it is shown that the field theory approach is more generally applicable and uniqueness cannot be claimed. Theoretical and experimental reasons are given showing that the Einsteinian limit appears to be unviable
Gravitation and bilocal field theory
Vollendorf, F.
1975-01-01
The starting point is the conjecture that a field theory of elementary particles can be constructed only in a bilocal version. Thus the 4-dimensional space time has to be replaced by the 8-dimensional manifold R 8 of all ordered pairs of space time events. With special reference to the Schwarzschild metric it is shown that the embedding of the time space into the manifold R 8 yields a description of the gravitational field. (orig.) [de
A modified Friedmann equation for a system with varying gravitational mass
Gorkavyi, Nick; Vasilkov, Alexander
2018-05-01
The Laser Interferometer Gravitational-Wave Observatory (LIGO) detection of gravitational waves that take away 5 per cent of the total mass of two merging black holes points out on the importance of considering varying gravitational mass of a system. Using an assumption that the energy-momentum pseudo-tensor of gravitational waves is not considered as a source of gravitational field, we analyse a perturbation of the Friedmann-Robertson-Walker metric caused by the varying gravitational mass of a system. This perturbation leads to a modified Friedmann equation that contains a term similar to the `cosmological constant'. Theoretical estimates of the effective cosmological constant quantitatively corresponds to observed cosmological acceleration.
Forces in electromagnetic field and gravitational field
Weng, Zihua
2008-01-01
The force can be defined from the linear momentum in the gravitational field and electromagnetic field. But this definition can not cover the gradient of energy. In the paper, the force will be defined from the energy and torque in a new way, which involves the gravitational force, electromagnetic force, inertial force, gradient of energy, and some other new force terms etc. One of these new force terms can be used to explain why the solar wind varies velocity along the magnetic force line in...
Generalized field theory of gravitation
Yilmaz, H.
1976-01-01
It is shown that if, on empirical grounds, one rules out the existence of cosmic fields of Dicke-Brans (scalar) and Will Nordvedt (vector, tensor) type, then the most general experimentally viable and theoretically reasonable theory of gravitation seems to be a LAMBDA-dependent generalization of Einstein and Yilmez theories, which reduces to the former for LAMBDA=0 and to the latter for LAMBDA=1
Relativity in Combinatorial Gravitational Fields
Mao Linfan
2010-04-01
Full Text Available A combinatorial spacetime $(mathscr{C}_G| uboverline{t}$ is a smoothly combinatorial manifold $mathscr{C}$ underlying a graph $G$ evolving on a time vector $overline{t}$. As we known, Einstein's general relativity is suitable for use only in one spacetime. What is its disguise in a combinatorial spacetime? Applying combinatorial Riemannian geometry enables us to present a combinatorial spacetime model for the Universe and suggest a generalized Einstein gravitational equation in such model. Forfinding its solutions, a generalized relativity principle, called projective principle is proposed, i.e., a physics law ina combinatorial spacetime is invariant under a projection on its a subspace and then a spherically symmetric multi-solutions ofgeneralized Einstein gravitational equations in vacuum or charged body are found. We also consider the geometrical structure in such solutions with physical formations, and conclude that an ultimate theory for the Universe maybe established if all such spacetimes in ${f R}^3$. Otherwise, our theory is only an approximate theory and endless forever.
Stationary two-variable gravitational vortex fields
Koppel, A.
1974-01-01
Some properties of stationary two-variable solutions of the Einstein equations were studied on the basis of rigorous analysis of the nonrelativistic limit of the relativistic gravitation theory. For this case a particular method was developed of determining so-called vortex gravitational fields described by vortex solutions, which in the nonrelativistic limit transform from → infinity to the nonnewtonian type solutions. The main formulae for such fields are derived and a scheme for their calculation is presented. It is shown that under certain conditions the exact stationary solutions of the Papapetrou type for vacuum relativistic equations are vortical. From this fact, first, the presence of particular exact vortical solutions for the Einstein equations is proved, and secondly, a new possibility of a physical interpretation is proposed for the Papapetrou solutions. It is also shown that the nonrelativistic limit of this class of solutions strongly depends on the structure of solution parameters (under certain conditions these solutions may also have the Newtonian limit). 'Multipole' and 'one-variable' partial solutions of the Papapetrou class solution are derived as particular examples of vortical solutions. It is shown that for a specific parameter structure the known NUT solution is also vortical, since it belongs to the Papapetrou class [ru
Space-time algebra for the generalization of gravitational field
The Maxwell–Proca-like field equations of gravitolectromagnetism are formulated using space-time algebra (STA). The gravitational wave equation with massive gravitons and gravitomagnetic monopoles has been derived in terms of this algebra. Using space-time algebra, the most generalized form of ...
Interaction of gravitational waves with magnetic and electric fields
Barrabes, C.; Hogan, P. A.
2010-01-01
The existence of large-scale magnetic fields in the universe has led to the observation that if gravitational waves propagating in a cosmological environment encounter even a small magnetic field then electromagnetic radiation is produced. To study this phenomenon in more detail we take it out of the cosmological context and at the same time simplify the gravitational radiation to impulsive waves. Specifically, to illustrate our findings, we describe the following three physical situations: (1) a cylindrical impulsive gravitational wave propagating into a universe with a magnetic field, (2) an axially symmetric impulsive gravitational wave propagating into a universe with an electric field and (3) a 'spherical' impulsive gravitational wave propagating into a universe with a small magnetic field. In cases (1) and (3) electromagnetic radiation is produced behind the gravitational wave. In case (2) no electromagnetic radiation appears after the wave unless a current is established behind the wave breaking the Maxwell vacuum. In all three cases the presence of the magnetic or electric fields results in a modification of the amplitude of the incoming gravitational wave which is explicitly calculated using the Einstein-Maxwell vacuum field equations.
Quantum field theory in gravitational background
Narnhofer, H.
1986-01-01
The author suggests ignoring the influence of the quantum field on the gravitation as the first step to combine quantum field theory and gravitation theory, but to consider the gravitational field as fixed and thus study quantum field theory on a manifold. This subject evoked interest when thermal radiation of a black hole was predicted. The author concentrates on the free quantum field and can split the problem into two steps: the Weyl-algebra of the free field and the Wightman functional on the tangent space
Theory of gravitational-inertial field of universe. 2
Davtyan, O.K.
1978-01-01
Application of the equations of the gravitational-inertial field to the problem of free motion in the inertial field (to the cosmologic problem) leads to results according to which (1) all Galaxies in the Universe 'disperse' from each other according to Hubble's law, (2) the 'dispersion' of bodies represents a free motion in the inertial field and Hubble's law represents a law of motion of free body in the inertial field, (3) for arbitrary mean distribution densities of space masses different from zero the space is Lobachevskian. All critical systems (with Schwarzschild radius) are specific because they exist in maximal-inertial and gravitational potentials. The Universe represents a critical system, it exists under the Schwarzschild radius. In high-potential inertial and gravitational fields the material mass in a static state or in motion with deceleration is subject to an inertial and gravitational 'annihilation'. At the maximal value of inertial and gravitational potentials (= c 2 ) the material mass is being completely 'evaporated' transforming into radiation mass. The latter is being concentrated in the 'horizon' of the critical system. All critical systems-black holes-represent geon systems, i.e. local formations of gravitational-electromagnetic radiations, held together by their own gravitational and inertial fields. The Universe, being a critical system, is 'wrapped' in a geon crown. (author)
Hydrodynamics, fields and constants in gravitational theory
Stanyukovich, K.P.; Mel'nikov, V.N.
1983-01-01
Results of original inveatigations into problems of standard gravitation theory and its generalizations are presented. The main attention is paid to the application of methods of continuous media techniques in the gravitation theory; to the specification of the gravitation role in phenomena of macro- and microworld, accurate solutions in the case, when the medium is the matter, assigned by hydrodynamic energy-momentum tensor; and to accurate solutions for the case when the medium is the field. GRT generalizations are analyzed, such as the new cosmologic hypothesis which is based on the gravitation vacuum theory. Investigations are performed into the quantization of cosmological models, effects of spontaneous symmetry violation and particle production in cosmology. Graeity theory with fundamental Higgs field is suggested in the framework of which in the atomic unit number one can explain possible variations of the effective gravitational bonds, and in the gravitation bond, variations of masses of all particles
Gravitational Field Shielding by Scalar Field and Type II Superconductors
Zhang B. J.
2013-01-01
Full Text Available The gravitational field shielding by scalar field and type II superconductors are theoret- ically investigated. In accord with the well-developed five-dimensional fully covariant Kaluza-Klein theory with a scalar field, which unifies the Einsteinian general relativity and Maxwellian electromagnetic theory, the scalar field cannot only polarize the space as shown previously, but also flatten the space as indicated recently. The polariza- tion of space decreases the electromagnetic field by increasing the equivalent vacuum permittivity constant, while the flattening of space decreases the gravitational field by decreasing the equivalent gravitational constant. In other words, the scalar field can be also employed to shield the gravitational field. A strong scalar field significantly shield the gravitational field by largely decreasing the equivalent gravitational constant. According to the theory of gravitational field shielding by scalar field, the weight loss experimentally detected for a sample near a rotating ceramic disk at very low tempera- ture can be explained as the shielding of the Earth gravitational field by the Ginzburg- Landau scalar field, which is produced by the type II superconductors. The significant shielding of gravitational field by scalar field produced by superconductors may lead to a new spaceflight technology in future.
Theory of gravitational-inertial field of universe. 1
Davtyan, O.K.
1978-01-01
A generalization of the real world tensor by the introduction of a inertial field tensor is proposed. On the basis of variational equations a system of more general covariant equations of the gravitational-inertial field is obtained. In the Einstein approximation these equations reduce to the field equations of Einstein. The solution of fundamental problems in the general theory of relativity by means of the new equations gives the same results as the solution by means of Einstein's equations. However, application of these equations to the cosmologic problem gives a result different from that obtained by Friedmann's theory. In particular, the solution gives the Hubble law as the law of motion of a free body in the inertial field - in contrast to Galileo-Newton's law. (author)
Relativistic gravitation from massless systems of scalar and vector fields
Fonseca Teixeira, A.F. da.
1979-01-01
Under the laws of Einstein's gravitational theory, a massless system consisting of the diffuse sources of two fields is discussed. One fields is scalar, of long range, the other is a vector field of short range. A proportionality between the sources is assumed. Both fields are minimally coupled to gravitation, and contribute positive definitely to the time component of the energy momentum tensor. A class of static, spherically symmetric solutions of the equations is obtained, in the weak field limit. The solutions are regular everywhere, stable, and can represent large or small physical systems. The gravitational field presents a Schwarzschild-type asymptotic behavior. The dependence of the energy on the various parameters characterizing the system is discussed in some detail. (Author) [pt
New Metrics from a Fractional Gravitational Field
El-Nabulsi, Rami Ahmad
2017-01-01
Agop et al. proved in Commun. Theor. Phys. (2008) that, a Reissner–Nordstrom type metric is obtained, if gauge gravitational field in a fractal spacetime is constructed by means of concepts of scale relativity. We prove in this short communication that similar result is obtained if gravity in D-spacetime dimensions is fractionalized by means of the Glaeske–Kilbas–Saigo fractional. Besides, non-singular gravitational fields are obtained without using extra-dimensions. We present few examples to show that these gravitational fields hold a number of motivating features in spacetime physics. (paper)
Stationary axisymmetric Einstein--Maxwell field equations
Catenacci, R.; Diaz Alonso, J.
1976-01-01
We show the existence of a formal identity between Einstein's and Ernst's stationary axisymmetric gravitational field equations and the Einstein--Maxwell and the Ernst equations for the electrostatic and magnetostatic axisymmetric cases. Our equations are invariant under very simple internal symmetry groups, and one of them appears to be new. We also obtain a method for associating two stationary axisymmetric vacuum solutions with every electrostatic known
Gravitational Field of Ultrarelativistic Objects with Angular Momentum
Fursaev, Dmitri V
2006-01-01
A brief review of recently found gyraton metrics which describe the gravitational field of objects having an angular momentum and moving with the velocity of light is given. The gyraton metrics belong to a class of exact plane wave solutions of four and higher dimensional Einstein equations in vacuum or in the presence of a negative cosmological constant
Gravitational field of spherical domain wall in higher dimension
and examine whether bound orbits are possible or not. This study will be of relevance to the structure formation because it gives some idea about the behaviour of the particles. (created at the early universe) in the gravitational field of the domain walls. Our paper is organized as follows: The basic equations are constructed ...
Gravitational Field of Ultrarelativistic Objects with Angular Momentum
Fursaev, Dmitri V [Dubna International University and Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141 980, Dubna, Moscow Region (Russian Federation)
2006-03-01
A brief review of recently found gyraton metrics which describe the gravitational field of objects having an angular momentum and moving with the velocity of light is given. The gyraton metrics belong to a class of exact plane wave solutions of four and higher dimensional Einstein equations in vacuum or in the presence of a negative cosmological constant.
Tao Fuzhen; He Zhiqiang
1983-01-01
If the effect of gravitational wave on electromagnetic fields is used, and the gravitational wave is detected through the changes in electromagnetic fields, one can expect that the difficulty about the weakness of the signal of mechanical receiver can be avoided. Because of the effect of gravitational wave, the electromagnetic field emits energy, therefore, the energy which is detected will be higher than that by the mechanical receiver. The authors consider the Maxwell equations on the curved spacetime. They give solutions when the detecting fields are a free electromagnetic wave, standing wave and a constant field. (Auth.)
On energy-momentum tensors of gravitational field
Nikishov, A.I.
2001-01-01
The phenomenological approach to gravitation is discussed in which the 3-graviton interaction is reduced to the interaction of each graviton with the energy-momentum tensor of two others. If this is so, (and in general relativity this is not so), then the problem of choosing the correct energy-momentum tensor comes to finding the right 3-graviton vertex. Several energy-momentum tensors od gravitational field are considered and compared in the lowest approximation. Each of them together with the energy-momentum tensor of point-like particles satisfies the conservation laws when equations of motion of particles are the same as in general relativity. It is shown that in Newtonian approximation the considered tensors differ one from other in the way their energy density is distributed between energy density of interaction (nonzero only at locations of particles) and energy density of gravitational field. Stating from Lorentz invariance, the Lagrangians for spin-2, mass-0 field are considered [ru
Physical optics in a uniform gravitational field
Hacyan, Shahen
2012-01-01
The motion of a (quasi-)plane wave in a uniform gravitational field is studied. It is shown that the energy of an elliptically polarized wave does not propagate along a geodesic, but in a direction that is rotated with respect to the gravitational force. The similarity with the walk-off effect in anisotropic crystals or the optical Magnus effect in inhomogeneous media is pointed out.
Exact Foldy-Wouthuysen transformation for gravitational waves and magnetic field background
Goncalves, Bruno; Obukhov, Yuri N.; Shapiro, Ilya L.
2007-01-01
We consider an exact Foldy-Wouthuysen transformation for the Dirac spinor field on the combined background of a gravitational wave and constant uniform magnetic field. By taking the classical limit of the spinor field Hamiltonian, we arrive at the equations of motion for the nonrelativistic spinning particle. Two different kinds of gravitational fields are considered and in both cases the effect of the gravitational wave on the spinor field and on the corresponding spinning particle may be enforced by a sufficiently strong magnetic field. This result can be relevant for astrophysical applications and, in principle, useful for creating the gravitational wave detectors based on atomic physics and precise interferometry
Hyperunified field theory and gravitational gauge-geometry duality
Wu, Yue-Liang
2018-01-01
A hyperunified field theory is built in detail based on the postulates of gauge invariance and coordinate independence along with the conformal scaling symmetry. All elementary particles are merged into a single hyper-spinor field and all basic forces are unified into a fundamental interaction governed by the hyper-spin gauge symmetry SP(1, D h - 1). The dimension D h of hyper-spacetime is conjectured to have a physical origin in correlation with the hyper-spin charge of elementary particles. The hyper-gravifield fiber bundle structure of biframe hyper-spacetime appears naturally with the globally flat Minkowski hyper-spacetime as a base spacetime and the locally flat hyper-gravifield spacetime as a fiber that is viewed as a dynamically emerged hyper-spacetime characterized by a non-commutative geometry. The gravitational origin of gauge symmetry is revealed with the hyper-gravifield that plays an essential role as a Goldstone-like field. The gauge-gravity and gravity-geometry correspondences bring about the gravitational gauge-geometry duality. The basic properties of hyperunified field theory and the issue on the fundamental scale are analyzed within the framework of quantum field theory, which allows us to describe the laws of nature in deriving the gauge gravitational equation with the conserved current and the geometric gravitational equations of Einstein-like type and beyond. (orig.)
Hyperunified field theory and gravitational gauge-geometry duality
Wu, Yue-Liang [International Centre for Theoretical Physics Asia-Pacific (ICTP-AP), Beijing (China); Chinese Academy of Sciences, Institute of Theoretical Physics, Beijing (China); University of Chinese Academy of Sciences (UCAS), Beijing (China)
2018-01-15
A hyperunified field theory is built in detail based on the postulates of gauge invariance and coordinate independence along with the conformal scaling symmetry. All elementary particles are merged into a single hyper-spinor field and all basic forces are unified into a fundamental interaction governed by the hyper-spin gauge symmetry SP(1, D{sub h} - 1). The dimension D{sub h} of hyper-spacetime is conjectured to have a physical origin in correlation with the hyper-spin charge of elementary particles. The hyper-gravifield fiber bundle structure of biframe hyper-spacetime appears naturally with the globally flat Minkowski hyper-spacetime as a base spacetime and the locally flat hyper-gravifield spacetime as a fiber that is viewed as a dynamically emerged hyper-spacetime characterized by a non-commutative geometry. The gravitational origin of gauge symmetry is revealed with the hyper-gravifield that plays an essential role as a Goldstone-like field. The gauge-gravity and gravity-geometry correspondences bring about the gravitational gauge-geometry duality. The basic properties of hyperunified field theory and the issue on the fundamental scale are analyzed within the framework of quantum field theory, which allows us to describe the laws of nature in deriving the gauge gravitational equation with the conserved current and the geometric gravitational equations of Einstein-like type and beyond. (orig.)
Hyperunified field theory and gravitational gauge-geometry duality
Wu, Yue-Liang
2018-01-01
A hyperunified field theory is built in detail based on the postulates of gauge invariance and coordinate independence along with the conformal scaling symmetry. All elementary particles are merged into a single hyper-spinor field and all basic forces are unified into a fundamental interaction governed by the hyper-spin gauge symmetry SP(1, D_h-1). The dimension D_h of hyper-spacetime is conjectured to have a physical origin in correlation with the hyper-spin charge of elementary particles. The hyper-gravifield fiber bundle structure of biframe hyper-spacetime appears naturally with the globally flat Minkowski hyper-spacetime as a base spacetime and the locally flat hyper-gravifield spacetime as a fiber that is viewed as a dynamically emerged hyper-spacetime characterized by a non-commutative geometry. The gravitational origin of gauge symmetry is revealed with the hyper-gravifield that plays an essential role as a Goldstone-like field. The gauge-gravity and gravity-geometry correspondences bring about the gravitational gauge-geometry duality. The basic properties of hyperunified field theory and the issue on the fundamental scale are analyzed within the framework of quantum field theory, which allows us to describe the laws of nature in deriving the gauge gravitational equation with the conserved current and the geometric gravitational equations of Einstein-like type and beyond.
Scalar, electromagnetic, and gravitational fields interaction: Particlelike solutions
Bronnikov, K.A.; Melnikov, V.N.; Shikin, G.N.; Staniukovich, K.P.
1979-01-01
Particlelike static spherically symmetric solutions to massless scalar and electromagnetic field equations combined with gravitational field equations are considered. Two criteria for particlelike solutions are formulated: the strong one (solutions are required to be singularity free) and the weak one (singularities are admitted but the total energy and material field energy should be finite). Exact solutions for the following physical systems are considered with their own gravitational field: (i) linear scalar (minimally coupled or conformal) plus electromagnetic field; (ii) the same fields with a bare mass source in the form of charged incoherent matter distributions; (iii) nonlinear electromagnetic field with an abritrary dependence on the invariant F/sub alphabeta/F/sup alphabeta/; and (iv) directly interacting scalar and electromagnetic fields. Case (i) solutions are not particlelike (except those with horizons, in which static regions formally satisfy the weak criterion). For systems (ii), examples of nonsingular models are constructed, in particular, a model for a particle--antiparticle pair of a Wheeler-handle type, without scalar field and explict electric charges. Besides, a number of limitations upon nonsingular model parameters is indicated. Systems (iii) are proved to violate the strong criterion for any type of nonlinearity but can satisfy the weak criterion (e.g., the Born--Infeld nonlinearity). For systems (iv) some particlelike solutions by the weak criterion are constructed and a regularizing role of gravitation is demonstrated. Finally, an example of a field system satisfying the strong criterion is given
Derivation of the Finslerian gauge field equations
Asanov, G.S.
1984-01-01
As is well known the simplest way of formulating the equations for the Yang-Mills gauge fields consists in taking the Lagrangian to be quadratic in the gauge tensor, whereas the application of such an approach to the gravitational field yields equations which are of essentially more complicated structure than the Einstein equations. On the other hand, in the gravitational field theory the Lagrangian can be constructed to be of forms which may be both quadratic and linear in the curvature tensor, whereas the latter possibility is absent in the current gauge field theories. In previous work it has been shown that the Finslerian structure of the space-time gives rise to certain gauge fields provided that the internal symmetries may be regarded as symmetries of a three-dimensional Riemannian space. Continuing this work we show that appropriate equations for these gauge fields can be formulated in both ways, namely on the basis of the quadratic Lagrangian or, if a relevant generalization of the Palatini method is applied, on the basis of a Lagrangian linear in the gauge field strength tensor. The latter possibility proves to result in equations which are similar to the Einstein equations, a distinction being that the Finslerian Cartan curvature tensor rather then the Riemann curvature tensor enters the equations. (author)
Neutron stars, magnetic fields, and gravitational waves
Lamb, F.K.
2001-01-01
The r-modes of rapidly spinning young neutron stars have recently attracted attention as a promising source of detectable gravitational radiation. These neutron stars are expected to have magnetic fields ∼ 10 12 G. The r-mode velocity perturbation causes differential motion of the fluid in the star; this is a kinematic effect. In addition, the radiation-reaction associated with emission of gravitational radiation by r-waves drives additional differential fluid motions; this is a dynamic effect. These differential fluid motions distort the magnetic fields of neutron stars and may therefore play an important role in determining the structure of neutron star magnetic fields. If the stellar field is ∼ 10 16 (Ω/Ω B ) G or stronger, the usual r-modes are no longer normal modes of the star; here Ω and Ω B are the angular velocities of the star and at which mass shedding occurs. Much weaker magnetic fields can prevent gravitational radiation from amplifying the r-modes or damp existing r-mode oscillations on a relatively short timescale by extracting energy from the modes faster than gravitational wave emission can pump energy into them. The onset of proton superconductivity in the cores of newly formed magnetic neutron stars typically increases the effect on the r-modes of the magnetic field in the core by many orders of magnitude. Once the core has become superconducting, magnetic fields of the order of 10 12 G or greater are usually sufficient to damp r-modes that have been excited by emission of gravitational radiation and to suppress any further emission. A rapid drop in the strength of r-mode gravitational radiation from young neutron stars may therefore signal the onset of superconductivity in the core and provide a lower bound on the strength of the magnetic field there. Hence, measurements of r-mode gravitational waves from newly formed neutron stars may provide valuable diagnostic information about magnetic field strengths, cooling processes, and the
Gravitational waves from scalar field accretion
Nunez, Dario; Degollado, Juan Carlos; Moreno, Claudia
2011-01-01
Our aim in this work is to outline some physical consequences of the interaction between black holes and scalar field halos in terms of gravitational waves. In doing so, the black hole is taken as a static and spherically symmetric gravitational source, i.e. the Schwarzschild black hole, and we work within the test field approximation, considering that the scalar field lives in the curved space-time outside the black hole. We focused on the emission of gravitational waves when the black hole is perturbed by the surrounding scalar field matter. The symmetries of the space-time and the simplicity of the matter source allow, by means of a spherical harmonic decomposition, to study the problem by means of a one-dimensional description. Some properties of such gravitational waves are discussed as a function of the parameters of the infalling scalar field, and allow us to make the conjecture that the gravitational waves carry information on the type of matter that generated them.
Two-time physics with gravitational and gauge field backgrounds
Bars, Itzhak
2000-01-01
It is shown that all possible gravitational, gauge and other interactions experienced by particles in ordinary d dimensions (one time) can be described in the language of two-time physics in a spacetime with d+2 dimensions. This is obtained by generalizing the world line formulation of two-time physics by including background fields. A given two-time model, with a fixed set of background fields, can be gauged fixed from d+2 dimensions to (d-1)+1 dimensions to produce diverse one-time dynamical models, all of which are dually related to each other under the underlying gauge symmetry of the unified two-time theory. To satisfy the gauge symmetry of the two-time theory the background fields must obey certain coupled differential equations that are generally covariant and gauge invariant in the target (d+2)-dimensional spacetime. The gravitational background obeys a closed homothety condition while the gauge field obeys a differential equation that generalizes a similar equation derived by Dirac in 1936. Explicit solutions to these coupled equations show that the usual gravitational, gauge, and other interactions in d dimensions may be viewed as embedded in the higher (d+2)-dimensional space, thus displaying higher spacetime symmetries that otherwise remain hidden
Gravitational field of charged gyratons
Frolov, Valeri P [Theoretical Physics Institute, University of Alberta, Edmonton, Alberta, T6G 2J1 (Canada); Zelnikov, Andrei [Theoretical Physics Institute, University of Alberta, Edmonton, Alberta, T6G 2J1 (Canada); Lebedev Physics Institute, Leninsky prospect 53, 119 991, Moscow (Russian Federation)
2006-03-21
We study relativistic gyratons which carry an electric charge. The Einstein-Maxwell equations in arbitrary dimensions are solved exactly in the case of a charged gyraton propagating in an asymptotically flat metric.
Covariant field equations in supergravity
Vanhecke, Bram [KU Leuven, Institute for Theoretical Physics, Leuven (Belgium); Ghent University, Faculty of Physics, Gent (Belgium); Proeyen, Antoine van [KU Leuven, Institute for Theoretical Physics, Leuven (Belgium)
2017-12-15
Covariance is a useful property for handling supergravity theories. In this paper, we prove a covariance property of supergravity field equations: under reasonable conditions, field equations of supergravity are covariant modulo other field equations. We prove that for any supergravity there exist such covariant equations of motion, other than the regular equations of motion, that are equivalent to the latter. The relations that we find between field equations and their covariant form can be used to obtain multiplets of field equations. In practice, the covariant field equations are easily found by simply covariantizing the ordinary field equations. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Covariant field equations in supergravity
Vanhecke, Bram; Proeyen, Antoine van
2017-01-01
Covariance is a useful property for handling supergravity theories. In this paper, we prove a covariance property of supergravity field equations: under reasonable conditions, field equations of supergravity are covariant modulo other field equations. We prove that for any supergravity there exist such covariant equations of motion, other than the regular equations of motion, that are equivalent to the latter. The relations that we find between field equations and their covariant form can be used to obtain multiplets of field equations. In practice, the covariant field equations are easily found by simply covariantizing the ordinary field equations. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Newtonian and non-newtonian limits of gravitational fields
Koppel', A.A.
1975-01-01
The nonrelativistic limit of the exact stationary axially-symmetric vacuum solution to Einstein equations, which is called the unified (generalized) Kerr-NUT solution, is investigated. Potentials for nonrelativistic gravitational fields, corresponding to this solution, have been calculated. The character of the c→infinity limit (c is the velocity of light) has been shown to depend on the structure of parameters of the Kerr-NUT solution. An example is given that shows the possibility of the existence of a nonrelativistic limit having an absolutely new, non-Newton (vortex) character. From the mathematically proved possibility of the existence of nonrelativistic vortex fields there follow also some implications of a more fundamental character. The Newton limit is commonly supposed to be the only nonrelativistic limit in the Einstein theory. Now there arises a dilemma: either gravitational fields having a non-Newton limit exist in nature and thus the Newton theory does not embrace all gravitational phenomena of nonrelativistic character or in the Newton solutions to the nonrelativistic gravitational equations a certain element of the Einstein theory is revealed that is alien to the true nonrelativistic theory of gravitation. In the former case, one cannot exclude the possibility that owing to a comprehensive analysis of properties, possible sources, etc. the vortex soltions to Einstein equations may prove important in cosmological and astrophysical applications of the general relativity theory. In the latter case, a detailed analysis of the non-Newton-limit solutions will at least enable one to gain a deeper insight into the structure of Einstein equations and their solutions
Newtonian and non-newtonian limits of gravitational fields
Koppel, A A [Tartuskij Gosudarstvennyj Univ., (USSR)
1975-09-01
The nonrelativistic limit of the exact stationary axially-symmetric vacuum solution to Einstein equations, which is called the unified (generalized) Kerr-NUT solution, is investigated. Potentials for nonrelativistic gravitational fields, corresponding to this solution, have been calculated. The character of the c..-->..infinity limit (c is the velocity of light) has been shown to depend on the structure of parameters of the Kerr-NUT solution. An example is given that shows the possibility of the existence of a nonrelativistic limit having an absolutely new, non-Newton (vortex) character. From the mathematically proved possibility of the existence of nonrelativistic vortex fields there follow also some implications of a more fundamental character. The Newton limit is commonly supposed to be the only nonrelativistic limit in the Einstein theory. Now there arises a dilemma: either gravitational fields having a non-Newton limit exist in nature and thus the Newton theory does not embrace all gravitational phenomena of nonrelativistic character or in the Newton solutions to the nonrelativistic gravitational equations a certain element of the Einstein theory is revealed that is alien to the true nonrelativistic theory of gravitation. In the former case, one cannot exclude the possibility that owing to a comprehensive analysis of properties, possible sources, etc. the vortex soltions to Einstein equations may prove important in cosmological and astrophysical applications of the general relativity theory. In the latter case, a detailed analysis of the non-Newton-limit solutions will at least enable one to gain a deeper insight into the structure of Einstein equations and their solutions.
Classical particles with spin in electromagnetic and gravitational fields
Amorim, R.M. de.
1977-02-01
Following a review of several problems connected with classical particles with intrinsic angular momentum are reproduced the Frenkel equations (with the condition S sup(μν)U sub(ν)=0) by means of a holonomic variational principle, and have related them to Bargann, Michel and Tededgie equations. The treatment is then generalized to the case in wich S sup(μν)U sub(ν)=0 and the resulting equation coincide in the linearized limit with those obtained by Suttorp and de Groot. Also, by using variational principles, the generalizations to Frenkel equations are obtained, as well as to those of Suttorp and de Groot when electromagnetic and gravitational interactions are considered. Finally, those equations are analysed according to a scheme proposed by Oliveira and Tiommo where the gravitational interactions are described by gravielectric and gravimagnetic fields. The analogies in these equations of motion between the gravitational and eletromagnetic interactions, in the case in which the particle has a giromagnetic factor g=1, are shown. The last results complete a previous study by wald. (Author) [pt
A Hamiltonian structure for the linearized Einstein vacuum field equations
Torres del Castillo, G.F.
1991-01-01
By considering the Einstein vacuum field equations linearized about the Minkowski metric, the evolution equations for the gauge-invariant quantities characterizing the gravitational field are written in a Hamiltonian form. A Poisson bracket between functionals of the field, compatible with the constraints satisfied by the field variables, is obtained (Author)
Determination of Gravitational Counterterms Near Four Dimensions from RG Equations
Hamada, Ken-ji
2014-01-01
The finiteness condition of renormalization gives a restriction on the form of the gravitational action. By reconsidering the Hathrell's RG equations for massless QED in curved space, we determine the gravitational counterterms and the conformal anomalies as well near four dimensions. As conjectured for conformal couplings in 1970s, we show that at all orders of the perturbation they can be combined into two forms only: the square of the Weyl tensor in $D$ dimensions and $E_D=G_4 +(D-4)\\chi(D...
Effect of the Earth's gravitational field on the detection of gravitational waves
Denisov, V.I.; Eliseev, V.A.
1988-01-01
We consider the laboratory detection of high-frequency gravitational waves in theories of gravitation based on a pseudo-Euclidean space-time. We analyze the effects due to the Earth's gravitational field on the propagation velocities of gravitational and electromagnetic waves in these theories. Experiments to test the predictions of this class of theories are discussed
Excitations of the gravitational field-I
Novello, M.
1978-01-01
The geometry of spacetime is treated as a stochastic variable. Fluctuations induce a deviation from Einstein's system of equations for the average geometry. A model is presented to deal with the fluctuations by expanding the perturbations on a series in the average geometry. As a consequence, some qualitatively new features appear. The influences on galaxy formation and on the propagation of gravitational waves are analyzed [pt
Chameleon scalar fields in relativistic gravitational backgrounds
Tsujikawa, Shinji; Tamaki, Takashi; Tavakol, Reza
2009-01-01
We study the field profile of a scalar field φ that couples to a matter fluid (dubbed a chameleon field) in the relativistic gravitational background of a spherically symmetric spacetime. Employing a linear expansion in terms of the gravitational potential Φ c at the surface of a compact object with a constant density, we derive the thin-shell field profile both inside and outside the object, as well as the resulting effective coupling with matter, analytically. We also carry out numerical simulations for the class of inverse power-law potentials V(φ) = M 4+n φ −n by employing the information provided by our analytical solutions to set the boundary conditions around the centre of the object and show that thin-shell solutions in fact exist if the gravitational potential Φ c is smaller than 0.3, which marginally covers the case of neutron stars. Thus the chameleon mechanism is present in the relativistic gravitational backgrounds, capable of reducing the effective coupling. Since thin-shell solutions are sensitive to the choice of boundary conditions, our analytic field profile is very helpful to provide appropriate boundary conditions for Φ c ∼< O(0.1)
Chameleon scalar fields in relativistic gravitational backgrounds
Tsujikawa, Shinji [Department of Physics, Faculty of Science, Tokyo University of Science, 1-3, Kagurazaka, Shinjuku-ku, Tokyo 162-8601 (Japan); Tamaki, Takashi [Department of Physics, Waseda University, Okubo 3-4-1, Tokyo 169-8555 (Japan); Tavakol, Reza, E-mail: shinji@rs.kagu.tus.ac.jp, E-mail: tamaki@gravity.phys.waseda.ac.jp, E-mail: r.tavakol@qmul.ac.uk [Astronomy Unit, School of Mathematical Sciences, Queen Mary University of London, London E1 4NS (United Kingdom)
2009-05-15
We study the field profile of a scalar field {phi} that couples to a matter fluid (dubbed a chameleon field) in the relativistic gravitational background of a spherically symmetric spacetime. Employing a linear expansion in terms of the gravitational potential {Phi}{sub c} at the surface of a compact object with a constant density, we derive the thin-shell field profile both inside and outside the object, as well as the resulting effective coupling with matter, analytically. We also carry out numerical simulations for the class of inverse power-law potentials V({phi}) = M{sup 4+n}{phi}{sup -n} by employing the information provided by our analytical solutions to set the boundary conditions around the centre of the object and show that thin-shell solutions in fact exist if the gravitational potential {Phi}{sub c} is smaller than 0.3, which marginally covers the case of neutron stars. Thus the chameleon mechanism is present in the relativistic gravitational backgrounds, capable of reducing the effective coupling. Since thin-shell solutions are sensitive to the choice of boundary conditions, our analytic field profile is very helpful to provide appropriate boundary conditions for {Phi}{sub c}{approx}
Optics of relativistic sources in a spherically symmetric gravitational field
Campbell, G.A.
1975-01-01
The effects of spectral shifts and gravitational focussing on radiation from sources moving geodesically in the Schwarzschild gravitational field is analyzed using the general-relativistic equations for geodesic motion and for the propagation of radiation along null geodesics in the geometrical optics approximation. The exact solutions of the Schwarzschild geodesic equations are briefly discussed for the null and time-like cases, and the method of classifying the orbital types of motion based on the effective radial potential is presented. A method of finding the stability of these orbits using this technique is discussed. The geometrical optics approximation for the propagation of radiation is discussed, and the area-intensity law for the Schwarzschild field is derived. The particularly interesting region near R = 3m is investigated by means of expansions of the exact equations. Numerical techniques for calculating radiation patterns from the propagation equations are discussed, including techniques for obtaining the time variation along geodesics and differences in propagation time along different null geodesics. Finally, the implications of these calculations for the apparent contradiction in energy requirements set by Joseph Weber's observations of galactic gravitational radiation and by astronomical observation are discussed. (Diss. Abstr. Int., B)
Canonical quantum theory of gravitational field with higher derivatives
Kawasaki, Shoichiro; Kimura, Tadahiko; Kitago, Koichi.
1981-01-01
A renormalizable gravitational theory with higher derivatives is canonically quantized in the Landau gauge. Field equations and various equal-time commutation relations are explicitly given. The main results obtained in this work are 1) the equal-time commutation relations involving b sub(μ) exhibit the tensor-like behaviour and 2) the theory has the 16-dimensional Poincare-like superalgebra. These results are just the same as those discovered by Nakanishi in the Einstein case. (author)
Induced forces in the gravitational field
Voracek, P.
1979-01-01
In this paper the expression for the magnitude of the so-called induced force, acting on a mass particle, is deduced. The origin of this force is causally connected to the increase of the rest mass of the particle in the gravitational field. (orig.)
Gravitational radiation from preheating with many fields
Jr, John T. Giblin; Price, Larry R.; Siemens, Xavier
2010-01-01
Parametric resonances provide a mechanism by which particles can be created just after inflation. Thus far, attention has focused on a single or many inflaton fields coupled to a single scalar field. However, generically we expect the inflaton to couple to many other relativistic degrees of freedom present in the early universe. Using simulations in an expanding Friedmann-Lemaître-Robertson-Walker spacetime, in this paper we show how preheating is affected by the addition of multiple fields coupled to the inflaton. We focus our attention on gravitational wave production — an important potential observational signature of the preheating stage. We find that preheating and its gravitational wave signature is robust to the coupling of the inflaton to more matter fields
Gravitational radiation from preheating with many fields
Jr, John T. Giblin [Department of Physics, Kenyon College, 201 North College Road, Gambier, OH 43022 (United States); Price, Larry R.; Siemens, Xavier, E-mail: giblinj@kenyon.edu, E-mail: larry@gravity.phys.uwm.edu, E-mail: siemens@gravity.phys.uwm.edu [Center for Gravitation and Cosmology, Department of Physics, University of Wisconsin — Milwaukee, P.O. Box 413, Milwaukee, WI 53201 (United States)
2010-08-01
Parametric resonances provide a mechanism by which particles can be created just after inflation. Thus far, attention has focused on a single or many inflaton fields coupled to a single scalar field. However, generically we expect the inflaton to couple to many other relativistic degrees of freedom present in the early universe. Using simulations in an expanding Friedmann-Lemaître-Robertson-Walker spacetime, in this paper we show how preheating is affected by the addition of multiple fields coupled to the inflaton. We focus our attention on gravitational wave production — an important potential observational signature of the preheating stage. We find that preheating and its gravitational wave signature is robust to the coupling of the inflaton to more matter fields.
New exact solution for the exterior gravitational field of a charged spinning mass
Chamorro, A.; Manko, V.S.; Denisova, T.E.
1991-01-01
An exact asymptotically flat solution of the Einstein-Maxwell equations describing the exterior gravitational field of a charged rotating axisymmetric mass possessing an arbitrary set of multipole moments is presented explicitly
New exact solution for the exterior gravitational field of a spinning mass
Manko, V.S.
1990-01-01
An exact asymptotically flat solution of the vacuum Einstein equations representing the exterior gravitational field of a stationary axisymmetric mass with an arbitrary mass-multipole structure is presented
Spin in stationary gravitational fields and rotating frames
Obukhov, Yuri N.; Silenko, Alexander J.; Teryaev, Oleg V.
2010-01-01
A spin motion of particles in stationary spacetimes is investigated in the framework of the classical gravity and relativistic quantum mechanics. We bring the Dirac equation for relativistic particles in nonstatic spacetimes to the Hamiltonian form and perform the Foldy-Wouthuysen transformation. We show the importance of the choice of tetrads for description of spin dynamics in the classical gravity. We derive classical and quantum mechanical equations of motion of the spin for relativistic particles in stationary gravitational fields and rotating frames and establish the full agreement between the classical and quantum mechanical approaches.
Topics in gravitation and gauge fields
Leen, T.K.
1982-01-01
The theoretical studies presented here address three distinct topics. The first deals with quantum-mechanical effects of classical gravitational radiation. Specifically, the use of the interstellar medium itself as a remote quantum-mechanical detector of gravitational waves is investigated. This study is motivated by the presumed existence of atomic hydrogen in the vicinity of astrophysical sources of gravitational radiation. Space-time curvature produces uniquely identifiable shifts in atomic hydrogen energy levels. The oscillating level shifts induced by a passing gravitational wave could conceivably be detected spectroscopically. Accordingly the level shifts for both low-lying and highly excited states of single electron atoms immersed in gravitational radiation have been studied. The second two topics deal with the theory of quantized fields on curved space-times. In the first of these studies, a naive model of cosmological baryon synthesis is examined. The model incorporates a hard CP violation as well as a baryon (and lepton) non-conserving interaction and is thus capable of generating an excess of matter over antimatter. The time dependent background geometry of the early universe drives the interaction producing net excess of baryon/lepton pairs. In the final topic, the question of renormalizability of non-Abelian gauge fields theories in a general curved space-time is addressed. All modern theories of elementary particle physics are gauge theories and one would like to know if their perturbative expansions continue to be well defined (i.e. renormalizable) on curved backgrounds. In general, one is interested in knowing if field theories renormalizable in Minkowski space remain so in a general curved space-time
GRAVITATIONAL FIELD SHIELDING AND SUPERNOVA EXPLOSIONS
Zhang, T. X.
2010-01-01
A new mechanism for supernova explosions called gravitational field shielding is proposed, in accord with a five-dimensional fully covariant Kaluza-Klein theory with a scalar field that unifies the four-dimensional Einsteinian general relativity and Maxwellian electromagnetic theory. It is shown that a dense compact collapsing core of a star will suddenly turn off or completely shield its gravitational field when the core collapses to a critical density, which is inversely proportional to the square of mass of the core. As the core suddenly turns off its gravity, the extremely large pressure immediately stops the core collapse and pushes the mantle material of supernova moving outward. The work done by the pressure in the expansion can be the order of energy released in a supernova explosion. The gravity will resume and stop the core from a further expansion when the core density becomes less than the critical density. Therefore, the gravitational field shielding leads a supernova to impulsively explode and form a compact object such as a neutron star as a remnant. It works such that a compressed spring will shoot the oscillator out when the compressed force is suddenly removed.
Minimal gravitational coupling in the Newtonian theory and the covariant Schroedinger equation
Duval, C.; Kuenzle, H.P.
1983-02-01
The role of the Bargmann group (11-dimensional extended Galilei group) in non relativistic gravitation theory is investigated. The generalized Newtonian gravitation theory (Newton-Cartan theory) achieves the status of a gauge theory about as much as General Relativity and couples minimally to a complex scalar field leading to a fourdimensionally covariant Schroedinger equation. Matter current and stress-energy tensor follow correctly from the Lagrangian. This theory on curved Newtonian space-time is also shown to be a limit of the Einstein-Klein-Gordon theory
Minimal gravitational coupling in the Newtonian theory and the covariant Schroedinger equation
Duval, C.; Kuenzle, H.P.
1984-01-01
The role of the Bargmann group (11-dimensional extended Galilei group) in nonrelativistic gravitation theory is investigated. The generalized Newtonian gravitation theory (Newton-Cartan theory) achieves the status of a gauge theory about as much as general relativity and couples minimally to a complex scalar field leading to a four-dimensionally covariant Schroedinger equation. Matter current and stress-energy tensor follow correctly from the Lagrangian. This theory on curved Newtonian space-time is also shown to be a limit of the Einstein-Klein-Gordon theory. (author)
Effective field equations for expectation values
Jordan, R.D.
1986-01-01
We discuss functional methods which allow calculation of expectation values, rather than the usual in-out amplitudes, from a path integral. The technique, based on Schwinger's idea of summing over paths which go from the past to the future and then back to the past, provides effective field equations satisfied by the expectation value of the field. These equations are shown to be real and causal for a general theory up to two-loop order, and unitarity is checked to this order. These methods are applied to a simple quantum-mechanical example to illustrate the differences between the new formalism and the standard theory. When applied to the gravitational field, the new effective field equations should be useful for studies of quantum cosmology
Effect of Earth gravitational field on the detection of gravitational waves
Denisov, V.I.; Eliseev, V.A.
1987-01-01
Results of laboratory detection of high-frequency gravitational waves from the view point of gravitation theories formulated on the basis of pseudoeuclidean space-time are calculated. Peculiarities due to different effects of the Earth gravitational field on the rates of gravitational and electromagnetic wave propagation in these theories are analysed. Experiments on check of predictions of the given class of theories are suggested
Conformal coupling of gravitational wave field to curvature
Grishchuk, L.P.; Yudin, V.
1980-01-01
Conformal properties of the equations for weak gravitational waves in a curved space--time are investigated. The basic equations are derived in the linear approximation from Einstein's equations. They represent, in fact, the equations for the second-rank tensor field h/sub alphabeta/, restricted by the auxiliary conditions h/sub α//sup β//sub ;/α =0, hequivalentγ/sub alphabeta/h/sup alphabeta/=0, and embedded into the background space--time with the metric tensor γ/sub alphabeta/. It is shown that the equations for h/sub alphabeta/ are not conformally invariant under the transformations gamma-circumflex/sub alphabeta/ =e/sup 2sigma/γ/sub alphabeta/ and h/sub alphabeta/ =e/sup sigma/h/sub alphabeta/, except for those metric rescalings which transform the Ricci scalar R of the original background space--time into e/sup -2sigma/R, where R is the Ricci scalar of the conformally related background space--time. The general form of the equations for h/sub alphabeta/ which are conformally invariant have been deduced. It is shown that these equations cannot be derived in the linear approximation from any tensor equations which generalize the Einstein equations
Barut, A.O.; Cruz, M.G.
1992-08-01
We use the method of analytic continuation of the equation of motion including the self-fields to evaluate the radiation reaction for a classical relativistic spinning point particle in interaction with scalar, tensor and linearized gravitational fields in flat spacetime. In the limit these equations reduce to those of spinless particles. We also show the renormalizability of these theories. (author). 10 refs
A Hamiltonian functional for the linearized Einstein vacuum field equations
Rosas-RodrIguez, R
2005-01-01
By considering the Einstein vacuum field equations linearized about the Minkowski metric, the evolution equations for the gauge-invariant quantities characterizing the gravitational field are written in a Hamiltonian form by using a conserved functional as Hamiltonian; this Hamiltonian is not the analog of the energy of the field. A Poisson bracket between functionals of the field, compatible with the constraints satisfied by the field variables, is obtained. The generator of spatial translations associated with such bracket is also obtained
Casimir apparatuses in a weak gravitational field
Bimonte, Giuseppe; Calloni, Enrico; Esposito, Giampiero
2009-01-01
We review and assess a part of the recent work on Casimir apparatuses in the weak gravitational field of the Earth. For a free, real massless scalar field subject to Dirichlet or Neumann boundary conditions on the parallel plates, the resulting regularized and renormalized energy-momentum tensor...... is covariantly conserved, while the trace anomaly vanishes if the massless field is conformally coupled to gravity. Conformal coupling also ensures a finite Casimir energy and finite values of the pressure upon parallel plates. These results have been extended to an electromagnetic field subject to perfect...... conductor (hence idealized) boundary conditions on parallel plates, by various authors. The regularized and renormalized energy-momentum tensor has beene valuated up to second order in the gravity acceleration. In both the scalar and the electromagnetic case, studied to first order in the gravity...
Dynamics of a bubble rising in gravitational field
De Bernardis Enrico
2016-03-01
Full Text Available The rising motion in free space of a pulsating spherical bubble of gas and vapour driven by the gravitational force, in an isochoric, inviscid liquid is investigated. The liquid is at rest at the initial time, so that the subsequent flow is irrotational. For this reason, the velocity field due to the bubble motion is described by means of a potential, which is represented through an expansion based on Legendre polynomials. A system of two coupled, ordinary and nonlinear differential equations is derived for the vertical position of the bubble center of mass and for its radius. This latter equation is a modified form of the Rayleigh-Plesset equation, including a term proportional to the kinetic energy associated to the translational motion of the bubble.
Topological geons with self-gravitating phantom scalar field
Kratovitch, P. V.; Potashov, I. M.; Tchemarina, Ju V.; Tsirulev, A. N.
2017-12-01
A topological geon is the quotient manifold M/Z 2 where M is a static spherically symmetric wormhole having the reflection symmetry with respect to its throat. We distinguish such asymptotically at solutions of the Einstein equations according to the form of the time-time metric function by using the quadrature formulas of the so-called inverse problem for self-gravitating spherically symmetric scalar fields. We distinguish three types of geon spacetimes and illustrate them by simple examples. We also study possible observational effects associated with bounded geodesic motion near topological geons.
Gravitational collapse of dark energy field configurations and supermassive black hole formation
Jhalani, V.; Kharkwal, H.; Singh, A.
2016-01-01
Dark energy is the dominant component of the total energy density of our Universe. The primary interaction of dark energy with the rest of the Universe is gravitational. It is therefore important to understand the gravitational dynamics of dark energy. Since dark energy is a low-energy phenomenon from the perspective of particle physics and field theory, a fundamental approach based on fields in curved space should be sufficient to understand the current dynamics of dark energy. Here, we take a field theory approach to dark energy. We discuss the evolution equations for a generic dark energy field in curved space-time and then discuss the gravitational collapse for dark energy field configurations. We describe the 3 + 1 BSSN formalism to study the gravitational collapse of fields for any general potential for the fields and apply this formalism to models of dark energy motivated by particle physics considerations. We solve the resulting equations for the time evolution of field configurations and the dynamics of space-time. Our results show that gravitational collapse of dark energy field configurations occurs and must be considered in any complete picture of our Universe. We also demonstrate the black hole formation as a result of the gravitational collapse of the dark energy field configurations. The black holes produced by the collapse of dark energy fields are in the supermassive black hole category with the masses of these black holes being comparable to the masses of black holes at the centers of galaxies.
Gravitational collapse of dark energy field configurations and supermassive black hole formation
Jhalani, V.; Kharkwal, H.; Singh, A., E-mail: anupamsingh.iitk@gmail.com [L. N. Mittal Institute of Information Technology, Physics Department (India)
2016-11-15
Dark energy is the dominant component of the total energy density of our Universe. The primary interaction of dark energy with the rest of the Universe is gravitational. It is therefore important to understand the gravitational dynamics of dark energy. Since dark energy is a low-energy phenomenon from the perspective of particle physics and field theory, a fundamental approach based on fields in curved space should be sufficient to understand the current dynamics of dark energy. Here, we take a field theory approach to dark energy. We discuss the evolution equations for a generic dark energy field in curved space-time and then discuss the gravitational collapse for dark energy field configurations. We describe the 3 + 1 BSSN formalism to study the gravitational collapse of fields for any general potential for the fields and apply this formalism to models of dark energy motivated by particle physics considerations. We solve the resulting equations for the time evolution of field configurations and the dynamics of space-time. Our results show that gravitational collapse of dark energy field configurations occurs and must be considered in any complete picture of our Universe. We also demonstrate the black hole formation as a result of the gravitational collapse of the dark energy field configurations. The black holes produced by the collapse of dark energy fields are in the supermassive black hole category with the masses of these black holes being comparable to the masses of black holes at the centers of galaxies.
Parallel Vector Fields and Einstein Equations of Gravity | Mahara ...
In this paper, we prove that no nontrivial timelike or spacelike parallel vector field exists in a region where the gravitational field created by macroscopic bodies and governed by Einstein's equations does not vanish. In other words, we prove that the existence of such vector fields in a region implies the vanishing of the ...
Hussain, Ibrar; Qadir, Asghar; Mahomed, F. M.
2009-01-01
Since gravitational wave spacetimes are time-varying vacuum solutions of Einstein's field equations, there is no unambiguous means to define their energy content. However, Weber and Wheeler had demonstrated that they do impart energy to test particles. There have been various proposals to define the energy content, but they have not met with great success. Here we propose a definition using 'slightly broken' Noether symmetries. We check whether this definition is physically acceptable. The procedure adopted is to appeal to 'approximate symmetries' as defined in Lie analysis and use them in the limit of the exact symmetry holding. A problem is noted with the use of the proposal for plane-fronted gravitational waves. To attain a better understanding of the implications of this proposal we also use an artificially constructed time-varying nonvacuum metric and evaluate its Weyl and stress-energy tensors so as to obtain the gravitational and matter components separately and compare them with the energy content obtained by our proposal. The procedure is also used for cylindrical gravitational wave solutions. The usefulness of the definition is demonstrated by the fact that it leads to a result on whether gravitational waves suffer self-damping.
Large Field Inflation and Gravitational Entropy
Kaloper, Nemanja; Kleban, Matthew; Lawrence, Albion
2016-01-01
species will lead to a violation of the covariant entropy bound at large $N$. If so, requiring the validity of the covariant entropy bound could limit the number of light species and their couplings, which in turn could severely constrain axion-driven inflation. Here we show that there is no such problem...... entropy of de Sitter or near-de Sitter backgrounds at leading order. Working in detail with $N$ scalar fields in de Sitter space, renormalized to one loop order, we show that the gravitational entropy automatically obeys the covariant entropy bound. Furthermore, while the axion decay constant is a strong...... in this light, and show that they are perfectly consistent with the covariant entropy bound. Thus, while quantum gravity might yet spoil large field inflation, holographic considerations in the semiclassical theory do not obstruct it....
Gravitational Goldstone fields from affine gauge theory
Tresguerres, Romualdo; Mielke, Eckehard W.
2000-08-01
In order to facilitate the application of standard renormalization techniques, gravitation should be described, in the pure connection formalism, as a Yang-Mills theory of a certain spacetime group, say the Poincaré or the affine group. This embodies the translational as well as the linear connection. However, the coframe is not the standard Yang-Mills-type gauge field of the translations, since it lacks the inhomogeneous gradient term in the gauge transformations. By explicitly restoring this ``hidden'' piece within the framework of nonlinear realizations, the usual geometrical interpretation of the dynamical theory becomes possible, and in addition one can avoid the metric or coframe degeneracy which would otherwise interfere with the integrations within the path integral. We claim that nonlinear realizations provide the general mathematical scheme for the foundation of gauge theories of spacetime symmetries. When applied to construct the Yang-Mills theory of the affine group, tetrads become identified with nonlinear translational connections; the anholonomic metric no longer constitutes an independent gravitational potential, since its degrees of freedom reveal a correspondence to eliminateable Goldstone bosons. This may be an important advantage for quantization.
Chifu E. N.
2009-07-01
Full Text Available General Relativistic metric tensors for gravitational fields exterior to homogeneous spherical mass distributions rotating with constant angular velocity about a fixed di- ameter are constructed. The coeffcients of affine connection for the gravitational field are used to derive equations of motion for test particles. The laws of conservation of energy and angular momentum are deduced using the generalized Lagrangian. The law of conservation of angular momentum is found to be equal to that in Schwarzschild’s gravitational field. The planetary equation of motion and the equation of motion for a photon in the vicinity of the rotating spherical mass distribution have rotational terms not found in Schwarzschild’s field.
Gravitational field of massive point particle in general relativity
Fiziev, P.P.
2003-10-01
Using various gauges of the radial coordinate we give a description of the static spherically symmetric space-times with point singularity at the center and vacuum outside the singularity. We show that in general relativity (GR) there exist infinitely many such solutions to the Einstein equations which are physically different and only some of them describe the gravitational field of a single massive point particle. In particular, we show that the widespread Hilbert's form of Schwarzschild solution does not solve the Einstein equations with a massive point particle's stress-energy tensor. Novel normal coordinates for the field and a new physical class of gauges are proposed, in this way achieving a correct description of a point mass source in GR. We also introduce a gravitational mass defect of a point particle and determine the dependence of the solutions on this mass defect. In addition we give invariant characteristics of the physically and geometrically different classes of spherically symmetric static space-times created by one point mass. (author)
Symmetries in tetrad theories. [of gravitational fields and general relativity
Chinea, F. J.
1988-01-01
The isometry conditions for gravitational fields are given directly at the tetrad level, rather than in terms of the metric. As an illustration, an analysis of the curvature collineations and Killing fields for a twisting type-N vacuum gravitational field is made.
A homogeneous static gravitational field and the principle of equivalence
Chernikov, N.A.
2001-01-01
In this paper any gravitational field (both in the Einsteinian case and in the Newtonian case) is described by the connection, called gravitational. A homogeneous static gravitational field is considered in the four-dimensional area z>0 of a space-time with Cartesian coordinates x, y, z, and t. Such field can be created by masses, disposed outside the area z>0 with a density distribution independent of x, y, and t. Remarkably, in the four-dimensional area z>0, together with the primitive background connection, the primitive gravitational connection has been derived. In concordance with the Principle of Equivalence all components of such gravitational connection are equal to zero in the uniformly accelerated frame system, in which the gravitational force of attraction is balanced by the inertial force. However, all components of such background connection are equal to zero in the resting frame system, but not in the accelerated frame system
Electromagnetic signatures of far-field gravitational radiation in the 1 + 3 approach
Chua, Alvin J K; Cañizares, Priscilla; Gair, Jonathan R
2015-01-01
Gravitational waves (GWs) from astrophysical sources can interact with background electromagnetic fields, giving rise to distinctive and potentially detectable electromagnetic signatures. In this paper, we study such interactions for far-field gravitational radiation using the 1 + 3 approach to relativity. Linearized equations for the electromagnetic field on perturbed Minkowski space are derived and solved analytically. The inverse Gertsenshteĭn conversion of GWs in a static electromagnetic field is rederived, and the resultant electromagnetic radiation is shown to be significant for highly magnetized pulsars in compact binary systems. We also obtain a variety of nonlinear interference effects for interacting gravitational and electromagnetic waves, although wave–wave resonances previously described in the literature are absent when the electric–magnetic self-interaction is taken into account. The fluctuation and amplification of electromagnetic energy flux as the GW strength increases towards the gravitational–electromagnetic frequency ratio is a possible signature of gravitational radiation from extended astrophysical sources. (paper)
Gravitational self-interactions of a degenerate quantum scalar field
Chakrabarty, Sankha S.; Enomoto, Seishi; Han, Yaqi; Sikivie, Pierre; Todarello, Elisa M.
2018-02-01
We develop a formalism to help calculate in quantum field theory the departures from the description of a system by classical field equations. We apply the formalism to a homogeneous condensate with attractive contact interactions and to a homogeneous self-gravitating condensate in critical expansion. In their classical descriptions, such condensates persist forever. We show that in their quantum description, parametric resonance causes quanta to jump in pairs out of the condensate into all modes with wave vector less than some critical value. We calculate, in each case, the time scale over which the homogeneous condensate is depleted and after which a classical description is invalid. We argue that the duration of classicality of inhomogeneous condensates is shorter than that of homogeneous condensates.
A possible unification of the electromagnetic and weak interaction with the gravitational field
Tauber, G.E.
1982-01-01
It is suggested that the generators of SL(6,c) containing the Lorentz group SL(2,c) and SU 3 as sub-groups, may be unified with the gravitational field. For that purpose they are combined into a single ''tetrad'' whose completeness relation then yields the gravitational potentials. The appropriate field equations are written down in analogy with previous formulations given by Einstein and others. Upon projecting on the space tetrad the contributions of these internal variables may be isolated and the relevant equations found. (Auth.)
Gravitational consequences of modern field theories
Horowitz, Gary T.
1989-01-01
Some gravitational consequences of certain extensions of Einstein's general theory of relativity are discussed. These theories are not alternative theories of gravity in the usual sense. It is assumed that general relativity is the appropriate description of all gravitational phenomena which were observed to date.
Comparison of approximate gravitational lens equations and a proposal for an improved new one
Bozza, V.
2008-01-01
Keeping the exact general relativistic treatment of light bending as a reference, we compare the accuracy of commonly used approximate lens equations. We conclude that the best approximate lens equation is the Ohanian lens equation, for which we present a new expression in terms of distances between observer, lens, and source planes. We also examine a realistic gravitational lensing case, showing that the precision of the Ohanian lens equation might be required for a reliable treatment of gravitational lensing and a correct extraction of the full information about gravitational physics.
On quantum field theory in gravitational background
Haag, R.; Narnhofer, H.; Stein, U.
1984-02-01
We discuss Quantum Fields on Riemannian space-time. A principle of local definitness is introduced which is needed beyond equations of motion and commutation relations to fix the theory uniquely. It also allows to formulate local stability. In application to a region with a time-like Killing vector field and horizons it yields the value of the Hawking temperature. The concept of vacuum and particles in a non stationary metric is treated in the example of the Robertson-Walker metric and some remarks on detectors in non inertial motion are added. (orig.)
Misner, Charles W; Wheeler, John Archibald
2017-01-01
First published in 1973, Gravitation is a landmark graduate-level textbook that presents Einstein’s general theory of relativity and offers a rigorous, full-year course on the physics of gravitation. Upon publication, Science called it “a pedagogic masterpiece,” and it has since become a classic, considered essential reading for every serious student and researcher in the field of relativity. This authoritative text has shaped the research of generations of physicists and astronomers, and the book continues to influence the way experts think about the subject. With an emphasis on geometric interpretation, this masterful and comprehensive book introduces the theory of relativity; describes physical applications, from stars to black holes and gravitational waves; and portrays the field’s frontiers. The book also offers a unique, alternating, two-track pathway through the subject. Material focusing on basic physical ideas is designated as Track 1 and formulates an appropriate one-semester graduate-level...
Gravitational F-terms through anomaly equations and deformed chiral rings
Alday, Luis F.; Gava, Edi; Cirafici, Michele; David, Justin R.; Narain, K.S.
2003-05-01
We study effective gravitational F-terms, obtained by integrating an U(N) adjoint chiral superfield Φ coupled to the N = 1 gauge chiral superfield W α and supergravity, to arbitrary orders in the gravitational background. The latter includes in addition to the N = 1 Weyl superfield G αβγ , the self-dual graviphoton field strength F αβ of the parent, broken N = 2 theory. We first study the chiral ring relations resulting from the above non-standard gravitational background and find agreement, for gauge invariant operators, with those obtained from the dual closed string side via Bianchi identities for N = 2 supergravity coupled to vector multiplets. We then derive generalized anomaly equations for connected correlators on the gauge theory side, which allow us to solve for the basic one-point function 2 /(z - Φ)> to all orders in F 2 . By generalizing the matrix model loop equation to the generating functional of connected correlators of resolvents, we prove that the gauge theory result coincides with the genus expansion of the associated matrix model, after identifying the expansion parameters on the two sides. (author)
Nonlinear dynamics in the relativistic field equation
Tanaka, Yosuke; Mizuno, Yuji; Kado, Tatsuhiko; Zhao, Hua-An
2007-01-01
We have investigated relativistic equations and chaotic behaviors of the gravitational field with the use of general relativity and nonlinear dynamics. The space component of the Friedmann equation shows chaotic behaviors in case of the inflation (h=G-bar /G>0) and open (ζ=-1) universe. In other cases (h= 0 andx-bar 0 ) and the parameters (a, b, c and d); (2) the self-similarity of solutions in the x-x-bar plane and the x-ρ plane. We carried out the numerical calculations with the use of the microsoft EXCEL. The self-similarity and the hierarchy structure of the universe have been also discussed on the basis of E-infinity theory
Microcanonical functional integral for the gravitational field
Brown, J.D.; York, J.W. Jr.
1993-01-01
The gravitational field in a spatially finite region is described as a microcanonical system. The density of states ν is expressed formally as a functional integral over Lorentzian metrics and is a functional of the geometrical boundary data that are fixed in the corresponding action. These boundary data are the thermodynamical extensive variables, including the energy and angular momentum of the system. When the boundary data are chosen such that the system is described semiclassically by any real stationary axisymmetric black hole, then in this same approximation lnν is shown to equal 1/4 the area of the black-hole event horizon. The canonical and grand canonical partition functions are obtained by integral transforms of ν that lead to ''imaginary-time'' functional integrals. A general form of the first law of thermodynamics for stationary black holes is derived. For the simpler case of nonrelativistic mechanics, the density of states is expressed as a real-time functional integral and then used to deduce Feynman's imaginary-time functional integral for the canonical partition function
Gravitational time dilation and length contraction in fields exterior to ...
Here, we use our new metric tensor exterior to a massiv3e oblate spheroid to study the gravitational phenomena of time dilation and length contraction. It turns out most profoundly that, the above phenomena hold good in the gravitational field exterior to an oblate spheroid. We then use the oblate spheroidal Earth to ...
Influence of tides on the gravitational field of Jupiter
Gavrilov, S.V.; Zharkov, V.N.; Leont'ev, V.V.
1975-01-01
The influence of tides on the gravitational field of giant planets is considered quantitatively. The ''gravitational noise'' due to tides can affect the determination of J 8 and J 10 for Jupiter. Tidal sounding of the giant planets is suggested. (author)
An application of information theory to stochastic classical gravitational fields
Angulo, J.; Angulo, J. C.; Angulo, J. M.
2018-06-01
The objective of this study lies on the incorporation of the concepts developed in the Information Theory (entropy, complexity, etc.) with the aim of quantifying the variation of the uncertainty associated with a stochastic physical system resident in a spatiotemporal region. As an example of application, a relativistic classical gravitational field has been considered, with a stochastic behavior resulting from the effect induced by one or several external perturbation sources. One of the key concepts of the study is the covariance kernel between two points within the chosen region. Using this concept and the appropriate criteria, a methodology is proposed to evaluate the change of uncertainty at a given spatiotemporal point, based on available information and efficiently applying the diverse methods that Information Theory provides. For illustration, a stochastic version of the Einstein equation with an added Gaussian Langevin term is analyzed.
Photonic chiral current and its anomaly in a gravitational field
Dolgov, A.D.; Khriplovich, I.B.; Vajnshtejn, A.I.; Zakharov, V.I.
1988-01-01
The notion of chirality for electromagnetic field which is conserved in interactions with gravitons is formulated. The correponding chiral current is the one-particle-state analogue of the Pauli-Lubansky vector. The anomaly of this current in an external gravitational field is found. The results obtained are used for the calculation of the electromagnetic radiative correction to the fermionic chiral anomaly in a gravitational field
Field Equations for Lovelock Gravity: An Alternative Route
Sumanta Chakraborty
2018-01-01
Full Text Available We present an alternative derivation of the gravitational field equations for Lovelock gravity starting from Newton’s law, which is closer in spirit to the thermodynamic description of gravity. As a warm up exercise, we have explicitly demonstrated that, projecting the Riemann curvature tensor appropriately and taking a cue from Poisson’s equation, Einstein’s equations immediately follow. The above derivation naturally generalizes to Lovelock gravity theories where an appropriate curvature tensor satisfying the symmetries as well as the Bianchi derivative properties of the Riemann tensor has to be used. Interestingly, in the above derivation, the thermodynamic route to gravitational field equations, suited for null hypersurfaces, emerges quiet naturally.
Scalar field vacuum expectation value induced by gravitational wave background
Jones, Preston; McDougall, Patrick; Ragsdale, Michael; Singleton, Douglas
2018-06-01
We show that a massless scalar field in a gravitational wave background can develop a non-zero vacuum expectation value. We draw comparisons to the generation of a non-zero vacuum expectation value for a scalar field in the Higgs mechanism and with the dynamical Casimir vacuum. We propose that this vacuum expectation value, generated by a gravitational wave, can be connected with particle production from gravitational waves and may have consequences for the early Universe where scalar fields are thought to play an important role.
Gravitational waves from self-ordering scalar fields
Fenu, Elisa; Durrer, Ruth; Figueroa, Daniel G.; García-Bellido, Juan
2009-01-01
Gravitational waves were copiously produced in the early Universe whenever the processes taking place were sufficiently violent. The spectra of several of these gravitational wave backgrounds on subhorizon scales have been extensively studied in the literature. In this paper we analyze the shape and amplitude of the gravitational wave spectrum on scales which are superhorizon at the time of production. Such gravitational waves are expected from the self ordering of randomly oriented scalar fields which can be present during a thermal phase transition or during preheating after hybrid inflation. We find that, if the gravitational wave source acts only during a small fraction of the Hubble time, the gravitational wave spectrum at frequencies lower than the expansion rate at the time of production behaves as Ω GW (f) ∝ f 3 with an amplitude much too small to be observable by gravitational wave observatories like LIGO, LISA or BBO. On the other hand, if the source is active for a much longer time, until a given mode which is initially superhorizon (kη * 1, we find that the gravitational wave energy density is frequency independent, i.e. scale invariant. Moreover, its amplitude for a GUT scale scenario turns out to be within the range and sensitivity of BBO and marginally detectable by LIGO and LISA. This new gravitational wave background can compete with the one generated during inflation, and distinguishing both may require extra information
Bach, Rudolf; Weyl, Hermann
2012-03-01
This is the English translation of the third of a series of 3 papers by Hermann Weyl (the third one jointly with Rudolf Bach), first published in 1917-1922, in which the authors derived and discussed the now-famous Weyl two-body static axially symmetric vacuum solution of Einstein's equations. The English translations of the other two papers are published alongside this one. The papers have been selected by the Editors of General Relativity and Gravitation for re-publication in the Golden Oldies series of the journal. This republication is accompanied by an editorial note written by Gernot Neugebauer, David Petroff and Bahram Mashhoon, and by a brief biography of R. Bach, written by H. Goenner.
Space-time algebra for the generalization of gravitational field ...
the analogy in formulation between massive gravitational theory and electromagnetism has ... as the dual mass, gravitomagnetic charge (monopole) or magnetic mass [7]. ... cation in the definitions of the GEM fields in the following manner:.
Backwards time travel induced by combined magnetic and gravitational fields
Novello, M.; Svaiter, N.F.; Guimaraes, M.E.X.
1990-01-01
We analyse the behaviour of an elementary microscopic particle submitted to combined Magnetic and Gravitational Fields on Goedel's Universe. The exam is made in a local Gaussian system of coordinates. (author)
Hamiltonian structure of gravitational field theory
Rayski, J.
1992-01-01
Hamiltonian generalizations of Einstein's theory of gravitation introducing a laminar structure of spacetime are discussed. The concepts of general relativity and of quasi-inertial coordinate systems are extended beyond their traditional scope. Not only the metric, but also the coordinate system, if quantized, undergoes quantum fluctuations
About the short-scale perturbations of plasma in gravitational field
Gedalin, M.E.; Machabeli, G.Z.
1985-01-01
The problem of plasma wave generation and propagation in the presence of strong gravitational fields is studied in the framework of general relativity theory. The coupled relativistic hydrodynamic and Maxwellian equations are solved in circumstances of the surface of the neutron star. The wave solution of the system of equation is analyzed, some limit cases are discussed in detail. The instability criteria of relativistic plasma are also found. (D.Gy.)
Evolution equations for Killing fields
Coll, B.
1977-01-01
The problem of finding necessary and sufficient conditions on the Cauchy data for Einstein equations which insure the existence of Killing fields in a neighborhood of an initial hypersurface has been considered recently by Berezdivin, Coll, and Moncrief. Nevertheless, it can be shown that the evolution equations obtained in all these cases are of nonstrictly hyperbolic type, and, thus, the Cauchy data must belong to a special class of functions. We prove here that, for the vacuum and Einstein--Maxwell space--times and in a coordinate independent way, one can always choose, as evolution equations for the Killing fields, a strictly hyperbolic system: The above theorems can be thus extended to all Cauchy data for which the Einstein evolution problem has been proved to be well set
On tidal phenomena in a strong gravitational field
Mashoon, B.
1975-01-01
A simple framework based on the concept of quadrupole tidal potential is presented for the calculation of tidal deformation of an extended test body in a gravitational field. This method is used to study the behavior of an initially faraway nonrotating spherical body that moves close to a Schwarzschild or an extreme Kerr black hole. In general, an extended body moving in an external gravitational field emits gravitational radiation due to its center of mass motion, internal tidal deformation, and the coupling between the internal and center of mass motions. Estimates are given of the amount of tidal radiation emitted by the body in the gravitational fields considered. The results reported in this paper are expected to be of importance in the dynamical evolution of a dense stellar system with a massive black hole in its center
Solutions of Einstein's field equations
Tomonaga, Y [Utsunomiya Univ. (Japan). Faculty of Education
1978-12-01
In this paper the author investigates the Einstein's field equations of the non-vacuum case and generalizes the solution of Robertson-Walker by the three dimensional Einstein spaces. In Section 2 the author shortly generalizes the dynamic space-time of G. Lemetre and A. Friedmann by a simple transformation.
Analysis of wave equation in electromagnetic field by Proca equation
Pamungkas, Oky Rio; Soeparmi; Cari
2017-01-01
This research is aimed to analyze wave equation for the electric and magnetic field, vector and scalar potential, and continuity equation using Proca equation. Then, also analyze comparison of the solution on Maxwell and Proca equation for scalar potential and electric field, both as a function of distance and constant wave number. (paper)
Winter, J.
1985-01-01
A covariant generalization of the Wigner transformation of quantum equations is proposed for gravitating many-particle systems, which modifies the Einstein-Liouville equations for the coupled gravity-matter problem by inclusion of quantum effects of the matter moving in its self-consistent classical gravitational field, in order to extend their realm of validity to higher particle densities. The corrections of the Vlasov equation (Liouville equation in one-particle phase space) are exhibited as combined effects of quantum mechanics and the curvature of space-time arranged in a semiclassical expansion in powers of h 2 , the first-order term of which is explicitly calculated. It is linear in the Riemann tensor and in its gradient; the Riemann tensor occurs in a similar position as the tensor of the Yang-Mills field strength in a corresponding Vlasov equation for systems with local gauge invariance in the purely classical limit. The performance of the Wigner transformation is based on expressing the equation of motion for the two-point function of the Klein-Gordon field, in particular the Beltrami operator, in terms of a midpoint and a distance vector covariantly defined for the two points. This implies the calculation of deviations of the geodesic between these points, the standard concept of which has to be refined to include infinitesimal variations of the second order. A differential equation for the second-order deviation is established
Gravitational field of spherical domain wall in higher dimension
An exact solution of Einstein's equations is found describing the gravitational ﬁeld of a spherical domain wall with nonvanishing stress component in the direction perpendicular to the plane of the wall. Also we have studied the motion of test particle around the domain wall.
Tolman temperature gradients in a gravitational field
Santiago, Jessica; Visser, Matt
2018-01-01
Tolman's relation for the temperature gradient in an equilibrium self-gravitating general relativistic fluid is broadly accepted within the general relativity community. However, the concept of temperature gradients in thermal equilibrium continues to cause confusion in other branches of physics, since it contradicts naive versions of the laws of classical thermodynamics. In this paper we discuss the crucial role of the universality of free fall, and how thermodynamics emphasises the great di...
Gravitational radiation resistance, radiation damping and field fluctuations
Schaefer, G.
1981-01-01
Application is made of two different generalised fluctuation-dissipation theorems and their derivations to the calculation of the gravitational quadrupole radiation resistance using the radiation-reaction force given by Misner, Thorne and Wheeler (Gravitation (San Francisco: Freeman) ch 36,37 (1973)) and the usual tidal force on one hand and the tidal force and the free gravitational radiation field on the other hand. The quantum-mechanical version (including thermal generalisations) of the well known classical quadrupole radiation damping formula is obtained as a function of the radiation resistance. (author)
Magnetic Field in the Gravitationally Stratified Coronal Loops B. N. ...
field for the longest (L = 406 Mm) coronal loops. The magnetic fields Bstr and Babs also increase with the number density, if the loop length does not vary much. The increment in the magnetic field due to gravitational stratification is small at the lower number densities, however, it is large at the higher number densities.
Quantum gravitational optics in the field of a gravitomagnetic monopole
Ahmadi, N [Department of Physics, North Karegar Avenue, University of Tehran, P O Box 14395-547, Tehran (Iran, Islamic Republic of); Khoeini-Moghaddam, S [Department of Physics, Sharif University of Technology, P O Box 19365-9161, Tehran (Iran, Islamic Republic of); Nouri-Zonoz, M [Department of Physics, North Karegar Avenue, University of Tehran, P O Box 14395-547, Tehran (Iran, Islamic Republic of)
2007-05-15
Vacuum polarization in QED in a background gravitational field induces interactions which effectively modify the classical picture of light rays as the null geodesies of spacetime. After a short introduction on the main aspects of the quantum gravitational optics, as a nontrivial example, we study this effect in the background of NUT space characterizing the spacetime of a spherical mass endowed with a gravitomagnetic monopole charge, the so called NUT factor.
Gravitational interaction of massless higher-spin fields
Fradkin, E S; Vasiliev, M A
1987-04-30
We show that, despite a widespread belief, the gravitational interaction of massless higher-spin fields (s>2) does exist at least in the first nontrivial order. The principal novel feature of the gravitational higher-spin interaction is its non-analyticity in the cosmological constant. Our construction is based on an infinite-dimensional higher-spin superalgebra proposed previously that leads to an infinite system of all spins s>1.
General Relativistic Theory of the VLBI Time Delay in the Gravitational Field of Moving Bodies
Kopeikin, Sergei
2003-01-01
The general relativistic theory of the gravitational VLBI experiment conducted on September 8, 2002 by Fomalont and Kopeikin is explained. Equations of radio waves (light) propagating from the quasar to the observer are integrated in the time-dependent gravitational field of the solar system by making use of either retarded or advanced solutions of the Einstein field equations. This mathematical technique separates explicitly the effects associated with the propagation of gravity from those associated with light in the integral expression for the relativistic VLBI time delay of light. We prove that the relativistic correction to the Shapiro time delay, discovered by Kopeikin (ApJ, 556, L1, 2001), changes sign if one retains direction of the light propagation but replaces the retarded for the advanced solution of the Einstein equations. Hence, this correction is associated with the propagation of gravity. The VLBI observation measured its speed, and that the retarded solution is the correct one.
The motion of a Dirac wave packet in a gravitational field
Pietropaolo, F.; Toller, M.
1983-01-01
It is studied the motion of a test particle provided with spin in a gravitational field with a nonvanishing torsion with the aim of clarifying the relationship between the approach based on the balance equations for energy, momentum and angular momentum and the approach based directly on a semiclassical approximation of the Dirac equation. The balance equations in the pole-dipole approximation are applied to a Dirac wave packet minimally coupled to the gravitational field and it is shown that, in this particular case, it is possible to compute the dipole moments of energy current, which are essential for a correct calculation of the motion of the centre of the particle and of the precession of its spin
Gravitational waves from self-ordering scalar fields
Fenu, Elisa; Durrer, Ruth; Garcia-Bellido, Juan
2009-01-01
Gravitational waves were copiously produced in the early Universe whenever the processes taking place were sufficiently violent. The spectra of several of these gravitational wave backgrounds on subhorizon scales have been extensively studied in the literature. In this paper we analyze the shape and amplitude of the gravitational wave spectrum on scales which are superhorizon at the time of production. Such gravitational waves are expected from the self ordering of randomly oriented scalar fields which can be present during a thermal phase transition or during preheating after hybrid inflation. We find that, if the gravitational wave source acts only during a small fraction of the Hubble time, the gravitational wave spectrum at frequencies lower than the expansion rate at the time of production behaves as $\\Omega_{\\rm GW}(f) \\propto f^3$ with an amplitude much too small to be observable by gravitational wave observatories like LIGO, LISA or BBO. On the other hand, if the source is active for a much longer tim...
Reheating signature in the gravitational wave spectrum from self-ordering scalar fields
Kuroyanagi, Sachiko [Asia Pacific Center for Theoretical Physics, Pohang, Gyeongbuk, 790-784 (Korea, Republic of); Hiramatsu, Takashi [Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto, 606-8502 Japan (Japan); Yokoyama, Jun' ichi, E-mail: skuro@nagoya-u.jp, E-mail: hiramatz@yukawa.kyoto-u.ac.jp, E-mail: yokoyama@resceu.s.u-tokyo.ac.jp [Research Center for the Early Universe (RESCEU), School of Science, The University of Tokyo, Tokyo, 113-0033 Japan (Japan)
2016-02-01
We investigate the imprint of reheating on the gravitational wave spectrum produced by self-ordering of multi-component scalar fields after a global phase transition. The equation of state of the Universe during reheating, which usually has different behaviour from that of a radiation-dominated Universe, affects the evolution of gravitational waves through the Hubble expansion term in the equations of motion. This gives rise to a different power-law behavior of frequency in the gravitational wave spectrum. The reheating history is therefore imprinted in the shape of the spectrum. We perform 512{sup 3} lattice simulations to investigate how the ordering scalar field reacts to the change of the Hubble expansion and how the reheating effect arises in the spectrum. We also compare the result with inflation-produced gravitational waves, which has a similar spectral shape, and discuss whether it is possible to distinguish the origin between inflation and global phase transition by detecting the shape with future direct detection gravitational wave experiments such as DECIGO.
Gravitational Collapse of Massless Fields in an Expanding Universe
Yoo Chul-Moon
2018-01-01
Full Text Available Gravitational collapse of a massless scalar field with the periodic boundary condition in a cubic box is reported. This system can be regarded as a lattice universe model. The initial data is constructed for a Gaussian like profile of the scalar field taking the integrability condition associated with the periodic boundary condition into account. For a large initial amplitude, a black hole is formed after a certain period of time. While the scalar field spreads out in the whole region for a small initial amplitude. The difference of the late time expansion law of the lattice universe depending on the final fate of the gravitational collapse is discussed.
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
Equations of motion for massive spin 2 field coupled to gravity
Buchbinder, I.L.; Gitman, D.M.; Krykhtin, V.A.; Pershin, V.D.
2000-01-01
We investigate the problems of consistency and causality for the equations of motion describing massive spin two field in external gravitational and massless scalar dilaton fields in arbitrary spacetime dimension. From the field theoretical point of view we consider a general classical action with non-minimal couplings and find gravitational and dilaton background on which this action describes a theory consistent with the flat space limit. In the case of pure gravitational background all field components propagate causally. We show also that the massive spin two field can be consistently described in arbitrary background by means of the lagrangian representing an infinite series in the inverse mass. Within string theory we obtain equations of motion for the massive spin two field coupled to gravity from the requirement of quantum Weyl invariance of the corresponding two-dimensional sigma-model. In the lowest order in α' we demonstrate that these effective equations of motion coincide with consistent equations derived in field theory
Some consequences of the law of local energy conservation in the gravitational field
Beshtoev, Kh.M.
2001-01-01
At gravitational interactions of bodies and particles there appears the defect of masses, i.e. the energy yields since the bodies (or particles) are attracted. It is shown that this changing of the effective mass of the body (or the particle) in the external gravitational field leads to changes of the measurement units: velocity and length (relative to the standard measurement units). The expression describing the advance of the perihelion of the planet (the Mercury) has been obtained. This expression is mathematically identical to Einstein's equation for the advance of the perihelion of the Mercury
Triyanta; Zen, F. P.; Supardi; Wardaya, A. Y.
2010-01-01
Gauge theory, under the framework of quantum field theory, has successfully described three fundamental interactions: electromagnetic, weak, and strong interactions. Problems of describing the gravitational interaction in a similar manner has not been satisfied yet until now. Teleparallel gravity (TG) is one proposal describing gravitational field as a gauge field. This theory is quite new and it is equivalent to Einstein's general relativity. But as gravitational field in TG is expressed by torsion, rather than curvature, it gives an alternative framework for solving problems on gravity. This paper will present solution of the dynamical equation of abelian vector fields under the framework of TG in the Bianchi type I spacetime.
A relativistic extended Fermi-Thomas-like equation for a self-gravitating system of fermions
Merloni, A.; Ruffini, R.; Torroni, V.
1998-01-01
The authors extend previous results of a Fermi-Thomas model, describing self-gravitating fermions in their ground state, to a relativistic gravitational theory in Minkowski space. In such a theory the source term of the gravitational potential depends both on the pressure and the density of the fluid. It is shown that, in correspondence of this relativistic treatment, still a Fermi-Thomas-like equation can be derived for the self-gravitating system, though the non-linearities are much more complex. No Fermi-Thomas-like equation can be obtained in the General Relativistic treatment. The canonical results for neutron stars and white dwarfs are recovered and also some erroneous statements in the scientific literature are corrected
Casimir effect of two conducting parallel plates in a general weak gravitational field
Nazari, Borzoo [University of Tehran, Faculty of Engineering Science, College of Engineering, P.O. Box 11155-4563, Tehran (Iran, Islamic Republic of)
2015-10-15
We calculate the finite vacuum energy density of the scalar and electromagnetic fields inside a Casimir apparatus made up of two conducting parallel plates in a general weak gravitational field. The metric of the weak gravitational field has a small deviation from flat spacetime inside the apparatus, and we find it by expanding the metric in terms of small parameters of the weak background. We show that the metric found can be transformed via a gauge transformation to the Fermi metric. We solve the Klein-Gordon equation exactly and find mode frequencies in Fermi spacetime. Using the fact that the electromagnetic field can be represented by two scalar fields in the Fermi spacetime, we find general formulas for the energy density and mode frequencies of the electromagnetic field. Some well-known weak backgrounds are examined and consistency of the results with the literature is shown. (orig.)
Einstein-Rosen gravitational waves
Astefanoaei, Iordana; Maftei, Gh.
2001-01-01
In this paper we analyse the behaviour of the gravitational waves in the approximation of the far matter fields, considering the indirect interaction between the matter sources and the gravitational field, in a cosmological model based on the Einstein-Rosen solution, Because the properties of the gravitational waves obtained as the solutions of Einstein fields equations (the gravitational field equations) are most obvious in the weak gravitational fields we consider here, the gravitational field in the linear approximation. Using the Newman-Penrose formalism, we calculate in the null-tetradic base (e a ), the spin coefficients, the directional derivates and the tetradic components of Ricci and Weyl tensors. From the Einstein field equations we obtained the solution for b(z, t) what described the behaviour of gravitational wave in Einstein-Rosen Universe and in the particular case, when t → ∞, p(z, t) leads us to the primordial gravitational waves in the Einstein-Rosen Universe. (authors)
Modelling of charged satellite motion in Earth's gravitational and magnetic fields
Abd El-Bar, S. E.; Abd El-Salam, F. A.
2018-05-01
In this work Lagrange's planetary equations for a charged satellite subjected to the Earth's gravitational and magnetic force fields are solved. The Earth's gravity, and magnetic and electric force components are obtained and expressed in terms of orbital elements. The variational equations of orbit with the considered model in Keplerian elements are derived. The solution of the problem in a fully analytical way is obtained. The temporal rate of changes of the orbital elements of the spacecraft are integrated via Lagrange's planetary equations and integrals of the normalized Keplerian motion obtained by Ahmed (Astron. J. 107(5):1900, 1994).
Smalley, L.L.; Prestage, J.
1976-01-01
Malin's gravitational theory, which was recently shown by Lindblom and Nester to be incorrect, is modified by means of a recently proposed method for obtaining viable gravitational theories. The resulting self-consistent theory, which is in effect a Rastall-type modification of the Einstein theory, exhibits nonconservation of momentum, yet agrees with all experimental limits known to date within the PPN framework
Boundary conditions for the gravitational field
Winicour, Jeffrey
2012-01-01
A review of the treatment of boundaries in general relativity is presented with the emphasis on application to the formulations of Einstein's equations used in numerical relativity. At present, it is known how to treat boundaries in the harmonic formulation of Einstein's equations and a tetrad formulation of the Einstein-Bianchi system. However, a universal approach valid for other formulations is not in hand. In particular, there is no satisfactory boundary theory for the 3+1 formulations which have been highly successful in binary black hole simulation. I discuss the underlying problems that make the initial-boundary-value problem much more complicated than the Cauchy problem. I review the progress that has been made and the important open questions that remain. Science is a differential equation. Religion is a boundary condition. (Alan Turing, quoted in J D Barrow, 'Theories of Everything') (topical review)
The intergalactic Newtonian gravitational field and the shell theorem
Zaninetti L.
2012-01-01
Full Text Available The release of the 2MASS Redshift Survey (2MRS with its 44599 galaxies allows the deduction of their masses in nearly complete sample. A cubic box with side of 37 Mpc containing 2429 galaxies is extracted and the Newtonian gravitational field is evaluated both at the center of the box as well as in 101 x 101 x 101 grid points of the box. The obtained results are then discussed in the light of the shell theorem which states that inside of a sphere the gravitational field is zero.
The static gravitational field near spatial infinity
Beig, R.
1980-01-01
A static solution to Einstein's equations, which is asymptotically flat near spatial infinity, is shown to be asymptotically Schwarzschildian. As an application of this result a technical lemma on the existence of asymptotically flat harmonic coordinates near infinity is proved. (author)
Weak gravitational field and Coriolis potential
In general case the vector du is not constant, as, for example, when passing through a rotating frame, this ... the point of view of Lagrangian and Hamiltonian mechanics is interesting from the general relativistic point of view ... known, Hamilton–Jacobi equation for a test particle in Kerr space-time separates whereas that for a ...
On the identification of gravitation with the massless spin 2 field
Meszaros, A.
1984-05-01
The identification of gravitation with the massless spin 2 gauge field (the gauge group is the group of translations) requires to restrict the solutions of Einstein's equations to the class of topologically trivial manifolds. It is shown that the validity of this restriction in nature is supported by the present-day empirical facts. The identification has a drastic impact on cosmology, because the fulfilment of the cosmological principle seems to be improbable. (author)
Quantum States of Neutron in Earth's Gravitational Field
Keywords. Neutron; gravitational field; Bohr-Sommerfeld-Wilson quantization; projectile motion; elastic collision; Olympiad. Author Affiliations. Vijay A Singh1 Praveen Pathak1 K Krishna Chaitanya2. Homi Bhabha Centre For Science Education (TIFR), V N Purav Marg, Mankhurd Mumbai 400088, India. Physics Department ...
Relativistic motion of spinning particles in a gravitational field
Chicone, C.; Mashhoon, B.; Punsly, B.
2005-01-01
The relative motion of a classical relativistic spinning test particle is studied with respect to a nearby free test particle in the gravitational field of a rotating source. The effects of the spin-curvature coupling force are elucidated and the implications of the results for the motion of rotating plasma clumps in astrophysical jets are discussed
Gravitating SO (3,1) gauge field
Aragone, C.; Restuccia, A.
1978-01-01
In this article, we postulate SO (3,1) as a local symmetry of any relativistic theory. This is equivalent to assuming the existence of a gauge field associated with this noncompact group. This SO (3,1) gauge field is the spinorial affinity which usually appears when we deal with weighting spinors, which, as is well known, cannot be coupled to the metric tensor field. Furthermore, according to the integral approach to gauge fields proposed by Yang, it is also recognized that in order to obtain models of gravity we have to introduce ordinary affinities as the gauge field associated with GL (4) (the local symmetry determined by the parallel transport). Thus if we assume both GL (4) and SO (3,1) as local independent symmetries we are led to analyze the dynamical gauge system constituted by the Einstein field interacting with the SO (3,1) Weyl--Yang gauge field. We think this system is a possible model of strong gravity. Once we give the first-order action for this Einstein--Weyl--Yang system we study whether the SO (3,1) gauge field could have a tetrad associated with it. It is also shown that both fields propagate along a unique characteristic cone. Algebraic and differential constraints are solved when the system evolves along a null coordinate. The unconstrained expression for the action of the system is found working in the Bondi gauge. That allows us to exhibit an explicit expression of the dynamical generator of the system. Its signature turns out to be nondefinite, due to the nondefinite contribution of the Weyl--Yang field, which has the typical spinorial behavior. A conjecture is made that such an unpleasant feature could be overcome in the quantized version of this model
Quantum field theory in a gravitational shock wave background
Klimcik, C.
1988-01-01
A scalar massless non-interacting quantum field theory on an arbitrary gravitational shock wave background is exactly solved. S-matrix and expectation values of the energy-momentum tensor are computed for an arbitrarily polarized sourceless gravitational shock wave and for a homogeneous infinite planar shell shock wave, all performed in any number of space-time dimensions. Expectation values of the energy density in scattering states exhibit a singularity which lies exactly at the location of the curvature singularity found in the infinite shell collision. (orig.)
Post-Newtonian celestial dynamics in cosmology: Field equations
Kopeikin, Sergei M.; Petrov, Alexander N.
2013-02-01
formulated in terms of the field variables which play a role of generalized coordinates in the Lagrangian formalism. It allows us to implement the powerful methods of variational calculus to derive the gauge-invariant field equations of the post-Newtonian celestial mechanics of an isolated astronomical system in an expanding universe. These equations generalize the field equations of the post-Newtonian theory in asymptotically flat spacetime by taking into account the cosmological effects explicitly and in a self-consistent manner without assuming the principle of liner superposition of the fields or a vacuole model of the isolated system, etc. The field equations for matter dynamic variables and gravitational field perturbations are coupled in the most general case of an arbitrary equation of state of matter of the background universe. We introduce a new cosmological gauge which generalizes the de Donder (harmonic) gauge of the post-Newtonian theory in asymptotically flat spacetime. This gauge significantly simplifies the gravitational field equations and allows one to find out the approximations where the field equations can be fully decoupled and solved analytically. The residual gauge freedom is explored and the residual gauge transformations are formulated in the form of the wave equations for the gauge functions. We demonstrate how the cosmological effects interfere with the local system and affect the local distribution of matter of the isolated system and its orbital dynamics. Finally, we worked out the precise mathematical definition of the Newtonian limit for an isolated system residing on the cosmological manifold. The results of the present paper can be useful in the Solar System for calculating more precise ephemerides of the Solar System bodies on extremely long time intervals, in galactic astronomy to study the dynamics of clusters of galaxies, and in gravitational wave astronomy for discussing the impact of cosmology on generation and propagation of
Neutrino's helicity in a gravitational field
Pansart, J.P.
1996-01-01
By using approximated solutions of Dirac's equation, we show that there is no helicity reversal for light neutrinos in the Schwarzschild metric nor in an expanding universe. The actual coupling between a particle spin and the angular momentum of a heavy rotating body induces a possible helicity reversal but with an unobservable probability proportional to m 2 p / E 2 , where m p is the particle mass and E its energy. In these calculations, the helicity is defined through the spin orientation with respect to the current and not with respect to the linear momentum. This definition gives simple expressions and is equal to the usual definition in the case of a flat space. (N.T.)
Static axially symmetric gravitational fields with shell sources
McCrea, J.D.
1976-01-01
Israel's (Israel, W., 1966, Nuovo Cim., vol.44, 1-14) method for treating surface layers in general relativity is applied to construct shell sources for exterior static axially symmetric gravitational fields. Consideration is restricted to cases in which the 3-cylinder representing the history of the shell is an equipotential surface of the exterior field and consequently the space-time inside this 3-cylinder is flat. (author)
Classical field theory on electrodynamics, non-Abelian gauge theories and gravitation
Scheck, Florian
2012-01-01
The book describes Maxwell's equations first in their integral, directly testable form, then moves on to their local formulation. The first two chapters cover all essential properties of Maxwell's equations, including their symmetries and their covariance in a modern notation. Chapter 3 is devoted to Maxwell theory as a classical field theory and to solutions of the wave equation. Chapter 4 deals with important applications of Maxwell theory. It includes topical subjects such as metamaterials with negative refraction index and solutions of Helmholtz' equation in paraxial approximation relevant for the description of laser beams. Chapter 5 describes non-Abelian gauge theories from a classical, geometric point of view, in analogy to Maxwell theory as a prototype, and culminates in an application to the U(2) theory relevant for electroweak interactions. The last chapter 6 gives a concise summary of semi-Riemannian geometry as the framework for the classical field theory of gravitation. The chapter concludes wit...
Linear and nonlinear stability criteria for compressible MHD flows in a gravitational field
Moawad, S. M.; Moawad
2013-10-01
The equilibrium and stability properties of ideal magnetohydrodynamics (MHD) of compressible flow in a gravitational field with a translational symmetry are investigated. Variational principles for the steady-state equations are formulated. The MHD equilibrium equations are obtained as critical points of a conserved Lyapunov functional. This functional consists of the sum of the total energy, the mass, the circulation along field lines (cross helicity), the momentum, and the magnetic helicity. In the unperturbed case, the equilibrium states satisfy a nonlinear second-order partial differential equation (PDE) associated with hydrodynamic Bernoulli law. The PDE can be an elliptic or a parabolic equation depending on increasing the poloidal flow speed. Linear and nonlinear Lyapunov stability conditions under translational symmetric perturbations are established for the equilibrium states.
The Schroedinger-Newton equation as model of self-gravitating quantum systems
Grossardt, Andre
2013-01-01
The Schroedinger-Newton equation (SN equation) describes a quantummechanical one-particle-system with gravitational self-interaction and might play a role answering the question if gravity must be quantised. As non-relativistic limit of semi-classical gravity, it provides testable predictions of the effects that classical gravity has on genuinely quantum mechanical systems in the mass regime between a few thousand proton masses and the Planck mass, which is experimentally unexplored. In this thesis I subsume the mathematical properties of the SN equation and justify it as a physical model. I will give a short outline of the controversial debate around semi-classical gravity as a fundamental theory, along with the idea of the SN equation as a model of quantum state reduction. Subsequently, I will respond to frequent objections against nonlinear Schrodinger equations. I will show how the SN equation can be obtained from Einstein's General Relativity coupled to either a KleinGordon or a Dirac equation, in the same sense as the linear Schroedinger equation can be derived in flat Minkowski space-time. The equation is, to this effect, a non-relativistic approximation of the semi-classical Einstein equations. Additionally, I will discuss, first by means of analytic estimations and later numerically, in which parameter range effects of gravitational selfinteraction - e.g. in molecular-interferometry experiments - should be expected. Besides the one-particle SN equation I will provide justification for a modified equation describing the centre-of-mass wave-function of a many-particle system. Furthermore, for this modified equation, I will examine, numerically, the consequences for experiments. Although one arrives at the conclusion that no effects of the SN equation can be expected for masses up to six or seven orders of magnitude above those considered in contemporary molecular interferometry experiments, tests of the equation, for example in satellite experiments, seem
Fedosin, Sergey G.
2018-01-01
For the relativistic uniform system with an invariant mass density the exact expressions are determined for the potentials and strengths of the gravitational field, the energy of particles and fields. It is shown that, as in the classical case for bodies with a constant mass density, in the system with a zero vector potential of the gravitational field, the energy of the particles, associated with the scalar field potential, is twice as large in the absolute value as the energy defined by the...
Roy, Fabrice
2004-01-01
We study the formation of self-gravitating systems and their properties by means of N-body simulations of gravitational collapse. First, we summarize the major analytical results concerning the collisionless Boltzmann equation and the Poisson's equation which describe the dynamics of collisionless gravitational systems. We present a study of some analytical solutions of this coupled system of equations. We then present the software used to perform the simulations. Some of this has been parallelized and implemented with the aid of MPI. For this reason we give a brief overview of it. Finally, we present the results of the numerical simulations. Analysis of these results allows us to explain some features of self-gravitating systems and the initial conditions needed to trigger the Antonov instability and the radial orbit instability. (author) [fr
Geometry of Kaluza-Klein theory. II. Field equations
Maia, M.D.
1985-01-01
In the preceding paper a geometric formulation of Kaluza-Klein theory was presented with the basic assumption that the space-time is locally and isometrically embedded in the high-dimensional space which emerged at the big bang. In the present note the Gauss-Codazzi-Ricci equations which are the integrability equations for the embedding are interpreted as the dynamical equations for a low-energy observer. The second quadratic form which results from the embedding is interpreted as a fundamental spin-two massless field. The dynamics for an observer with high-energy probes is described as usual by the Einstein-Hilbert action defined in the high-dimensional space and dimensionally reduced by integration over the internal space. The behavior of fermion masses under different gravitational field strengths is implemented by use of the mass operator defined with the second-order Casimir operator of the embedding symmetry group
On possible conceptual difficulties of quantum field theories involving gravitation
Markov, M.A.
1975-01-01
The paper outlines principles on the basis of which one would conclude that the gravitational radius of test bodies can impose fundamental limitations on the measurability of coordinates and time in quantum theory, limitations of the type ΔxΔT(>=)(thetak)/csup(4)(more precisely Δrsub(gr)ΔT(>=)(thetak)/csup(4)) as a consequence of the relation ΔEΔT(>=)theta. Corresponding limitations arise for measurability of the average electrostatic field Δanti ΣΔT(>=)(theta√k)/rsub(gr)sup(2)c and of the gravitational field (the Cristoffel symbols [sub(μγ)sup(α)]):Δ[sub(44)sup(1)]ΔT(>=)(thetak)/(rsub(gr)sup(2)c)
Measuring the neutron star equation of state with gravitational wave observations
Read, Jocelyn S.; Markakis, Charalampos; Creighton, Jolien D. E.; Friedman, John L.; Shibata, Masaru; Uryu, Koji
2009-01-01
We report the results of a first study that uses numerical simulations to estimate the accuracy with which one can use gravitational wave observations of double neutron-star inspiral to measure parameters of the neutron-star equation of state. The simulations use the evolution and initial-data codes of Shibata and Uryu to compute the last several orbits and the merger of neutron stars, with matter described by a parametrized equation of state. Previous work suggested the use of an effective cutoff frequency to place constraints on the equation of state. We find, however, that greater accuracy is obtained by measuring departures from the point-particle limit of the gravitational waveform produced during the late inspiral. As the stars approach their final plunge and merger, the gravitational wave phase accumulates more rapidly for smaller values of the neutron-star compactness (the ratio of the mass of the neutron-star to its radius). We estimate that realistic equations of state will lead to gravitational waveforms that are distinguishable from point-particle inspirals at an effective distance (the distance to an optimally oriented and located system that would produce an equivalent waveform amplitude) of 100 Mpc or less. As Lattimer and Prakash observed, neutron-star radius is closely tied to the pressure at density not far above nuclear. Our results suggest that broadband gravitational wave observations at frequencies between 500 and 1000 Hz will constrain this pressure, and we estimate the accuracy with which it can be measured. Related first estimates of radius measurability show that the radius can be determined to an accuracy of δR∼1 km at 100 Mpc.
Hydrodynamic representation of the Klein-Gordon-Einstein equations in the weak field limit
Suárez, Abril; Chavanis, Pierre-Henri
2015-01-01
Using a generalization of the Madelung transformation, we derive the hydrodynamic representation of the Klein-Gordon-Einstein equations in the weak field limit. We consider a complex self-interacting scalar field with an arbitrary potential of the form V(|ϕ| 2 ). We compare the results with simplified models in which the gravitational potential is introduced by hand in the Klein-Gordon equation, and assumed to satisfy a (generalized) Poisson equation. Nonrelativistic hydrodynamic equations based on the Schrodinger-Poisson equations or on the Gross-Pitaevskii-Poisson equations are recovered in the limit c → +∞. (paper)
Stability of a Kahler-type neutrino-gravitational field
Lynch, J.T.
1999-01-01
In this work the deficiencies, suffered by the model for the neutrino-gravitational field using Kahler-type fermion fields, are removed by a more appropriate choice for the right-acting connection group of the spinor geometry, namely the two-parameter Abelian subgroup of SU(3). The action of this two-parameter group from the right on the 4x4 sixteen component Kahler spinor field also has interesting consequences in regard to Pauli's excursion principle and the structure of massive particles
Physical effects in gravitational field of black holes
Frolov, V.P.
1986-01-01
A large number of problems related to peculiarities of physical processes in a strong gravitational field of black holes has been considered. Energy shift and the complete structure of physical fields for charged sources near a black hole have been investigated. Density matrix and generating functional for quantum effects in stationary black holes have been calculated. Contributions of massless and massive fields to vacuum polarization in black holes have been investigated and influence of quantum effects on the global structure of a black hole has been discussed
Higher order field equations. II
Tolhoek, H.A.
1977-01-01
In a previous paper wave propagation was studied according to a sixth-order partial differential equation involving a complex mass M. The corresponding Yang-Feldman integral equations (indicated as SM-YF-equations), were formulated using modified Green's functions Gsub(R)sup(M)(x) and Gsub(A)sup(M)(x), which then incorporate the partial differential equation together with certain boundary conditions. In this paper certain limit properties of these modified Green's functions are derived: (a) It is shown that for mod(M)→infinity the Green's functions Gsub(R)sup(M)(x) and Gsub(A)sup(M)(x) approach the Green's functions Δsub(R)(x) and Δsub(A)(x) of the corresponding KG-equation (Klein-Gordon equation). (b) It is further shown that the asymptotic behaviour of Gsub(R)sup(M)(x) and Gsub(A)sup(M)(x) is the same as of Δsub(R)(x) and Δsub(A)(x)-and also the same as for Dsub(R)(x) and Dsub(A)(x) for t→+-infinity;, where Dsub(R) and Dsub(A) are the Green's functions for the KG-equation with mass zero. It is essential to take limits in the sense of distribution theory in both cases (a) and (b). The property (b) indicates that the wave propagation properties of the SM-YF-equations, the KG-equation with finite mass and the KG-equation with mass zero are closely related in an asymptotic sense. (Auth.)
Do Gravitational Fields Have Mass? Or on the Nature of Dark Matter
Kunst, Ernst Karl
1999-01-01
As has been shown before (a brief comment will be given in the text), relativistic mass and relativistic time dilation of moving bodies are equivalent as well as time and mass in the rest frame. This implies that the time dilation due to the gravitational field is combined with inertial and gravitational mass as well and permits the computation of the gravitational action of the vacuum constituting the gravitational field in any distance from the source of the field. Theoretical predictions a...
Jankiewicz, Cz; Sikora, D [Wyzsza Szkola Pedagogiczna, Rzeszow (Poland)
1980-01-01
It is shwon that in the post-Newtonian approximation the gravitational momentum of a system of point particles is equal to the sum of field momentum and inertial momentum only in two classes of coordinate systems. This equality may be treated as a natural condition on a coordinate system in which the generally covariant Einstein equations are to be solved.
Einstein-Cartan Theory of Gravitation: Kinematical Parameters and Maxwell Equations
Katkar, L. N.
2015-03-01
In the space-time manifold of Einstein-Cartan Theory (ECT) of gravitation, the expressions for the time-like kinematical parameters are derived and the propagation equation for expansion is obtained.It has been observed that when the spin tensor is u-orthogonal the spin of the gravitating matter has no influence on the propagation equation of expansion while it has influence when it is not u-orthogonal. The usual formula for the curl of gradient of a scalar function is not zero in ECT. So is the case with the divergence of the curl of a vector.Their expressions on the space-time manifold of ECT are derived. A new derivative operator d ∗ is introduced to develop the calculus on space-time manifold of ECT. It is obtained by taking the covariant derivative of an associated tensor of a form with respect to an asymmetric connections. We have used this differential operator to obtain the form of the Maxwell's equations in the ECT of gravitation. Cartan's equations of structure are also derived through the new derivative operator. It has been shown that unlike the consequences of exterior derivative in Einstein space-time, the repetition of d ∗ on a form of any degree is not zero.
Coupling non-gravitational fields with simplicial spacetimes
McDonald, Jonathan R; Miller, Warner A
2010-01-01
The inclusion of source terms in discrete gravity is a long-standing problem. Providing a consistent coupling of source to the lattice in the Regge calculus (RC) yields a robust unstructured spacetime mesh applicable to both numerical relativity and quantum gravity. RC provides a particularly insightful approach to this problem with its purely geometric representation of spacetime. The simplicial building blocks of RC enable us to represent all matter and fields in a coordinate-free manner. We provide an interpretation of RC as a discrete exterior calculus framework into which non-gravitational fields naturally couple with the simplicial lattice. Using this approach we obtain a consistent mapping of the continuum action for non-gravitational fields to the Regge lattice. In this paper we apply this framework to scalar, vector and tensor fields. In particular we reconstruct the lattice action for (1) the scalar field, (2) Maxwell field tensor and (3) Dirac particles. The straightforward application of our discretization techniques to these three fields demonstrates a universal implementation of the coupling source to the lattice in RC.
Peters, Thomas; Klessen, Ralf S.; Federrath, Christoph; Smith, Rowan J.; Schleicher, Dominik R. G.; Banerjee, Robi; Sur, Sharanya
2012-01-01
Stars form by the gravitational collapse of interstellar gas. The thermodynamic response of the gas can be characterized by an effective equation of state. It determines how gas heats up or cools as it gets compressed, and hence plays a key role in regulating the process of stellar birth on virtually all scales, ranging from individual star clusters up to the galaxy as a whole. We present a systematic study of the impact of thermodynamics on gravitational collapse in the context of high-redshift star formation, but argue that our findings are also relevant for present-day star formation in molecular clouds. We consider a polytropic equation of state, P = kρ Γ , with both sub-isothermal exponents Γ 1. We find significant differences between these two cases. For Γ > 1, pressure gradients slow down the contraction and lead to the formation of a virialized, turbulent core. Weak magnetic fields are strongly tangled and efficiently amplified via the small-scale turbulent dynamo on timescales corresponding to the eddy-turnover time at the viscous scale. For Γ < 1, on the other hand, pressure support is not sufficient for the formation of such a core. Gravitational contraction proceeds much more rapidly and the flow develops very strong shocks, creating a network of intersecting sheets and extended filaments. The resulting magnetic field lines are very coherent and exhibit a considerable degree of order. Nevertheless, even under these conditions we still find exponential growth of the magnetic energy density in the kinematic regime.
Quantum limit on time measurement in a gravitational field
Sinha, Supurna; Samuel, Joseph
2015-01-01
Good clocks are of importance both to fundamental physics and for applications in astronomy, metrology and global positioning systems. In a recent technological breakthrough, researchers at NIST have been able to achieve a stability of one part in 10 18 using an ytterbium clock. This naturally raises the question of whether there are fundamental limits to time keeping. In this article we point out that gravity and quantum mechanics set a fundamental limit on the fractional frequency uncertainty of clocks. This limit comes from a combination of the uncertainty relation, the gravitational redshift and the relativistic time dilation effect. For example, a single ion aluminium clock in a terrestrial gravitational field cannot achieve a fractional frequency uncertainty better than one part in 10 22 . This fundamental limit explores the interaction between gravity and quantum mechanics on a laboratory scale. (paper)
Reconstructing the gravitational field of the local Universe
Desmond, Harry; Ferreira, Pedro G.; Lavaux, Guilhem; Jasche, Jens
2018-03-01
Tests of gravity at the galaxy scale are in their infancy. As a first step to systematically uncovering the gravitational significance of galaxies, we map three fundamental gravitational variables - the Newtonian potential, acceleration and curvature - over the galaxy environments of the local Universe to a distance of approximately 200 Mpc. Our method combines the contributions from galaxies in an all-sky redshift survey, haloes from an N-body simulation hosting low-luminosity objects, and linear and quasi-linear modes of the density field. We use the ranges of these variables to determine the extent to which galaxies expand the scope of generic tests of gravity and are capable of constraining specific classes of model for which they have special significance. Finally, we investigate the improvements afforded by upcoming galaxy surveys.
Skew differential fields, differential and difference equations
van der Put, M
2004-01-01
The central question is: Let a differential or difference equation over a field K be isomorphic to all its Galois twists w.r.t. the group Gal(K/k). Does the equation descend to k? For a number of categories of equations an answer is given.
Radiation reaction force and unification of electromagnetic and gravitational fields
Lo, C.Y.; Goldstein, G.R.; Napier, A.
1981-04-01
A unified theory of electromagnetic and gravitational fields should modify classical electrodynamics such that the radiation reaction force is accounted for. The analysis leads to a five-dimensional unified theory of five variables. The theory is supported by showing that, for the case of a charged particle moving in a constant magnetic field, the radiation reaction force is indeed included. Moreover, this example shows explicitly that physical changes are associated with the fifth variable. Thus, the notion of a physical five-dimensional space should be seriously taken into consideration
Chertock, Alina; Cui, Shumo; Kurganov, Alexander; Özcan, Şeyma Nur; Tadmor, Eitan
2018-04-01
We develop a second-order well-balanced central-upwind scheme for the compressible Euler equations with gravitational source term. Here, we advocate a new paradigm based on a purely conservative reformulation of the equations using global fluxes. The proposed scheme is capable of exactly preserving steady-state solutions expressed in terms of a nonlocal equilibrium variable. A crucial step in the construction of the second-order scheme is a well-balanced piecewise linear reconstruction of equilibrium variables combined with a well-balanced central-upwind evolution in time, which is adapted to reduce the amount of numerical viscosity when the flow is at (near) steady-state regime. We show the performance of our newly developed central-upwind scheme and demonstrate importance of perfect balance between the fluxes and gravitational forces in a series of one- and two-dimensional examples.
Dynamic field theory and equations of motion in cosmology
Kopeikin, Sergei M., E-mail: kopeikins@missouri.edu [Department of Physics and Astronomy, University of Missouri, 322 Physics Bldg., Columbia, MO 65211 (United States); Petrov, Alexander N., E-mail: alex.petrov55@gmail.com [Sternberg Astronomical Institute, Lomonosov Moscow State University, Universitetskij Prospect 13, Moscow 119992 (Russian Federation)
2014-11-15
We discuss a field-theoretical approach based on general-relativistic variational principle to derive the covariant field equations and hydrodynamic equations of motion of baryonic matter governed by cosmological perturbations of dark matter and dark energy. The action depends on the gravitational and matter Lagrangian. The gravitational Lagrangian depends on the metric tensor and its first and second derivatives. The matter Lagrangian includes dark matter, dark energy and the ordinary baryonic matter which plays the role of a bare perturbation. The total Lagrangian is expanded in an asymptotic Taylor series around the background cosmological manifold defined as a solution of Einstein’s equations in the form of the Friedmann–Lemaître–Robertson–Walker (FLRW) metric tensor. The small parameter of the decomposition is the magnitude of the metric tensor perturbation. Each term of the series expansion is gauge-invariant and all of them together form a basis for the successive post-Friedmannian approximations around the background metric. The approximation scheme is covariant and the asymptotic nature of the Lagrangian decomposition does not require the post-Friedmannian perturbations to be small though computationally it works the most effectively when the perturbed metric is close enough to the background FLRW metric. The temporal evolution of the background metric is governed by dark matter and dark energy and we associate the large scale inhomogeneities in these two components as those generated by the primordial cosmological perturbations with an effective matter density contrast δρ/ρ≤1. The small scale inhomogeneities are generated by the condensations of baryonic matter considered as the bare perturbations of the background manifold that admits δρ/ρ≫1. Mathematically, the large scale perturbations are given by the homogeneous solution of the linearized field equations while the small scale perturbations are described by a particular solution of
Stavroulakis N.
2008-04-01
Full Text Available The equations of gravitation together with the equations of electromagnetism in terms of the General Theory of Relativity allow to conceive an interdependence between the gravitational field and the electromagnetic field. However the technical difficulties of the relevant problems have precluded from expressing clearly this interdependence. Even the simple problem related to the field generated by a charged spherical mass is not correctly solved. In the present paper we reexamine from the outset this problem and propose a new solution.
Covariant field equations, gauge fields and conservation laws from Yang-Mills matrix models
Steinacker, Harold
2009-01-01
The effective geometry and the gravitational coupling of nonabelian gauge and scalar fields on generic NC branes in Yang-Mills matrix models is determined. Covariant field equations are derived from the basic matrix equations of motions, known as Yang-Mills algebra. Remarkably, the equations of motion for the Poisson structure and for the nonabelian gauge fields follow from a matrix Noether theorem, and are therefore protected from quantum corrections. This provides a transparent derivation and generalization of the effective action governing the SU(n) gauge fields obtained in [1], including the would-be topological term. In particular, the IKKT matrix model is capable of describing 4-dimensional NC space-times with a general effective metric. Metric deformations of flat Moyal-Weyl space are briefly discussed.
Hawking radiation of a vector field and gravitational anomalies
Murata, Keiju; Miyamoto, Umpei
2007-01-01
Recently, the relation between Hawking radiation and gravitational anomalies has been used to estimate the flux of Hawking radiation for a large class of black objects. In this paper, we extend the formalism, originally proposed by Robinson and Wilczek, to the Hawking radiation of vector particles (photons). It is explicitly shown, with the Hamiltonian formalism, that the theory of an electromagnetic field on d-dimensional spherical black holes reduces to one of an infinite number of massive complex scalar fields on 2-dimensional spacetime, for which the usual anomaly-cancellation method is available. It is found that the total energy emitted from the horizon for the electromagnetic field is just (d-2) times that for a scalar field. The results support the picture that Hawking radiation can be regarded as an anomaly eliminator on horizons. Possible extensions and applications of the analysis are discussed
The 'gravitating' tensor in the dualistic theory
Mahanta, M.N.
1989-01-01
The exact microscopic system of Einstein-type field equations of the dualistic gravitation theory is investigated as well as an analysis of the modified energy-momentum tensor or so called 'gravitating' tensor is presented
A model of Saturn inferred from its measured gravitational field
Kong, Dali; Zhang, Keke; Schubert, Gerald; Anderson, John D.
2018-04-01
We present an interior model of Saturn with an ice-rock core, a metallic region, an outer molecular envelope and a thin transition layer between the metallic and molecular regions. The shape of Saturn’s 1 bar surface is irregular and determined fully self-consistently by the required equilibrium condition. While the ice-rock core is assumed to have a uniform density, three different equations of state are adopted for the metallic, molecular and transition regions. The Saturnian model is constrained by its known mass, its known equatorial and polar radii, and its known zonal gravitational coefficients, J 2n , n = 1, 2, 3. The model produces an ice-rock core with equatorial radius 0.203 R S, where R S is the equatorial radius of Saturn at the 1-bar pressure surface; the core density ρ c = 10388.1 kgm‑3 corresponding to 13.06 Earth masses; and an analytical expression describing the Saturnian irregular shape of the 1-bar pressure level. The model also predicts the values of the higher-order gravitational coefficients, J 8, J 10 and J 12, for the hydrostatic Saturn and suggests that Saturn’s convective dynamo operates in the metallic region approximately defined by 0.2 R S < r e < 0.7 R S, where r e denotes the equatorial radial distance from the Saturnian center of figure.
Braginsky, V.B.; Kardashev, N.S.; Polnarev, A.G.; Novikov, I.D.
1989-12-01
Propagation of an electromagnetic wave in the field of gravitational waves is considered. Attention is given to the principal difference between the electromagnetic wave propagation in the field of random gravitational waves and the electromagnetic wave propagation in a medium with a randomly-inhomogeneous refraction index. It is shown that in the case of the gravitation wave field the phase shift of an electromagnetic wave does not increase with distance. The capability of space radio interferometry to detect relic gravitational waves as well as gravitational wave bursts of non cosmological origin are analyzed. (author). 64 refs, 2 figs
Equation of state with scale-invariant hidden local symmetry and gravitational waves
Lee Hyun Kyu
2018-01-01
Full Text Available The equation of state (EoS for the effective theory proposed recently in the frame work of the scale-invariant hidden local symmetry is discussed briefly. The EoS is found to be relatively stiffer at lower density and but relatively softer at higher density. The particular features of EoS on the gravitational waves are discussed. A relatively stiffer EoS for the neutron stars with the lower density induces a larger deviation of the gravitational wave form from the point-particle-approximation. On the other hand, a relatively softer EoS for the merger remnant of the higher density inside might invoke a possibility of the immediate formation of a black hole for short gamma ray bursts or the appearance of the higher peak frequency for gravitational waves from remnant oscillations. It is anticipated that this particular features could be probed in detail by the detections of gravitational waves from the binary neutron star mergers.
Numerical computation of gravitational field for general axisymmetric objects
Fukushima, Toshio
2016-10-01
We developed a numerical method to compute the gravitational field of a general axisymmetric object. The method (I) numerically evaluates a double integral of the ring potential by the split quadrature method using the double exponential rules, and (II) derives the acceleration vector by numerically differentiating the numerically integrated potential by Ridder's algorithm. Numerical comparison with the analytical solutions for a finite uniform spheroid and an infinitely extended object of the Miyamoto-Nagai density distribution confirmed the 13- and 11-digit accuracy of the potential and the acceleration vector computed by the method, respectively. By using the method, we present the gravitational potential contour map and/or the rotation curve of various axisymmetric objects: (I) finite uniform objects covering rhombic spindles and circular toroids, (II) infinitely extended spheroids including Sérsic and Navarro-Frenk-White spheroids, and (III) other axisymmetric objects such as an X/peanut-shaped object like NGC 128, a power-law disc with a central hole like the protoplanetary disc of TW Hya, and a tear-drop-shaped toroid like an axisymmetric equilibrium solution of plasma charge distribution in an International Thermonuclear Experimental Reactor-like tokamak. The method is directly applicable to the electrostatic field and will be easily extended for the magnetostatic field. The FORTRAN 90 programs of the new method and some test results are electronically available.
On synthetic gravitational waves from multi-field inflation
Ozsoy, Ogan
2018-04-01
We revisit the possibility of producing observable tensor modes through a continuous particle production process during inflation. Particularly, we focus on the multi-field realization of inflation where a spectator pseudoscalar σ induces a significant amplification of the U(1) gauge fields through the coupling propto σFμνtilde Fμν. In this model, both the scalar σ and the Abelian gauge fields are gravitationally coupled to the inflaton sector, therefore they can only affect the primordial scalar and tensor fluctuations through their mixing with gravitational fluctuations. Recent studies on this scenario show that the sourced contributions to the scalar correlators can be dangerously large to invalidate a large tensor power spectrum through the particle production mechanism. In this paper, we re-examine these recent claims by explicitly calculating the dominant contribution to the scalar power and bispectrum. Particularly, we show that once the current limits from CMB data are taken into account, it is still possible to generate a signal as large as r ≈ 10‑3 and the limitations on the model building are more relaxed than what was considered before.
Asanov, G.S.
1979-01-01
It is shown the description of gravitational field in the riemannian space-time by means of the absolute parallelism structure makes it possible to formulate an integrable covariant law of energy-momentum conservation for gravitational field, by imposing on the energy-momentum tensor the condition of vanishing of the covariant divergence (in the sense of the absolute parallelism). As a result of taking into account covariant constraints for the tetrads of the absolute parallelism, the Lagrangian density turns out to be not geometrised anymore and leads to the unambiguous conservation law of the type mentioned in the N-body problem. Covariant field equations imply the existence of the special euclidean coordinates outside of static neighbourhoods of gravitationing bodies. In these coordinates determined by the tetrads of the absolute parallelism, the linear approximation is not connected with any noncovariant assumptions
Scheck, Florian [Mainz Univ. (Germany). Inst. fuer Physik
2017-09-01
The following topics are dealt with: Maxwell's equations together with their symmetry and covariance, the Maxwell theory as classical field theory, simple applications of Maxwell's theory, local gauge theories, classical field theory of gravitation. (HSI)
Spinor approach to gravitational motion and precession
Hestenes, D.
1986-01-01
The translational and rotational equations of motion for a small rigid body in a gravitational field are combined in a single spinor equation. Besides its computational advantages, this unifies the description of gravitational interaction in classical and quantum theory. Explicit expressions for gravitational precession rates are derived. (author)
Behera, Harihar
2017-12-01
Recently reported [Eur. Phys. J. C., 77, 549 (2017). https://doi.org/10.1140/epjc/s10052-017-5116-y] gravitoelectromagnetic equations of Ummarino and Gallerati (UG) in their linearized version of general relativity (GR) are shown to match with (a) our previously reported special relativistic Maxwellian Gravity equations in the non-relativistic limit and with (b) the non-relativistic equations derived here, when the speed of gravity c_g (an undetermined parameter of the theory here) is set equal to c (the speed of light in vacuum). Seen in the light of our new results, the UG equations satisfy the Correspondence Principle (cp), while many other versions of linearized GR equations that are being (or may be) used to interpret the experimental data defy the cp. Such new findings assume significance and relevance in the contexts of recent detection of gravitational waves and the gravitomagnetic field of the spinning earth and their interpretations. Being well-founded and self-consistent, the equations may be of interest and useful to researchers exploring the phenomenology of gravitomagnetism, gravitational waves and the novel interplay of gravity with different states of matter in flat space-time like UG's interesting work on superconductors in weak gravitational fields.
Gravitational field strength and generalized Komar-integral
Simon, W.
1984-01-01
We define a 'gravitational field strength' in theories of the Einstein-Cartan type admitting a Killing-vector. This field strength is a second rank, antisymmetric, divergence-free tensor, whose ('Komar-') integral over a closed 2-surface gives a physically meaningful quantity. We find conditions on the Lagrange-density of the theory which ensure the existence of such a tensor, and show that they are satisfied for N = 2-supergravity and for a special case of the bosonic sector of N = 4-supergravity. We discuss a possible application of the generalized Komar-integral in the theory of stationary black holes. We also consider the Kaluza-Klein-approach to the 'field-strength-problem', which turns out to be particularly rewarding in the application to black holes. (Author)
Vector-tensor interaction of gravitation
Zhang Yuan-zhong; Guo han-ying
1982-11-01
In the paper, by using the equation of motion a particle, we show that the antigravity exist in the vector-tensor model of gravitation. Thus the motion of a particle deviates from the geodesic equation. In Newtonian approximation and weak gravitational field, acceleration of a particle in a spherically symmetric and astatic gravitation field is zero. The result is obviously not in agreement with gravitational phenomena.
Gravitation field algorithm and its application in gene cluster
Zheng Ming
2010-09-01
Full Text Available Abstract Background Searching optima is one of the most challenging tasks in clustering genes from available experimental data or given functions. SA, GA, PSO and other similar efficient global optimization methods are used by biotechnologists. All these algorithms are based on the imitation of natural phenomena. Results This paper proposes a novel searching optimization algorithm called Gravitation Field Algorithm (GFA which is derived from the famous astronomy theory Solar Nebular Disk Model (SNDM of planetary formation. GFA simulates the Gravitation field and outperforms GA and SA in some multimodal functions optimization problem. And GFA also can be used in the forms of unimodal functions. GFA clusters the dataset well from the Gene Expression Omnibus. Conclusions The mathematical proof demonstrates that GFA could be convergent in the global optimum by probability 1 in three conditions for one independent variable mass functions. In addition to these results, the fundamental optimization concept in this paper is used to analyze how SA and GA affect the global search and the inherent defects in SA and GA. Some results and source code (in Matlab are publicly available at http://ccst.jlu.edu.cn/CSBG/GFA.
Reentering the Gravitational Fringe Field of the Solar System
Fisher, P. C.
A 1998 proposal to the National Aeronautics and Space Administration (NASA) described how to update an earlier proposal outline for an experiment involving a manned spacecraft that traveled to just outside the gravitational field of the solar system. The recent proposal briefly describes how to initiate a 25-year program to launch a seven-year mission. Very little thought has been given to astronomical/astrophysical investigations that might be carried out over seven years, but one or more generations of NASA's Terrestrial Planet Finder program might be included. Only a little serious thought has been given to how to reenter the solar system's gravitational fringe field, but access to several procedures and three-fold redundancy seems desirable. Some details of the proposed paper study will be given. Non-responsibility statement, from source document of calendar 1973. This document was prepared while the author was on an unpaid leave of absence from The Lockheed Missiles and Space Company (LMSC) of Palo Alto, California. The comments made herein are partly the results of experiments carried out over a number of years. For a portion of this time, both NASA and LMSC financed the author's space astronomy investigations. It may be that either or both these institutions may possess some proprietary rights to portions of the ideas and information presented. This work was supported by Ruffner Associates, Inc.
Nariai, Hidekazu.
1986-06-01
In similar to Misner and Sharp's formalism in general relativity for a spherical gravitational collapse, a formalism for the spherical gravitational collapse is presented on the basis of a generalized theory of gravitation in the sense of Utiyama-DeWitt (which was later extended by Parker's school and Zel'dovich's one). The resulted formalism is somewhat similar to that developed by me in 1972 based on the scalar-tensor theory of gravity. (author)
The circle equation over finite fields
Aabrandt, Andreas; Hansen, Vagn Lundsgaard
2017-01-01
Interesting patterns in the geometry of a plane algebraic curve C can be observed when the defining polynomial equation is solved over the family of finite fields. In this paper, we examine the case of C the classical unit circle defined by the circle equation x2 + y2 = 1. As a main result, we es...
A model unified field equation
Perring, J.K.; Skyrme, T.H.R.
1994-01-01
The classical solutions of a unified field theory in a two-dimensional space-time are considered. This system, a model of a interacting mesons and baryons, illustrates how the particle can be built from a wave-packet of mesons and how reciprocally the meson appears as a tightly bound combination of particle and antiparticle. (author). 6 refs
String field equation from renormalization group
Sakai, Kenji.
1988-10-01
We derive an equation of motion for an open bosonic string field which is introduced as a background field in a sigma model. By using the method of Klebanov and Susskind, we obtain the β-function for this background field and investigate its properties. (author)
Determining Symmetry Properties of Gravitational Fields of Terrestrial Group Planets
R.A. Kascheev
2016-09-01
Full Text Available Numerous models of gravity fields of the Solar system bodies have been constructed recently owing to successful space missions. These models are sets of harmonic coefficients of gravity potential expansion in series of spherical functions, which is Laplace series. The sets of coefficients are different in quantity of numerical parameters, sources and composition of the initial observational data, methods to obtain and process them, and, consequently, in a variety of properties and accuracy characteristics. For this reason, the task of comparison of different models of celestial bodies considered in the paper is of interest and relevant. The main purpose of this study is comparison of the models of gravitational potential of the Earth, Moon, Mars, and Venus with the quantitative criteria of different types of symmetries developed by us. It is assumed that some particular symmetry of the density distribution function of the planetary body causes similar symmetry of its gravitational potential. The symmetry of gravitational potential, in its turn, imposes additional conditions (restrictions, which must be satisfied by the harmonic coefficients. The paper deals with seven main types of symmetries: central, axial, two symmetries specular relative to the equatorial planes and prime meridian, as well as three rotational symmetries (at π angle around the coordinate system axes. According to the results of calculations carried out for the Earth, Moon, Mars, and Venus, the values of the criteria vary considerably for different types of symmetries and for different planets. It means that the specific value of each criterion corresponding to a particular celestial body is indicative of the properties and internal structure characteristics of the latter and, therefore, it can be used as a tool for comparative planetology. On the basis of the performed calculations, it is possible to distinguish two groups of celestial bodies having similar properties of
Pair production in the gravitational field of a cosmic string
Harari, Diego D.; Skarzhinsky, Vladimir D.
1990-04-01
We show that many elementary particle physics processes, such as pair production by a high energy photon, that take place in Minkowski space only if a non-uniform external field provides for momentum non-conservation, do occur in the space-time around a straight cosmic string, even though the space is locally flat and there is no local gravitational potential. We exemplify this mechanism through the evaluation of the cross section per unit length of string for the decay of a massless scalar particle into a pair of massive particles. The cross sections for this kind of processes are typically small. Nevertheless, it is interesting to realize how these reactions occur due to topological properties of space, rather than to the action of a local field. V.S. is grateful to Mario Castagnino for hospitality at the Instituto de Astronomía y Física del Espacio during a visit while this work was done.
Gravitational field self-limitation and its role in the Universe
Gershtein, Semen S; Logunov, Anatolii A; Mestvirishvili, Mirian A [State Research Center ' Institute of High Energy Physics' , Protvino, Moscow Region (Russian Federation)
2006-11-30
It is shown that according to the relativistic theory of gravity, the gravitational field slows down the rate of time flow but stops doing so when the field is strong, thus displaying its tendency toward self-limitation of the gravitational potential. This property of the gravitational field prevents massive bodies from collapsing and allows a homogeneous isotropic universe to evolve cyclically. (physics of our days)
Fokker-Planck-Rosenbluth-type equations for self-gravitating systems in the 1PN approximation
Ramos-Caro, Javier; Gonzalez, Guillermo A
2008-01-01
We present two formulations of Fokker-Planck-Rosenbluth-type (FPR) equations for many-particle self-gravitating systems, with first-order relativistic corrections in the post-Newtonian approach (1PN). The first starts from a covariant Fokker-Planck equation for a simple gas, introduced recently by Chacon-Acosta and Kremer (2007 Phys. Rev. E 76 021201). The second derivation is based on the establishment of an 1PN-BBGKY hierarchy, developed systematically from the 1PN microscopic law of force and using the Klimontovich-Dupree (KD) method. We close the hierarchy by the introduction of a two-point correlation function that describes adequately the relaxation process. This picture reveals an aspect that is not considered in the first formulation: the contribution of ternary correlation patterns to the diffusion coefficients, as a consequence of the nature of 1PN interaction. Both formulations can be considered as a generalization of the equation derived by Rezania and Sobouti (2000 Astron. Astrophys. 354 1110), to stellar systems where the relativistic effects of gravitation play a significant role
Numerical study of primordial magnetic field amplification by inflation-produced gravitational waves
Kuroyanagi, Sachiko; Tashiro, Hiroyuki; Sugiyama, Naoshi
2010-01-01
We numerically study the interaction of inflation-produced magnetic fields with gravitational waves, both of which originate from quantum fluctuations during inflation. The resonance between the magnetic field perturbations and the gravitational waves has been suggested as a possible mechanism for magnetic field amplification. However, some analytical studies suggest that the effect of the inflationary gravitational waves is too small to provide significant amplification. Our numerical study shows more clearly how the interaction affects the magnetic fields and confirms the weakness of the influence of the gravitational waves. We present an investigation based on the magnetohydrodynamic approximation and take into account the differences of the Alfven speed.
The electromagnetic field equations for moving media
Ivezić, T
2017-01-01
In this paper a formulation of the field equation for moving media is developed by the generalization of an axiomatic geometric formulation of the electromagnetism in vacuum (Ivezić T 2005 Found. Phys. Lett. 18 401). First, the field equations with bivectors F ( x ) and ℳ ( x ) are presented and then these equations are written with the 4D vectors E ( x ), B ( x ), P ( x ) and M ( x ). The latter contain both the 4D velocity vector u of a moving medium and the 4D velocity vector v of the observers who measure E and B fields. They do not appear in previous literature. All these equations are also written in the standard basis and compared with Maxwell’s equations with 3D vectors. In this approach the Ampère-Maxwell law and Gauss’s law are inseparably connected in one law and the same happens with Faraday’s law and the law that expresses the absence of magnetic charge. It is shown that Maxwell’s equations with 3D vectors and the field equations with 4D geometric quantities are not equivalent in 4D spacetime (paper)
Salim, J.M.
1982-01-01
The perturbation theory of cosmological models, in particular Friedmann models, following the quasi-Maxwellian equations are systematically developed. Perturbations to imperfect sources are directly generalized. It is shown that Friedmann models are unstable by fluid vorticity perturbations. It is also shown that the study of gravitational waves can not be done independently of the coupling with the matter. Lifshitz results concerning matter density perturbation are found again and it is shown that some soluctions, considered in literature as physically acceptable, are naive coordinate transformations. (L.C.) [pt
Critical Effects in Gravitational Collapse
Chmaj, T.
2000-01-01
The models of gravitational collapse of a dynamical system are investigated by means of the Einstein equations. Different types conjunctions to gravitational field are analyzed and it is shown that in the case of week scalar field (low energy density) the system evaluated to flat space while in the case of strong field (high energy density) to black hole
Einstein-Podolsky-Rosen correlation in a gravitational field
Terashima, Hiroaki; Ueda, Masahito
2004-01-01
For quantum communication in a gravitational field, the properties of the Einstein-Podolsky-Rosen (EPR) correlation are studied within the framework of general relativity. Acceleration and gravity are shown to deteriorate the perfect anticorrelation of an EPR pair of spins in the same direction, and apparently decrease the degree of the violation of Bell's inequality. To maintain the perfect EPR correlation and the maximal violation of Bell's inequality, observers must measure the spins in appropriately chosen different directions which depend on the velocity of the particles, the curvature of the space-time, and the positions of the observers. Near the event horizon of a black hole, the appropriate directions depend so sensitively on the positions of the observers that even a very small uncertainty in the identification of the observers' positions leads to a fatal error in quantum communication, unless the observers fall into the black hole together with the particles
Static Einstein--Maxwell field equations
Das, A.
1979-01-01
The static Einstein--Maxwell field equations are investigated in the presence of both electric and magnetic fields. The sources or bodies are assumed to be of finite size and to not affect the connectivity of the associated space. Furthermore, electromagnetic and metric fields are assumed to have reasonable differentiabilities. It is then proved that the electric and magnetic field vectors are constant multiples of one another. Moreover, the static Einstein--Maxwell equations reduce to the static magnetovac case. If, furthermore, the variational derivation of the Einstein--Maxwell equations is assumed, then both the total electric and magnetic charge of each body must vanish. As a physical consequence it is pointed out that if a suspended magnet be electrically charged then it must experience a purely general relativistic torque
Massive spin-two particle in a gravitational field
Tauber, G.
1980-01-01
The spin-two particle is described by a symmetric tensor hsub(μupsilon) subject to the subsidiary conditions hsub(α)sup(α) deltasub(α)hsup(αβ) = O. Their covariant generalization and the 'wave equation' have been obtained directly from the Eulerian variational equations by algebraic methods only. In addition to the tensor field hsub(μupsilon) a symmetric third-rank tensor suplambda)GAMMAsub(μupsilon) sup(lambda)GAMMAsub(upsilonμ) as well as a vector field Asub(μ) have been added, neither of which enter in the final result. The Lagrangian function is taken as a linear sum of all combinations which can be constructed from these functions, as well as terms involving the curvature and its two possible contractions. Variation with respect to hsup(μupsilon), sup(lambda)GAMMAsub(μupsilon) and Asub(μ) independently gives the Euler equations. Combining the various trace equations and choice of arbitrary constants yields the subsidiary conditions, while the Euler equations themselves give the connection between the auxiliary functions and the tensor hsub(μupsilon) Finally, variation with respect to gsup(μupsilon) yields the energy-momentum tensor. (author)
Gravitational waves in bouncing cosmologies from gauge field production
Ben-Dayan, Ido, E-mail: ido.bendayan@gmail.com [Department of Physics, Ben-Gurion University of the Negev, P.O. Box 653, Be' er-Sheva 8410500 (Israel)
2016-09-01
We calculate the gravitational waves (GW) spectrum produced in various Early Universe scenarios from gauge field sources, thus generalizing earlier inflationary calculations to bouncing cosmologies. We consider generic couplings between the gauge fields and the scalar field dominating the energy density of the Universe. We analyze the requirements needed to avoid a backreaction that will spoil the background evolution. When the scalar is coupled only to F F-tilde term, the sourced GW spectrum is exponentially enhanced and parametrically the square of the vacuum fluctuations spectrum, P {sup s} {sub T} ∼ (P {sup v} {sub T} ){sup 2}, giving an even bluer spectrum than the standard vacuum one. When the scalar field is also coupled to F {sup 2} term, the amplitude is still exponentially enhanced, but the spectrum can be arbitrarily close to scale invariant (still slightly blue), n {sub T} ∼> 0, that is distinguishable form the slightly red inflationary one. Hence, we have a proof of concept of observable GW on CMB scales in a bouncing cosmology.
Selfinteraction force in a theory of gravitation with higher derivatives
Jankiewicz, C.
1981-01-01
Approximate equations of motion are derived from gravitational field equations with higher derivatives. The approximation takes into account the selfinteraction force. The selfinteraction force coincides with the analogous force resulting from the Einstein field equations. (author)
Dirac equation in magnetic-solenoid field
Gavrilov, S.P. [Dept. Fisica e Quimica, UNESP, Campus de Guaratingueta (Brazil); Gitman, D.M.; Smirnov, A.A. [Instituto de Fisica, Universidade de Sao Paulo (Brazil)
2004-07-01
We consider the Dirac equation in the magnetic-solenoid field (the field of a solenoid and a collinear uniform magnetic field). For the case of Aharonov-Bohm solenoid, we construct self-adjoint extensions of the Dirac Hamiltonian using von Neumann's theory of deficiency indices. We find self-adjoint extensions of the Dirac Hamiltonian and boundary conditions at the AB solenoid. Besides, for the first time, solutions of the Dirac equation in the magnetic-solenoid field with a finite radius solenoid were found. We study the structure of these solutions and their dependence on the behavior of the magnetic field inside the solenoid. Then we exploit the latter solutions to specify boundary conditions for the magnetic-solenoid field with Aharonov-Bohm solenoid. (orig.)
Equations of motion for massive spin 2 field coupled to gravity
Buchbinder, I.L. E-mail: ilb@mail.tomsknet.ru; Gitman, D.M. E-mail: gitman@fma.if.usp.br; Krykhtin, V.A. E-mail: krykhtin@phys.dfe.tpu.edu.ru; Pershin, V.D. E-mail: pershin@ic.tsu.ru
2000-09-18
We investigate the problems of consistency and causality for the equations of motion describing massive spin two field in external gravitational and massless scalar dilaton fields in arbitrary spacetime dimension. From the field theoretical point of view we consider a general classical action with non-minimal couplings and find gravitational and dilaton background on which this action describes a theory consistent with the flat space limit. In the case of pure gravitational background all field components propagate causally. We show also that the massive spin two field can be consistently described in arbitrary background by means of the lagrangian representing an infinite series in the inverse mass. Within string theory we obtain equations of motion for the massive spin two field coupled to gravity from the requirement of quantum Weyl invariance of the corresponding two-dimensional sigma-model. In the lowest order in {alpha}' we demonstrate that these effective equations of motion coincide with consistent equations derived in field theory.
Strong field gravitational lensing by a charged Galileon black hole
Zhao, Shan-Shan; Xie, Yi, E-mail: clefairy035@163.com, E-mail: yixie@nju.edu.cn [School of Astronomy and Space Science, Nanjing University, Nanjing 210093 (China)
2016-07-01
Strong field gravitational lensings are dramatically disparate from those in the weak field by representing relativistic images due to light winds one to infinity loops around a lens before escaping. We study such a lensing caused by a charged Galileon black hole, which is expected to have possibility to evade no-hair theorem. We calculate the angular separations and time delays between different relativistic images of the charged Galileon black hole. All these observables can potentially be used to discriminate a charged Galileon black hole from others. We estimate the magnitudes of these observables for the closest supermassive black hole Sgr A*. The strong field lensing observables of the charged Galileon black hole can be close to those of a tidal Reissner-Nordström black hole or those of a Reissner-Nordström black hole. It will be helpful to distinguish these black holes if we can separate the outermost relativistic images and determine their angular separation, brightness difference and time delay, although it requires techniques beyond the current limit.
Nonlinear gravitational self-force: Field outside a small body
Pound, Adam
2012-10-01
A small extended body moving through an external spacetime gαβ creates a metric perturbation hαβ, which forces the body away from geodesic motion in gαβ. The foundations of this effect, called the gravitational self-force, are now well established, but concrete results have mostly been limited to linear order. Accurately modeling the dynamics of compact binaries requires proceeding to nonlinear orders. To that end, I show how to obtain the metric perturbation outside the body at all orders in a class of generalized wave gauges. In a small buffer region surrounding the body, the form of the perturbation can be found analytically as an expansion for small distances r from a representative worldline. Given only a specification of the body’s multipole moments, the field obtained in the buffer region suffices to find the metric everywhere outside the body via a numerical puncture scheme. Following this procedure at first and second order, I calculate the field in the buffer region around an arbitrarily structured compact body at sufficiently high order in r to numerically implement a second-order puncture scheme, including effects of the body’s spin. I also define nth-order (local) generalizations of the Detweiler-Whiting singular and regular fields and show that in a certain sense, the body can be viewed as a skeleton of multipole moments.
On quantum electrodynamics in an external gravitational field. Part 2. Discussion of the effects
Lotze, K.H.
1978-01-01
The S matrix constructed in Part I of this work is evaluated for processes which it includes. Some of them are discussed in more detail: pair creation and scattering in an external gravitational field, pair creation by a photon and creation of an electron-positron pair and a photon in an external gravitational field. (author)
On the possibility of a fourth test of general relativity in earth's gravitational field
Zhang Yuan-zhong.
1981-03-01
In the paper the possibility for a fourth test of general relativity (i.e. relativistic time delay) in Earth's gravitational field is discussed. The effects of Earth's gravitational field on an interferometer and a resonant cavity are calculated by means of both two definitions of physical length. (author)
Classical field theory. On electrodynamics, non-Abelian gauge theories and gravitation. 2. ed.
Scheck, Florian
2018-04-01
Scheck's successful textbook presents a comprehensive treatment, ideally suited for a one-semester course. The textbook describes Maxwell's equations first in their integral, directly testable form, then moves on to their local formulation. The first two chapters cover all essential properties of Maxwell's equations, including their symmetries and their covariance in a modern notation. Chapter 3 is devoted to Maxwell's theory as a classical field theory and to solutions of the wave equation. Chapter 4 deals with important applications of Maxwell's theory. It includes topical subjects such as metamaterials with negative refraction index and solutions of Helmholtz' equation in paraxial approximation relevant for the description of laser beams. Chapter 5 describes non-Abelian gauge theories from a classical, geometric point of view, in analogy to Maxwell's theory as a prototype, and culminates in an application to the U(2) theory relevant for electroweak interactions. The last chapter 6 gives a concise summary of semi-Riemannian geometry as the framework for the classical field theory of gravitation. The chapter concludes with a discussion of the Schwarzschild solution of Einstein's equations and the classical tests of general relativity. The new concept of this edition presents the content divided into two tracks: the fast track for master's students, providing the essentials, and the intensive track for all wanting to get in depth knowledge of the field. Cleary labeled material and sections guide students through the preferred level of treatment. Numerous problems and worked examples will provide successful access to Classical Field Theory.
Gravitational waves from non-Abelian gauge fields at a tachyonic transition
Tranberg, Anders; Tähtinen, Sara; Weir, David J.
2018-04-01
We compute the gravitational wave spectrum from a tachyonic preheating transition of a Standard Model-like SU(2)-Higgs system. Tachyonic preheating involves exponentially growing IR modes, at scales as large as the horizon. Such a transition at the electroweak scale could be detectable by LISA, if these non-perturbatively large modes translate into non-linear dynamics sourcing gravitational waves. Through large-scale numerical simulations, we find that the spectrum of gravitational waves does not exhibit such IR features. Instead, we find two peaks corresponding to the Higgs and gauge field mass, respectively. We find that the gravitational wave production is reduced when adding non-Abelian gauge fields to a scalar-only theory, but increases when adding Abelian gauge fields. In particular, gauge fields suppress the gravitational wave spectrum in the IR. A tachyonic transition in the early Universe will therefore not be detectable by LISA, even if it involves non-Abelian gauge fields.
Spherically Symmetric Solutions of the Einstein-Bach Equations and a Consistent Spin-2 Field Theory
Janda, A.
2006-01-01
We briefly present a relationship between General Relativity coupled to certain spin-0 and spin-2 field theories and higher derivatives metric theories of gravity. In a special case, described by the Einstein-Bach equations, the spin-0 field drops out from the theory and we obtain a consistent spin-two field theory interacting gravitationally, which overcomes a well known inconsistency of the theory for a linear spin-two field coupled to the Einstein's gravity. Then we discuss basic properties of static spherically symmetric solutions of the Einstein-Bach equations. (author)
Conservation laws and gravitational radiation
Rastall, P.
1977-01-01
A total stress-momentum is defined for gravitational fields and their sources. The Lagrangian density is slightly different from that in the previous version of the theory, and the field equations are considerably simplified. The post-Newtonian approximation of the theory is unchanged. The existence and nature of weak gravitational waves are discussed. (author)
Lagrangian procedures for higher order field equations
Bollini, C.G.
1987-01-01
A Lagrangian procedure for a pedagogical way is presented for the treatment of higher order field equations. The energy-momentum tensor and the conserved density current are built. In particular the case in which the derivatives appear only in the invariant D'Alembertian operator is discussed. Some examples are discussed. The fields are quantized and the corresponding Hamilonian which is shown not to be positive defructed. Rules are given to write the causal propagators. (author) [pt
Lagrangian procedures for higher order field equations
Bollini, C.G.; Giambiagi, J.J.
1986-01-01
We present in a pedagogical way a Lagrangian procedure for the treatment of higher order field equations. We build the energy-momentum tensor and the conserved density current. In particular we discuss the case in which the derivatives appear only in the invariant D'Alembertian operator. We discuss some examples. We quantize the fields and construct the corresponding Hamiltonian which is shown not to be positive definite. We give the rules for the causal propagators. (Author) [pt
Bose, Sukanta
2015-01-01
The Advanced LIGO detectors began observation runs a few weeks ago. This has afforded relativists and astronomers the opportunity to use gravitational waves to improve our understanding of a variety of astronomical objects and phenomena. In this talk I will examine how well gravitational wave observations of coalescing binaries involving neutron stars might constrain the neutron star (NS) equation of state. These astrophysical constraints can improve our understanding of nuclear interactions in ways that complement the knowledge acquired from terrestrial labs. I will study the effects of different NS equations of states in both NS-NS and NS-Black Hole systems, with and without spin, on these constraint. (author)
Conformal anomalies and the Einstein field equations
Godazgar, Hadi [Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut), Mühlenberg 1, D-14476 Potsdam (Germany); Meissner, Krzysztof A. [Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw (Poland); Nicolai, Hermann [Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut), Mühlenberg 1, D-14476 Potsdam (Germany)
2017-04-28
We compute corrections to the Einstein field equations which are induced by the anomalous effective actions associated to the type A conformal anomaly, both for the (non-local) Riegert action, as well as for the local action with dilaton. In all cases considered we find that these corrections can be very large.
ZONAL TOROIDAL HARMONIC EXPANSIONS OF EXTERNAL GRAVITATIONAL FIELDS FOR RING-LIKE OBJECTS
Fukushima, Toshio, E-mail: Toshio.Fukushima@nao.ac.jp [National Astronomical Observatory, Ohsawa, Mitaka, Tokyo 181-8588 (Japan)
2016-08-01
We present an expression of the external gravitational field of a general ring-like object with axial and plane symmetries such as oval toroids or annular disks with an arbitrary density distribution. The main term is the gravitational field of a uniform, infinitely thin ring representing the limit of zero radial width and zero vertical height of the object. The additional term is derived from a zonal toroidal harmonic expansion of a general solution of Laplace’s equation outside the Brillouin toroid of the object. The special functions required are the point value and the first-order derivative of the zonal toroidal harmonics of the first kind, namely, the Legendre function of the first kind of half integer degree and an argument that is not less than unity. We developed a recursive method to compute them from two pairs of seed values explicitly expressed by some complete elliptic integrals. Numerical experiments show that appropriately truncated expansions converge rapidly outside the Brillouin toroid. The truncated expansion can be evaluated so efficiently that, for an oval toroid with an exponentially damping density profile, it is 3000–10,000 times faster than the two-dimensional numerical quadrature. A group of the Fortran 90 programs required in the new method and their sample outputs are available electronically.
Addendum. Relation for the Light Absorption in the Presence of Gravitation Field
R.Vlokh; M.Kostyrko
2005-01-01
We argue for the validity of relation for electromagnetic wave electric field derived by us earlier. It includes an imaginary part responsible for the absorption induced by gravitation field of spherically symmetric mass.
A gravitational entropy proposal
Clifton, Timothy; Tavakol, Reza; Ellis, George F R
2013-01-01
We propose a thermodynamically motivated measure of gravitational entropy based on the Bel–Robinson tensor, which has a natural interpretation as the effective super-energy–momentum tensor of free gravitational fields. The specific form of this measure differs depending on whether the gravitational field is Coulomb-like or wave-like, and reduces to the Bekenstein–Hawking value when integrated over the interior of a Schwarzschild black hole. For scalar perturbations of a Robertson–Walker geometry we find that the entropy goes like the Hubble weighted anisotropy of the gravitational field, and therefore increases as structure formation occurs. This is in keeping with our expectations for the behaviour of gravitational entropy in cosmology, and provides a thermodynamically motivated arrow of time for cosmological solutions of Einstein’s field equations. It is also in keeping with Penrose’s Weyl curvature hypothesis. (paper)
Short guide to direct gravitational field modelling with Hotine's equations
Sebera, Josef; Wagner, C. A.; Bezděk, Aleš; Klokočník, Jaroslav
2013-01-01
Roč. 87, č. 3 (2013), s. 223-238 ISSN 0949-7714 R&D Projects: GA MŠk(CZ) LC506 Grant - others:ESA(XE) ESA- PECS projec No. C98056 Institutional support: RVO:67985815 Keywords : geopotential coefficients * spherical harmonics * acceleration vector Subject RIV: BN - Astronomy, Celestial Mechanics, Astrophysics Impact factor: 3.917, year: 2013
arXiv Gravitational-wave constraints on the neutron-star-matter Equation of State
Annala, Eemeli; Kurkela, Aleksi; Vuorinen, Aleksi
The LIGO/Virgo detection of gravitational waves originating from a neutron-star merger, GW170817, has recently provided new stringent limits on the tidal deformabilities of the stars involved in the collision. Combining this measurement with the existence of two-solar-mass stars, we generate a generic family of neutron-star-matter Equations of State (EoSs) that interpolate between state-of-the-art theoretical results at low and high baryon density. Comparing the results to ones obtained without the tidal-deformability constraint, we witness a dramatic reduction in the family of allowed EoSs. Based on our analysis, we conclude that the maximal radius of a 1.4-solar-mass neutron star is 13.6 km, and that smallest allowed tidal deformability of a similar-mass star is $\\Lambda(1.4 M_\\odot) = 120$.
Effects of QCD equation of state on the stochastic gravitational wave background
Anand, Sampurn; Mohanty, Subhendra [Physical Research Laboratory, Ahmedabad 380009 (India); Dey, Ujjal Kumar, E-mail: sampurn@prl.res.in, E-mail: ujjal@cts.iitkgp.ernet.in, E-mail: mohanty@prl.res.in [Centre for Theoretical Studies, Indian Institute of Technology, Kharagpur 721302 (India)
2017-03-01
Cosmological phase transitions can be a source of Stochastic Gravitational Wave (SGW) background. Apart from the dynamics of the phase transition, the characteristic frequency and the fractional energy density Ω{sub gw} of the SGW depends upon the temperature of the transition. In this article, we compute the SGW spectrum in the light of QCD equation of state provided by the lattice results. We find that the inclusion of trace anomaly from lattice QCD, enhances the SGW signal generated during QCD phase transition by ∼ 50% and the peak frequency of the QCD era SGW are shifted higher by ∼ 25% as compared to the earlier estimates without trace anomaly. This result is extremely significant for testing the phase transition dynamics near QCD epoch.
Gravitational-Wave Constraints on the Neutron-Star-Matter Equation of State
Annala, Eemeli; Gorda, Tyler; Kurkela, Aleksi; Vuorinen, Aleksi
2018-04-01
The detection of gravitational waves originating from a neutron-star merger, GW170817, by the LIGO and Virgo Collaborations has recently provided new stringent limits on the tidal deformabilities of the stars involved in the collision. Combining this measurement with the existence of two-solar-mass stars, we generate a generic family of neutron-star-matter equations of state (EOSs) that interpolate between state-of-the-art theoretical results at low and high baryon density. Comparing the results to ones obtained without the tidal-deformability constraint, we witness a dramatic reduction in the family of allowed EOSs. Based on our analysis, we conclude that the maximal radius of a 1.4-solar-mass neutron star is 13.6 km, and that the smallest allowed tidal deformability of a similar-mass star is Λ (1.4 M⊙)=120 .
arXiv Gravitational-wave constraints on the neutron-star-matter Equation of State
Annala, Eemeli; Kurkela, Aleksi; Vuorinen, Aleksi
2018-04-26
The detection of gravitational waves originating from a neutron-star merger, GW170817, by the LIGO and Virgo Collaborations has recently provided new stringent limits on the tidal deformabilities of the stars involved in the collision. Combining this measurement with the existence of two-solar-mass stars, we generate a generic family of neutron-star-matter equations of state (EOSs) that interpolate between state-of-the-art theoretical results at low and high baryon density. Comparing the results to ones obtained without the tidal-deformability constraint, we witness a dramatic reduction in the family of allowed EOSs. Based on our analysis, we conclude that the maximal radius of a 1.4-solar-mass neutron star is 13.6 km, and that the smallest allowed tidal deformability of a similar-mass star is Λ(1.4 M⊙)=120.
To a physical interpretation of a weak gravitational field in GRT
Pavlov, N.V.
1981-01-01
The problem of separation of Newton components of weak vacuum gravitational fields is discussed. Chronometric- invariant (CI) characteristics of space-time and the corresponding Newton values are compared in the fixed systems of reference. Attention is paid to the following facts. ''Weak'' sources of weak gravitational fields do not interact gravitationally. If the CI characteristics of vacuum space- time permit series expansion in 1/c powers then the coefficients at odd 1/c powers are connected with the presence of non-gravitational material fields inside the sources. Masses producing gravitational field may not be the sources of gravitational waves in the form of which this field manifests itself. Perspectives of detecting laboratory gravitational waves are discussed: the simplest metrics of plane wave is considered in the quasi-inertial reference system; the flowsheet of the generator of this wave is suggested; relativistic oscillation of a test massive particle is calculated in the postnewtonian approximation. The numerical evaluations show that attempts of mechanical detection of laboratory gravitational waves are hopeless [ru
Improved Gravitation Field Algorithm and Its Application in Hierarchical Clustering
Zheng, Ming; Sun, Ying; Liu, Gui-xia; Zhou, You; Zhou, Chun-guang
2012-01-01
Background Gravitation field algorithm (GFA) is a new optimization algorithm which is based on an imitation of natural phenomena. GFA can do well both for searching global minimum and multi-minima in computational biology. But GFA needs to be improved for increasing efficiency, and modified for applying to some discrete data problems in system biology. Method An improved GFA called IGFA was proposed in this paper. Two parts were improved in IGFA. The first one is the rule of random division, which is a reasonable strategy and makes running time shorter. The other one is rotation factor, which can improve the accuracy of IGFA. And to apply IGFA to the hierarchical clustering, the initial part and the movement operator were modified. Results Two kinds of experiments were used to test IGFA. And IGFA was applied to hierarchical clustering. The global minimum experiment was used with IGFA, GFA, GA (genetic algorithm) and SA (simulated annealing). Multi-minima experiment was used with IGFA and GFA. The two experiments results were compared with each other and proved the efficiency of IGFA. IGFA is better than GFA both in accuracy and running time. For the hierarchical clustering, IGFA is used to optimize the smallest distance of genes pairs, and the results were compared with GA and SA, singular-linkage clustering, UPGMA. The efficiency of IGFA is proved. PMID:23173043
Quadrupole mass detector in the field of weak plane gravitational waves
Borisova, L.B.
1978-01-01
Studied is the behaviour of the system which consists of two test particles connected by a string (quadrupole mass detector) and placed in the field of weak plane monochromatic gravitational waves. It is shown that at cross orientation of the detector the gravitational wave effecting such a system excites oscillations in it with the frequency equal to that of the gravitational wave source. The role of the driving force is played by the periodical change with the time of the equilibrium position. The gravitational wave does not influence the detector at its longitudinal orientation
Quantum phenomena in gravitational field; Phenomenes quantiques dans le champ gravitationnel
Bourdel, Th. [Laboratoire Charles-Fabry de l' Institut d' Optique, CNRS, Univ. Paris-Sud, Campus Polytechnique RD128, 91127 Palaiseau (France); Doser, M. [CERN, Geneva 23, CH-1211 (Switzerland); Ernest, A.D. [Faculty of Science, Charles Sturt University, Wagga Wagga (Australia); Voronin, A.Y. [Lebedev Institute, 53 Leninskii pr., Moscow, RU-119991 (Russian Federation); Voronin, V.V. [PNPI, Orlova Roscha, Gatchina, RU-188300 (Russian Federation)
2010-10-15
The subjects presented here are very different. Their common feature is that they all involve quantum phenomena in a gravitational field: gravitational quantum states of ultracold anti-hydrogen above a material surface and measuring a gravitational interaction of anti-hydrogen in AEGIS, a quantum trampoline for ultracold atoms, and a hypothesis on naturally occurring gravitational quantum states, an Eoetvoes-type experiment with cold neutrons and others. Considering them together, however, we could learn that they have many common points both in physics and in methodology. (authors)
General relativity: An introduction to the theory of the gravitational field
Stephani, H.
1985-01-01
The entire treatment presented here is framed by questions which led to and now lead out of the general theory of relativity: can an absolute acceleration be defined meaningfully? Do gravitational effects propagate with infinite velocity as Newton required? Can the general theory correctly reflect the dynamics of the whole universe while consistently describing stellar evolution? Can a theory which presupposes measurement of properties of space through the interaction of matter be made compatible with a theory in which dimensions of the objects measured are so small that location loses meaning? The book gives the mathematics necessary to understand the theory and begins in Riemannian geometry. Contents, abridged: Foundations of Riemannian geometry. Foundations of Einstein's theory of gravitation. Linearised theory of gravitation, far fields and gravitational waves. Invariant characterisation of exact solutions. Gravitational collapse and black holes. Cosmology. Non-Einsteinian theories of gravitation. Index
Energy-momentum tensor of the gravitational field for material spheres
Sokolov, S.N.
1990-01-01
Density of the energy-momentum tensor of a gravitational field which can be defined in the general relativity theory with the help of ideas of the relativistic gravitational theory is found for the case of material spheres. A relationship of this quantity with the Riemann tensor R αβγδ is discussed
Massive and mass-less Yang-Mills and gravitational fields
Veltman, M.J.G.; Dam, H. van
1970-01-01
Massive and mass-less Yang-Mills and gravitational fields are considered. It is found that there is a discrete difference between the zero-mass theories and the very small, but non-zero mass theories. In the case of gravitation, comparison of massive and mass-less theories with experiment, in
Comment on 'Late-time tails of a self-gravitating massless scalar field revisited'
Szpak, Nikodem
2009-01-01
Bizon et al (2009 Class. Quantum Grav. 26 175006) discuss the power-law tail in the long-time evolution of a spherically symmetric self-gravitating massless scalar field in odd spatial dimensions. They derive explicit expressions for the leading-order asymptotics for solutions with small initial data by using formal series expansions. Unfortunately, this approach misses an interesting observation that the actual decay rate is a product of asymptotic cancellations occurring due to a special structure of the nonlinear terms. Here, we show that one can calculate the leading asymptotics more directly by recognizing the special structure and cancellations already on the level of the wave equation. (comments and replies)
Spinning gravitating objects in the effective field theory in the post-Newtonian scheme
Levi, Michele [Université Pierre et Marie Curie-Paris VI, CNRS-UMR 7095,Institut d’Astrophysique de Paris, 98 bis Boulevard Arago, 75014 Paris (France); Sorbonne Universités, Institut Lagrange de Paris,98 bis Boulevard Arago, 75014 Paris (France); Steinhoff, Jan [Max-Planck-Institute for Gravitational Physics (Albert-Einstein-Institute),Am Mühlenberg 1, 14476 Potsdam-Golm (Germany); Centro Multidisciplinar de Astrofisica, Instituto Superior Tecnico, Universidade de Lisboa,Avenida Rovisco Pais 1, 1049-001 Lisboa (Portugal)
2015-09-30
We introduce a formulation for spinning gravitating objects in the effective field theory in the post-Newtonian scheme in the context of the binary inspiral problem. We aim at an effective action, where all field modes below the orbital scale are integrated out. We spell out the relevant degrees of freedom, in particular the rotational ones, and the associated symmetries. Building on these symmetries, we introduce the minimal coupling part of the point particle action in terms of gauge rotational variables, and construct the spin-induced nonminimal couplings, where we obtain the leading order couplings to all orders in spin. We specify the gauge for the rotational variables, where the unphysical degrees of freedom are eliminated already from the Feynman rules, and all the orbital field modes are integrated out. The equations of motion of the spin can be directly obtained via a proper variation of the action, and Hamiltonians may be straightforwardly derived. We implement this effective field theory for spin to derive all spin dependent potentials up to next-to-leading order to quadratic level in spin, namely up to the third post-Newtonian order for rapidly rotating compact objects. In particular, the proper next-to-leading order spin-squared potential and Hamiltonian for generic compact objects are also derived. For the implementations we use the nonrelativistic gravitational field decomposition, which is found here to eliminate higher-loop Feynman diagrams also in spin dependent sectors, and facilitates derivations. This formulation for spin is thus ideal for treatment of higher order spin dependent sectors.
Multivector field formulation of Hamiltonian field theories: equations and symmetries
Echeverria-Enriquez, A.; Munoz-Lecanda, M.C.; Roman-Roy, N. [Departamento de Matematica Aplicada y Telematica, Edificio C-3, Campus Norte UPC, Barcelona (Spain)
1999-12-03
We state the intrinsic form of the Hamiltonian equations of first-order classical field theories in three equivalent geometrical ways: using multivector fields, jet fields and connections. Thus, these equations are given in a form similar to that in which the Hamiltonian equations of mechanics are usually given. Then, using multivector fields, we study several aspects of these equations, such as the existence and non-uniqueness of solutions, and the integrability problem. In particular, these problems are analysed for the case of Hamiltonian systems defined in a submanifold of the multimomentum bundle. Furthermore, the existence of first integrals of these Hamiltonian equations is considered, and the relation between Cartan-Noether symmetries and general symmetries of the system is discussed. Noether's theorem is also stated in this context, both the 'classical' version and its generalization to include higher-order Cartan-Noether symmetries. Finally, the equivalence between the Lagrangian and Hamiltonian formalisms is also discussed. (author)
Gravitational waves from Abelian gauge fields and cosmic strings at preheating
Dufaux, Jean-Francois; Figueroa, Daniel G.; Garcia-Bellido, Juan
2010-01-01
Primordial gravitational waves provide a very important stochastic background that could be detected soon with interferometric gravitational wave antennas or indirectly via the induced patterns in the polarization anisotropies of the cosmic microwave background. The detection of these waves will open a new window into the early Universe, and therefore it is important to characterize in detail all possible sources of primordial gravitational waves. In this paper we develop theoretical and numerical methods to study the production of gravitational waves from out-of-equilibrium gauge fields at preheating. We then consider models of preheating after hybrid inflation, where the symmetry breaking field is charged under a local U(1) symmetry. We analyze in detail the dynamics of the system in both momentum and configuration space. We show that gauge fields leave specific imprints in the resulting gravitational wave spectra, mainly through the appearance of new peaks at characteristic frequencies that are related to the mass scales in the problem. We also show how these new features in the spectra correlate with stringlike spatial configurations in both the Higgs and gauge fields that arise due to the appearance of topological winding numbers of the Higgs around Nielsen-Olesen strings. We study in detail the time evolution of the spectrum of gauge fields and gravitational waves as these strings evolve and decay before entering a turbulent regime where the gravitational wave energy density saturates.
Killing vector fields in three dimensions: a method to solve massive gravity field equations
Guerses, Metin, E-mail: gurses@fen.bilkent.edu.t [Department of Mathematics, Faculty of Sciences, Bilkent University, 06800 Ankara (Turkey)
2010-10-21
Killing vector fields in three dimensions play an important role in the construction of the related spacetime geometry. In this work we show that when a three-dimensional geometry admits a Killing vector field then the Ricci tensor of the geometry is determined in terms of the Killing vector field and its scalars. In this way we can generate all products and covariant derivatives at any order of the Ricci tensor. Using this property we give ways to solve the field equations of topologically massive gravity (TMG) and new massive gravity (NMG) introduced recently. In particular when the scalars of the Killing vector field (timelike, spacelike and null cases) are constants then all three-dimensional symmetric tensors of the geometry, the Ricci and Einstein tensors, their covariant derivatives at all orders, and their products of all orders are completely determined by the Killing vector field and the metric. Hence, the corresponding three-dimensional metrics are strong candidates for solving all higher derivative gravitational field equations in three dimensions.
Plocková, Jana; Chmelík, Josef
2006-01-01
Roč. 1118, č. 2 (2006), s. 253-260 ISSN 0021-9673 R&D Projects: GA MZe QD1005 Institutional research plan: CEZ:AV0Z40310501 Keywords : gravitational field flow fractionation * focusing elution mode * carrier liquid density Subject RIV: CB - Analytical Chemistry, Separation Impact factor: 3.554, year: 2006
Primordial gravitational waves induced by magnetic fields in an ekpyrotic scenario
Asuka Ito
2017-08-01
Full Text Available Both inflationary and ekpyrotic scenarios can account for the origin of the large scale structure of the universe. It is often said that detecting primordial gravitational waves is the key to distinguish both scenarios. We show that this is not true if the gauge kinetic function is present in the ekpyrotic scenario. In fact, primordial gravitational waves sourced by the gauge field can be produced in an ekpyrotic universe. We also study scalar fluctuations sourced by the gauge field and show that it is negligible compared to primordial gravitational waves. This comes from the fact that the fast roll condition holds in ekpyrotic models.
Gravitation: Field theory par excellence Newton, Einstein, and beyond
Yilmaz, H.
1984-01-01
Newtonian gravity satifies the two principles of equivalence m/sub i/ = m/sub p/ (the passive principle) and m/sub a/ = m/sub p/ (the active principle). A relativistic gauge field concept in D = s+1 dimensional curved-space will, in general, violate these two principles as in m/sub p/ = αm/sub i/, m/sub a/ = lambdam/sub p/ where α = D: 3 and lambda measures the presence of the field stress-energy t/sup ν//sub μ/ in the field equations. It is shown that α = 1, lambda = 0 corresponds to general relativity and α = 1, lambda = 1 to the theory of the author. It is noted that the correspondence limit of general relativity is not Newton's theory but a theory suggested by Robert Hooke a few years before Newton published his in Principia. The gauge is independent of the two principles but had to do with local special relativistic correspondence and compatibility with quantum mechanics. It is shown that unless α = 1, lambda = 1 the generalized theory cannot predict correctly many observables effects, including the 532'' per century Newtonian part in Mercury's perihelion advance
General projective relativity and the vector-tensor gravitational field
Arcidiacono, G.
1986-01-01
In the general projective relativity, the induced 4-dimensional metric is symmetric in three cases, and we obtain the vector-tensor, the scalar-tensor, and the scalar-vector-tensor theories of gravitation. In this work we examine the vector-tensor theory, similar to the Veblen's theory, but with a different physical interpretation
Electromagnetic Waves in a Uniform Gravitational Field and Planck's Postulate
Acedo, Luis; Tung, Michael M.
2012-01-01
The gravitational redshift forms the central part of the majority of the classical tests for the general theory of relativity. It could be successfully checked even in laboratory experiments on the earth's surface. The standard derivation of this effect is based on the distortion of the local structure of spacetime induced by large masses. The…
On gravitational wave energy in Einstein gravitational theory
Folomeshkin, V.N.; Vlasov, A.A.
1978-01-01
By the example of precise wave solutions for the Einstein equations it is shown that a standard commonly adopted formulation of energy-momentum problem with pseudotensors provides us either with a zero or sign-variable values for the energy of gravitational waves. It is shown that if in the Einstein gravitational theory a strict transition to the limits of weak fields is realised then the theory gives us an unambiguous zero result for weak gravitational waves. The well-known non-zero result arises due to incorrect transition to weak field approximation in the Einstein gravitation theory
Dhiman, Joginder Singh; Sharma, Rajni
2017-12-01
The effects of nonuniform rotation and magnetic field on the instability of a self gravitating infinitely extending axisymmetric cylinder of viscoelastic ferromagnetic medium have been studied using the Generalised Hydrodynamic (GH) model. The non-uniform magnetic field and rotation are acting along the axial direction of the cylinder and the propagation of the wave is considered along the radial direction, while the ferrofluid magnetization is taken collinear with the magnetic field. A general dispersion relation representing magnetization, magnetic permeability and viscoelastic relaxation time parameters is obtained using the normal mode analysis method in the linearized perturbation equation system. Jeans criteria which represent the onset of instability of self gravitating medium are obtained under the limits; when the medium behaves like a viscous liquid (strongly coupled limit) and a Newtonian liquid (weakly coupled limit). The effects of various parameters on the Jeans instability criteria and on the growth rate of self gravitating viscoelastic ferromagnetic medium have been discussed. It is found that the magnetic polarizability due to ferromagnetization of medium marginalizes the effect of non-uniform magnetic field on the Jeans instability, whereas the viscoelasticity of the medium has the usual stabilizing effect on the instability of the system. Further, it is found that the cylindrical geometry is more stable than the Cartesian one. The variation of growth rate against the wave number and radial distance has been depicted graphically.
Dark matter cosmic string in the gravitational field of a black hole
Nakonieczny, Łukasz; Nakonieczna, Anna; Rogatko, Marek
2018-03-01
We examined analytically and proposed a numerical model of an Abelian Higgs dark matter vortex in the spacetime of a stationary axisymmetric Kerr black hole. In analytical calculations the dark matter sector was modeled by an addition of a U(1)-gauge field coupled to the visible sector. The backreaction analysis revealed that the impact of the dark vortex presence is far more complicated than causing only a deficit angle. The vortex causes an ergosphere shift and the event horizon velocity is also influenced by its presence. These phenomena are more significant than in the case of a visible vortex sector. The area of the event horizon of a black hole is diminished and this decline is larger in comparison to the Kerr black hole with an Abelian Higgs vortex case. After analyzing the gravitational properties for the general setup, we focused on the subset of models that are motivated by particle physics. We retained the Abelian Higgs model as a description of the dark matter sector (this sector contained a heavy dark photon and an additional complex scalar) and added a real scalar representing the real component of the Higgs doublet in the unitary gauge, as well as an additional U(1)-gauge field representing an ordinary electromagnetic field. Moreover, we considered two coupling channels between the visible and dark sectors, which were the kinetic mixing between the gauge fields and a quartic coupling between the scalar fields. After solving the equations of motion for the matter fields numerically we analyzed properties of the cosmic string in the dark matter sector and its influence on the visible sector fields that are directly coupled to it. We found out that the presence of the cosmic string induced spatial variation in the vacuum expectation value of the Higgs field and a nonzero electromagnetic field around the black hole.
Canonical field quantization in an external time-dependent gravitational field
Il'yn, S.B.; Tagirov, E.A.
1975-01-01
The Green functions of the quantum scalar fiels interacting with gravitation of the homogeneous isotropic closed Universe are studied. They have been determined as an expectation value of the time-ordered product of two field operators in the cyclic states of various, in general, unitary-nonequivalent representations of canonical commutation relations. The reqularity properties of these functions are shown to be the same as of the Feynman propagator obtained for arbitrary Riemannian space-time only in the representations that from a class unitary equivalence
Kong, Dali; Zhang, Keke; Schubert, Gerald; Anderson, John
2017-10-01
The structure/amplitude of the Jovian equatorially symmetric gravitational field is affected by both rotational distortion and the fast equatorially symmetric zonal flow. We construct a fully self-consistent, four-layer, non-spheroidal (i.e, the shape is irregular) model of Jupiter that comprises an inner core, a metallic region, an outer molecular envelope and a thin transition layer between the metallic and molecular regions. While the core is assumed to have a uniform density, three different equations of state are adopted for the metallic, molecular and transition regions. We solve the governing equations via a perturbation approach. The leading-order problem accounts for the full effect of rotational distortion, and determines the density, size and shape of the core, the location and thickness of the transition layer, and the shape of the 1-bar pressure level; it also produces the mass, the equatorial and polar radii of Jupiter, and the even zonal gravitational coefficients caused by the rotational distortion. The next-order problem determines the corrections caused by the zonal flow which is assumed to be confined within the molecular envelope and on cylinders parallel to the rotation axis. Our model provides the total even gravitational coefficients that can be compared with those acquired by the Juno spacecraft.
Some aspects of gravitational waves in an isotropic background universe
Pandey, S.N.
1981-06-01
Gravitational waves are an inescapable consequence of the relativistic theory of gravitation. They are meaningfully comparable with electromagnetic waves. However, they are not conformally invariant. So, to investigate this property for gravitational waves, modified field equations are obtained of which the underlying Lagrangian is based on gravitation only. It gives, if helicity is preserved, amplitude modification, and the wave is represented by Bessel function of zero order. Some aspects of this theory are discussed with reference to gravitational waves only. (author)
Equations of motion of higher-spin gauge fields as a free differential algebra
Vasil'ev, M.A.
1988-01-01
It is shown that the introduction of auxiliary dynamical variables that generalize the gravitational Weyl tensor permits one to reduce the equations of motion of free massless fields of all spins in the anti-de Sitter O(3,2) space to a form characteristic of free differential algebras. The equations of motion of auxiliary gauge fields introduced previously are modified analogously. Arguments are presented to the effect that the equations of motion of interacting massless fields of all spins should be described in terms of a free differential algebra which is a deformation of a known free differential algebra generated by 1- and 0-forms in the adjoint representation of a nonabelian superalgebra of higher spins and auxiliary fields
Considerations concerning the definition and distribution of gravitational energy
Gottlieb, I.; Ionescu-Pallas, N.
1986-01-01
In this paper the author reviews Einstein's gravitational field equations in a covariant form in a flat space-time. Several equations are examined for gravitational energy distribution. For a single pointlike gravitational source at rest, of mass, M/sub o/, they obtain E = M/sub o/c/sup 2/. For the case of Cartesian coordinates, agreement is obtained with Landau-Fock formulation of gravitational energy
Droplet rotation model apply in steam uniform flow and gravitational field
Zhang Jinyi; Bo Hanliang; Sun Yuliang; Wang Dazhong
2012-01-01
The mechanism droplet movement behavior and the qualitative description of droplet trajectory in the steam uniform flow field in the gravitational field were researched with droplet rotation model. According to the mechanism of gravitational field and uniform flow fields, the effects on droplets movement were analyzed and the importance of lift forces was also discussed. Finally, a general trajectory and mechanism of the droplets movement was derived which lays the groundwork for the qualitative analysis of the single-drop model and could be general enough to be used in many applications. (authors)
Performance and Flow Field of a Gravitation Vortex Type Water Turbine
Nishi, Yasuyuki; Inagaki, Terumi
2017-01-01
A gravitation vortex type water turbine, which mainly comprises a runner and a tank, generates electricity by introducing a flow of water into the tank and using the gravitation vortex generated when the water drains from the bottom of the tank. This water turbine is capable of generating electricity using a low head and a low flow rate with relatively simple structure. However, because its flow field has a free surface, this water turbine is extremely complicated, and thus its relevance to p...
Behera, Harihar [BIET Higher Secondary School, Physics Department, Dhenkanal, Odisha (India)
2017-12-15
Recently reported [Eur. Phys. J. C., 77, 549 (2017). https://doi.org/10.1140/epjc/s10052-017-5116-y] gravitoelectromagnetic equations of Ummarino and Gallerati (UG) in their linearized version of general relativity (GR) are shown to match with (a) our previously reported special relativistic Maxwellian Gravity equations in the non-relativistic limit and with (b) the non-relativistic equations derived here, when the speed of gravity c{sub g} (an undetermined parameter of the theory here) is set equal to c (the speed of light in vacuum). Seen in the light of our new results, the UG equations satisfy the Correspondence Principle (cp), while many other versions of linearized GR equations that are being (or may be) used to interpret the experimental data defy the cp. Such new findings assume significance and relevance in the contexts of recent detection of gravitational waves and the gravitomagnetic field of the spinning earth and their interpretations. Being well-founded and self-consistent, the equations may be of interest and useful to researchers exploring the phenomenology of gravitomagnetism, gravitational waves and the novel interplay of gravity with different states of matter in flat space-time like UG's interesting work on superconductors in weak gravitational fields. (orig.)
The gravitational field of a charged global monopole
Min-Qiang Lu [East China Univ. of Science and Tecnology, Shangai (China). School of Fundamental Education]|[East China Inst. for Theoretical Physics, Shangai (China)
1998-10-01
A charged global monopole formed as a consequence of the spontaneous breakdown of a global symmetry should have a mass that grows linearly with the distance off its core where the gravitational effect of this configuration is equivalent to that of the deficit solid angle in the metric and the relatively tiny mass at the origin. In this paper it is shown that this small effective mass depends on the charge in that there exists a negative mass when the charge number Q is less than a critical value Q{sub c}r and that there appears a positive one when Q>Q{sub c}r.
On the hyperbolicity of Einstein's and other gauge field equations
Friedrich, H.
1985-01-01
It is shown that Einstein's vacuum field equations (respectively the conformal vacuum field equations) in a frame formalism imply a symmetric hyperbolic system of ''reduce'' propagation equations for any choice of coordinate system and frame field (and conformal factor). Certain freely specifiable ''gauge source'' functions occurring in the reduced equations reflect the choice of gauge. Together with the initial data they determine the gauge uniquely. Their choice does not affect the isometry class (conformal class) of a solution of an initial value problem. By the same method symmetric hyperbolic propagation equations are obtained from other gauge field equations, irrespective of the gauge. Using the concept of source functions one finds that Einstein's field equation, considered as second order equations for the metric coefficients, are of wave equation type in any coordinate system. (orig.)
A class of exact solutions to the Einstein field equations
Goyal, Nisha; Gupta, R K
2012-01-01
The Einstein-Rosen metric is considered and a class of new exact solutions of the field equations for stationary axisymmetric Einstein-Maxwell fields is obtained. The Lie classical approach is applied to obtain exact solutions. By using the Lie classical method, we are able to derive symmetries that are used for reducing the coupled system of partial differential equations into ordinary differential equations. From reduced differential equations we have derived some new exact solutions of Einstein-Maxwell equations. (paper)
Coupled Higgs field equation and Hamiltonian amplitude equation ...
Home; Journals; Pramana – Journal of Physics; Volume 79; Issue 1. Coupled Higgs ﬁeld equation and ... School of Mathematics and Computer Applications, Thapar University, Patiala 147 004, India; Department of Mathematics, Jaypee University of Information Technology, Waknaghat, Distt. Solan 173 234, India ...
Coupled Higgs field equation and Hamiltonian amplitude equation ...
the rational functions are obtained. Keywords. ... differential equations as is evident by the number of research papers, books and a new symbolic software .... Now using (2.11), (2.14) in (2.8) with C1 = 0 and integrating once we get. P. 2 = − β.
On the effects of gravitational fields on the electrical properties of matter
Opat, G.I.
1993-01-01
A discussion of the electrical state of a conducting solid in a static gravitational field is presented. The analysis of the stress-gravitational force balance inside the solid is complicated, however, outside the solid, in the evanescent electron field, the analysis of such a balance simplifies greatly. As a consequence of this external analysis, an expression for the electric field external to the body is presented which includes the direct effect of gravity on the electrons, as well as the indirect effect due to the stress induced by gravity acting on the bulk solid. Such fields are an important determinant of the gravitational motion of charged particles within metallic shields. 4 refs., 1 fig
Nelson's stochastic quantization of free linearized gravitational field and its Markovian structure
Lim, S.C.
1983-05-01
It is shown that by applying Nelson's stochastic quantization scheme to free linearized gravitational field tensor one can associate with the resulting stochastic system a stochastic tensor field which coincides with the ''space'' part of the Riemannian tensor in Euclidean space-time. However, such a stochastic field fails to satisfy the Markov property. Instead, it satisfies the reflection positivity. The Markovian structure of the stochastic fields associated with the electromagnetic field is also discussed. (author)
Static equilibria of the interstellar gas in the presence of magnetic and gravitational fields
Mouschovias, T.C.
1975-01-01
No exact self-consistent equilibrium calculations exist for (any model of) the system of the interstellar gas and the frozen-in magnetic field. On a large scale (approximately 1 kpc) this system is affected by the vertical galactic gravitational field, while on a small scale (approximately 1 pc) the self-gravitation of the gas comes into play and is responsible for the collapse of some clouds to form stars. Accessible equilibrium states are determined for the gas--field system on both of these scales. (U.S.)
Palenzuela, Carlos; Lehner, Luis; Yoshida, Shin
2010-01-01
In addition to producing loud gravitational waves, the dynamics of a binary black hole system could induce emission of electromagnetic radiation by affecting the behavior of plasmas and electromagnetic fields in their vicinity. We study how the electromagnetic fields are affected by a pair of orbiting black holes through the merger. In particular, we show how the binary's dynamics induce a variability in possible electromagnetically induced emissions as well as an enhancement of electromagnetic fields during the late-merge and merger epochs. These time dependent features will likely leave their imprint in processes generating detectable emissions and can be exploited in the detection of electromagnetic counterparts of gravitational waves.
Relaxation methods for gauge field equilibrium equations
Adler, S.L.; Piran, T.
1984-01-01
This article gives a pedagogical introduction to relaxation methods for the numerical solution of elliptic partial differential equations, with particular emphasis on treating nonlinear problems with delta-function source terms and axial symmetry, which arise in the context of effective Lagrangian approximations to the dynamics of quantized gauge fields. The authors present a detailed theoretical analysis of three models which are used as numerical examples: the classical Abelian Higgs model (illustrating charge screening), the semiclassical leading logarithm model (illustrating flux confinement within a free boundary or ''bag''), and the axially symmetric Bogomol'nyi-Prasad-Sommerfield monopoles (illustrating the occurrence of p topological quantum numbers in non-Abelian gauge fields). They then proceed to a self-contained introduction to the theory of relaxation methods and allied iterative numerical methods and to the practical aspects of their implementation, with attention to general issues which arise in the three examples. The authors conclude with a brief discussion of details of the numerical solution of the models, presenting sample numerical results
Stability of self-gravitating homogeneous spheroid with azimuthal magnetic field. I
Antonov, V.A.; Zheleznyak, O.A.
1988-01-01
The influence of a frozen magnetic field on the stability of a self-gravitating homogeneous spheroid with respect to a deformation that transforms it into a triaxial ellipsoid is investigated. It is shown that an azimuthal magnetic field is a stabilizing factor, allowing the spheroid to be stable at e > e/sub cr/ = 0.95285
Gravitational lensing beyond the weak-field approximation
Perlick, Volker
2014-01-01
Gravitational lensing is considered in the full spacetime formalism of general relativity, assuming that the light rays are lightlike geodesics in a Lorentzian manifold. The review consists of three parts. The first part is devoted to spherically symmetric and static spacetimes. In particular, an exact lens map for this situation is discussed. The second part is on axisymmetric and stationary spacetimes. It concentrates on the investigation of the photon region, i.e., the region filled by spherical lightlike geodesics, in the Kerr spacetime. The photon region is of crucial relevance for the formation of a shadow. Finally, the third part briefly addresses two topics that apply to spacetimes without symmetry, namely Fermat's principle and the exact lens map of Frittelli and Newman.
Gravitational lensing beyond the weak-field approximation
Perlick, Volker, E-mail: perlick@zarm.uni-bremen.de [ZARM, University of Bremen, 28359 Bremen (Germany)
2014-01-14
Gravitational lensing is considered in the full spacetime formalism of general relativity, assuming that the light rays are lightlike geodesics in a Lorentzian manifold. The review consists of three parts. The first part is devoted to spherically symmetric and static spacetimes. In particular, an exact lens map for this situation is discussed. The second part is on axisymmetric and stationary spacetimes. It concentrates on the investigation of the photon region, i.e., the region filled by spherical lightlike geodesics, in the Kerr spacetime. The photon region is of crucial relevance for the formation of a shadow. Finally, the third part briefly addresses two topics that apply to spacetimes without symmetry, namely Fermat’s principle and the exact lens map of Frittelli and Newman.
Equations of motion for a (non-linear) scalar field model as derived from the field equations
Kaniel, S.; Itin, Y.
2006-01-01
The problem of derivation of the equations of motion from the field equations is considered. Einstein's field equations have a specific analytical form: They are linear in the second order derivatives and quadratic in the first order derivatives of the field variables. We utilize this particular form and propose a novel algorithm for the derivation of the equations of motion from the field equations. It is based on the condition of the balance between the singular terms of the field equation. We apply the algorithm to a non-linear Lorentz invariant scalar field model. We show that it results in the Newton law of attraction between the singularities of the field moved on approximately geodesic curves. The algorithm is applicable to the N-body problem of the Lorentz invariant field equations. (Abstract Copyright [2006], Wiley Periodicals, Inc.)
Gravitational Field effects on the Decoherence Process and the Quantum Speed Limit.
Dehdashti, Sh; Avazzadeh, Z; Xu, Z; Shen, J Q; Mirza, B; Wang, H
2017-11-08
In this paper we use spinor transformations under local Lorentz transformations to investigate the curvature effect on the quantum-to-classical transition, described in terms of the decoherence process and of the quantum speed limit. We find that gravitational fields (introduced adopting the Schwarzschild and anti-de Sitter geometries) affect both the decoherence process and the quantum speed limit of a quantum particle with spin-1/2. In addition, as a tangible example, we study the effect of the Earth's gravitational field, characterized by the Rindler space-time, on the same particle. We find that the effect of the Earth's gravitational field on the decoherence process and quantum speed limit is very small, except when the mean speed of the quantum particle is comparable to the speed of light.
Gravitational field of static p -branes in linearized ghost-free gravity
Boos, Jens; Frolov, Valeri P.; Zelnikov, Andrei
2018-04-01
We study the gravitational field of static p -branes in D -dimensional Minkowski space in the framework of linearized ghost-free (GF) gravity. The concrete models of GF gravity we consider are parametrized by the nonlocal form factors exp (-□/μ2) and exp (□2/μ4) , where μ-1 is the scale of nonlocality. We show that the singular behavior of the gravitational field of p -branes in general relativity is cured by short-range modifications introduced by the nonlocalities, and we derive exact expressions of the regularized gravitational fields, whose geometry can be written as a warped metric. For large distances compared to the scale of nonlocality, μ r →∞ , our solutions approach those found in linearized general relativity.
Chiral symmetry breaking in d=3 NJL model in external gravitational and magnetic fields
Gitman, D. M.; Odintsov, S. D.; Shil'nov, Yu. I.
1996-01-01
The phase structure of $d=3$ Nambu-Jona-Lasinio model in curved spacetime with magnetic field is investigated in the leading order of the $1/N$-expansion and in linear curvature approximation (an external magnetic field is treated exactly). The possibility of the chiral symmetry breaking under the combined action of the external gravitational and magnetic fields is shown explicitly. At some circumstances the chiral symmetry may be restored due to the compensation of the magnetic field by the ...
Gravitational waves — A review on the theoretical foundations of gravitational radiation
Dirkes, Alain
2018-05-01
In this paper, we review the theoretical foundations of gravitational waves in the framework of Albert Einstein’s theory of general relativity. Following Einstein’s early efforts, we first derive the linearized Einstein field equations and work out the corresponding gravitational wave equation. Moreover, we present the gravitational potentials in the far away wave zone field point approximation obtained from the relaxed Einstein field equations. We close this review by taking a closer look on the radiative losses of gravitating n-body systems and present some aspects of the current interferometric gravitational waves detectors. Each section has a separate appendix contribution where further computational details are displayed. To conclude, we summarize the main results and present a brief outlook in terms of current ongoing efforts to build a spaced-based gravitational wave observatory.
On the creation of gravitational wave by photon in external electromagnetic field
Hoang Ngoc Long; Le Khac Huong
1989-08-01
The creation of the gravitational wave by the photon in an electromagnetic field is considered. We show that when the momentum of the photon is perpendicular to the field, the probability of the gravitational wave creation is largest in the direction of the motion of the photon. A numerical evaluation shows that the probability of creation in the direction mentioned is much larger than that in the direction considered, namely in the direction perpendicular to the photon momentum and may have the observable value in the present technical conditions. (author). 10 refs
Astrometric and Timing Effects of Gravitational Waves from Localized Sources
Kopeikin, Sergei M.; Schafer, Gerhard; Gwinn, Carl R.; Eubanks, T. Marshall
1998-01-01
A consistent approach for an exhaustive solution of the problem of propagation of light rays in the field of gravitational waves emitted by a localized source of gravitational radiation is developed in the first post-Minkowskian and quadrupole approximation of General Relativity. We demonstrate that the equations of light propagation in the retarded gravitational field of an arbitrary localized source emitting quadrupolar gravitational waves can be integrated exactly. The influence of the gra...
Mapping Orbits regarding Perturbations due to the Gravitational Field of a Cube
Flaviane C. F. Venditti
2015-01-01
Full Text Available The orbital dynamics around irregular shaped bodies is an actual topic in astrodynamics, because celestial bodies are not perfect spheres. When it comes to small celestial bodies, like asteroids and comets, it is even more import to consider the nonspherical shape. The gravitational field around them may generate trajectories that are different from Keplerian orbits. Modeling an irregular body can be a hard task, especially because it is difficult to know the exact shape when observing it from the Earth, due to their small sizes and long distances. Some asteroids have been observed, but it is still a small amount compared to all existing asteroids in the Solar System. An approximation of their shape can be made as a sum of several known geometric shapes. Some three-dimensional figures have closed equations for the potential and, in this work, the formulation of a cube is considered. The results give the mappings showing the orbits that are less perturbed and then have a good potential to be used by spacecrafts that need to minimize station-keeping maneuvers. Points in the orbit that minimizes the perturbations are found and they can be used for constellations of nanosatellites.
Gravitation Field Dynamics in Jeans Theory A. A. Stupka
Key words. Time equations—Jeans ... A as longitudinal vector potential, however, one should remember that it is a new generalized co-ordinate of .... Further, it is convenient to consider the equation (9) in the picture of spatial depen- dence of ...
Gravitation radiation observations
Glass, E. N.
2017-01-01
The notion of gravitational radiation begins with electromagnetic radiation. In 1887 Heinrich Hertz, working in one room, generated and received electromagnetic radiation. Maxwell's equations describe the electromagnetic field. The quanta of electromagnetic radiation are spin 1 photons. They are fundamental to atomic physics and quantum electrodynamics.
Marek, A.; Janka, H.-T.; Müller, E.
2009-03-01
We present two-dimensional (axisymmetric) neutrino-hydrodynamic simulations of the long-time accretion phase of a 15 M_⊙ progenitor star after core bounce and before the launch of a supernova explosion, when non-radial hydrodynamic instabilities like convection occur in different regions of the collapsing stellar core and the standing accretion shock instability (SASI) leads to large-amplitude oscillations of the stalled shock with a period of tens of milliseconds. Our simulations were performed with the Prometheus-Vertex code, which includes a multi-flavor, energy-dependent neutrino transport scheme and employs an effective relativistic gravitational potential. Testing the influence of a stiff and a soft equation of state for hot neutron star matter, we find that the non-radial mass motions in the supernova core impose a time variability on the neutrino and gravitational-wave signals with larger amplitudes, as well as higher frequencies in the case of a more compact nascent neutron star. After the prompt shock-breakout burst of electron neutrinos, a more compact accreting remnant produces higher neutrino luminosities and higher mean neutrino energies. The observable neutrino emission in the SASI sloshing direction exhibits a modulation of several ten percent in the luminosities and around 1 MeV in the mean energies with most power at typical SASI frequencies between roughly 20 and 100 Hz. The modulation is caused by quasi-periodic variations in the mass accretion rate of the neutron star in each hemisphere. At times later than ~50-100 ms after bounce, the gravitational-wave amplitude is dominated by the growing low-frequency (⪉200 Hz) signal associated with anisotropic neutrino emission. A high-frequency wave signal results from nonradial gas flows in the outer layers of the anisotropically accreting neutron star. Right after bounce such nonradial mass motions occur due to prompt post-shock convection in both considered cases and contribute mostly to the early
Rudolph, E [Max-Planck-Institut fuer Physik und Astrophysik, Muenchen (F.R. Germany)
1975-01-01
As a model for gravitational radiation damping of a planet the electromagnetic radiation damping of an extended charged body moving in an external gravitational field is calculated in harmonic coordinates using a weak field, slowing-motion approximation. Special attention is paid to the case where this gravitational field is a weak Schwarzschild field. Using Green's function methods for this purpose it is shown that in a slow-motion approximation there is a strange connection between the tail part and the sharp part: radiation reaction terms of the tail part can cancel corresponding terms of the sharp part. Due to this cancelling mechanism the lowest order electromagnetic radiation damping force in an external gravitational field in harmonic coordinates remains the flat space Abraham Lorentz force. It is demonstrated in this simplified model that a naive slow-motion approximation may easily lead to divergent higher order terms. It is shown that this difficulty does not arise up to the considered order.
Nonlinear scalar field equations. Pt. 1
Berestycki, H.; Lions, P.L.
1983-01-01
This paper as well as a subsequent one is concerned with the existence of nontrivial solutions for some semi-linear elliptic equations in Rsup(N). Such problems are motivated in particular by the search for certain kinds of solitary waves (stationary states) in nonlinear equations of the Klein-Gordon or Schroedinger type. (orig./HSI)
Nath, G.; Vishwakarma, J. P.
2016-11-01
Similarity solutions are obtained for the flow behind a spherical shock wave in a non-ideal gas under gravitational field with conductive and radiative heat fluxes, in the presence of a spatially decreasing azimuthal magnetic field. The shock wave is driven by a piston moving with time according to power law. The radiation is considered to be of the diffusion type for an optically thick grey gas model and the heat conduction is expressed in terms of Fourier's law for heat conduction. Similarity solutions exist only when the surrounding medium is of constant density. The gas is assumed to have infinite electrical conductivity and to obey a simplified van der Waals equation of state. It is shown that an increase of the gravitational parameter or the Alfven-Mach number or the parameter of the non-idealness of the gas decreases the compressibility of the gas in the flow-field behind the shock, and hence there is a decrease in the shock strength. The pressure and density vanish at the inner surface (piston) and hence a vacuum is formed at the center of symmetry. The shock waves in conducting non-ideal gas under gravitational field with conductive and radiative heat fluxes can be important for description of shocks in supernova explosions, in the study of a flare produced shock in the solar wind, central part of star burst galaxies, nuclear explosion etc. The solutions obtained can be used to interpret measurements carried out by space craft in the solar wind and in neighborhood of the Earth's magnetosphere.
Responses of the Brans-Dicke field due to gravitational collapses
Hwang, Dong-il; Yeom, Dong-han
2010-01-01
We study responses of the Brans-Dicke field due to gravitational collapses of scalar field pulses using numerical simulations. Double-null formalism is employed to implement the numerical simulations. If we supply a scalar field pulse, it will asymptotically form a black hole via dynamical interactions of the Brans-Dicke field. Hence, we can observe the responses of the Brans-Dicke field by two different regions. First, we observe the late time behaviors after the gravitational collapse, which include formations of a singularity and an apparent horizon. Second, we observe the fully dynamical behaviors during the gravitational collapse and view the energy-momentum tensor components. For the late time behaviors, if the Brans-Dicke coupling is greater (or smaller) than -1.5, the Brans-Dicke field decreases (or increases) during the gravitational collapse. Since the Brans-Dicke field should be relaxed to the asymptotic value with the elapse of time, the final apparent horizon becomes time-like (or space-like). For the dynamical behaviors, we observed the energy-momentum tensors around ω ∼ -1.5. If the Brans-Dicke coupling is greater than -1.5, the T uu component can be negative at the outside of the black hole. This can allow an instantaneous inflating region during the gravitational collapse. If the Brans-Dicke coupling is less than -1.5, the oscillation of the T vv component allows the apparent horizon to shrink. This allows a combination that violates weak cosmic censorship. Finally, we discuss the implications of the violation of the null energy condition and weak cosmic censorship.
Responses of the Brans-Dicke field due to gravitational collapses
Hwang, Dong-il; Yeom, Dong-han, E-mail: enotsae@gmail.co, E-mail: innocent@muon.kaist.ac.k [Department of Physics, KAIST, Daejeon 305-701 (Korea, Republic of)
2010-10-21
We study responses of the Brans-Dicke field due to gravitational collapses of scalar field pulses using numerical simulations. Double-null formalism is employed to implement the numerical simulations. If we supply a scalar field pulse, it will asymptotically form a black hole via dynamical interactions of the Brans-Dicke field. Hence, we can observe the responses of the Brans-Dicke field by two different regions. First, we observe the late time behaviors after the gravitational collapse, which include formations of a singularity and an apparent horizon. Second, we observe the fully dynamical behaviors during the gravitational collapse and view the energy-momentum tensor components. For the late time behaviors, if the Brans-Dicke coupling is greater (or smaller) than -1.5, the Brans-Dicke field decreases (or increases) during the gravitational collapse. Since the Brans-Dicke field should be relaxed to the asymptotic value with the elapse of time, the final apparent horizon becomes time-like (or space-like). For the dynamical behaviors, we observed the energy-momentum tensors around {omega} {approx} -1.5. If the Brans-Dicke coupling is greater than -1.5, the T{sub uu} component can be negative at the outside of the black hole. This can allow an instantaneous inflating region during the gravitational collapse. If the Brans-Dicke coupling is less than -1.5, the oscillation of the T{sub vv} component allows the apparent horizon to shrink. This allows a combination that violates weak cosmic censorship. Finally, we discuss the implications of the violation of the null energy condition and weak cosmic censorship.
Electromagnetic-gravitational conversion cross sections in external electromagnetic fields
Hoang Ngoc Long; Dang Van Soa; Tuan Tran, A.
1994-09-01
The classical processes: the conversion of photons into gravitons in the static electromagnetic fields are considered by using Feynman perturbation techniques. The differential cross sections are presented for the conversion in the electric field of the flat condenser and the magnetic field of the solenoid. A numerical evaluation shows that the cross sections may have the observable value in the present technical scenario. (author). 11 refs
Anne M. Hofmeister
2017-11-01
Full Text Available Galactic mass consistent with luminous mass is obtained by fitting rotation curves (RC = tangential velocities vs. equatorial radius r using Newtonian force models, or can be unambiguously calculated from RC data using a model based on spin. In contrast, mass exceeding luminous mass is obtained from multi-parameter fits using potentials associated with test particles orbiting in a disk around a central mass. To understand this disparity, we explore the premises of these mainstream disk potential models utilizing the theorem of Gauss, thermodynamic concepts of Gibbs, the findings of Newton and Maclaurin, and well-established techniques and results from analytical mathematics. Mainstream models assume that galactic density in the axial (z and r directions varies independently: we show that this is untrue for self-gravitating objects. Mathematics and thermodynamic principles each show that modifying Poisson’s equation by summing densities is in error. Neither do mainstream models differentiate between interior and exterior potentials, which is required by potential theory and has been recognized in seminal astronomical literature. The theorem of Gauss shows that: (1 density in Poisson’s equation must be averaged over the interior volume; (2 logarithmic gravitational potentials implicitly assume that mass forms a long, line source along the z axis, unlike any astronomical object; and (3 gravitational stability for three-dimensional shapes is limited to oblate spheroids or extremely tall cylinders, whereas other shapes are prone to collapse. Our findings suggest a mechanism for the formation of the flattened Solar System and of spiral galaxies from gas clouds. The theorem of Gauss offers many advantages over Poisson’s equation in analyzing astronomical problems because mass, not density, is the key parameter.
Guiding-center equations for electrons in ultraintense laser fields
Moore, J.E.; Fisch, N.J.
1994-01-01
The guiding-center equations are derived for electrons in arbitrarily intense laser fields also subject to external fields and ponderomotive forces. Exhibiting the relativistic mass increase of the oscillating electrons, a simple frame-invariant equation is shown to govern the behavior of the electrons for sufficiently weak background fields and ponderomotive forces. The parameter regime for which such a formulation is valid is made precise, and some predictions of the equation are checked by numerical simulation
The effect of the equatorially symmetric zonal winds of Saturn on its gravitational field
Kong, Dali; Zhang, Keke; Schubert, Gerald; Anderson, John D.
2018-04-01
The penetration depth of Saturn’s cloud-level winds into its interior is unknown. A possible way of estimating the depth is through measurement of the effect of the winds on the planet’s gravitational field. We use a self-consistent perturbation approach to study how the equatorially symmetric zonal winds of Saturn contribute to its gravitational field. An important advantage of this approach is that the variation of its gravitational field solely caused by the winds can be isolated and identified because the leading-order problem accounts exactly for rotational distortion, thereby determining the irregular shape and internal structure of the hydrostatic Saturn. We assume that (i) the zonal winds are maintained by thermal convection in the form of non-axisymmetric columnar rolls and (ii) the internal structure of the winds, because of the Taylor-Proundman theorem, can be uniquely determined by the observed cloud-level winds. We calculate both the variation ΔJn , n = 2, 4, 6 … of the axisymmetric gravitational coefficients Jn caused by the zonal winds and the non-axisymmetric gravitational coefficients ΔJnm produced by the columnar rolls, where m is the azimuthal wavenumber of the rolls. We consider three different cases characterized by the penetration depth 0.36, R S, 0.2, R S and 0.1, R S, where R S is the equatorial radius of Saturn at the 1-bar pressure level. We find that the high-degree gravitational coefficient (J 12 + ΔJ 12) is dominated, in all the three cases, by the effect of the zonal flow with |ΔJ 12/J 12| > 100% and that the size of the non-axisymmetric coefficients ΔJ mn directly reflects the depth and scale of the flow taking place in the Saturnian interior.
Note on the evolution of the gravitational potential in Rastall scalar field theories
Fabris, J.C.; Hamani Daouda, M.; Piattella, O.F.
2012-01-01
We investigate the evolution of the gravitational potential in Rastall scalar field theories. In a single component model a consistent perturbation theory, formulated in the Newtonian gauge, is possible only for γ=1, which is the General Relativity limit. On the other hand, the addition of another canonical fluid component allows to consider the case γ≠1.
Post-Newtonian (and higher order) observational constraints on gravitation field theories
Nordtvedt, K.
1982-01-01
The empirically confirmed premise that gravity is a metric theory is accepted. The general class of all Lagrangian-based metric field theories of gravity is considered. A collection of observational tests of gravitational phenomena which points to a specific metric theory of gravity and rules out alternatives is created
Rumpf, H.
1984-01-01
Synchronization by slow clock transport is shown to be equivalent so that by electromagnetic signals for clocks moving along the trajectories of a timelike Killing vector field, provided the gravitational redshift is corrected for and the synchronization paths are the same. (Author)
Statistical metastability of a classical ideal gas in the Schwarzschild gravitational field
Gaina, A.B.; Zaslavskii, O.B.
1990-01-01
A classical ideal gas in the Schwarzschild gravitational field is considered. The lifetime of a gas influenced by thermal fluctuations has been calculated. It is shown that thermal effects can lead to the electric charging of a black hole in a plasma containing particles with different masses. (author)
Vogt, D.; Letelier, P.S.
2005-01-01
An exact but simple general relativistic model for the gravitational field of active galactic nuclei is constructed, based on the superposition in Weyl coordinates of a black hole, a Chazy-Curzon disk and two rods, which represent matter jets. The influence of the rods on the matter properties of
Zhu Chunhua; Zha Chaozheng
2005-01-01
The detection of a particle in electromagnetic plus gravitational fields is investigated. We obtain a set of quantum nondemolition variables. The continuous measurements of these nondemolition parameters are analyzed in the framework of restricted path integral formalism. We manipulate the corresponding propagators, and deduce the probabilities associated with the possible measurement outputs.
Palatnik, Dmitriy
2002-01-01
In this note one suggests a possibility of direct observation of the $\\theta$-parameter, introduced in the Born--Infeld theory of electroweak and gravitational fields, developed in quant-ph/0202024. Namely, one may treat $\\theta$ as a universal constant, responsible for correction to the Coulomb and Newton laws, allowing direct interaction between electrical charges and masses.
A study of fermions coupled to gauge and gravitational fields on a cylinder
Lano, R.P. [Iowa Univ., Iowa City, IA (United States). Dept. of Physics and Astronomy; Rodgers, V.G.J. [Iowa Univ., Iowa City, IA (United States). Dept. of Physics and Astronomy
1995-03-06
Fermions on a cylinder coupled to background gravitation and gauge fields are examined by studying the geometric action associated with the symmetries of such a system. We are able to show that the gauge coupling constant is constrained to a value of 1/N where N is an integer. Furthermore, in direct analogy with a Yang-Mills theory a new gravitational theory is introduced which couples to the fermions by promoting the coadjoint vector of the diffeomorphism sector to a dynamical variable. The classical dynamics of this theory are examined by displaying its symplectic structure and showing that it is equivalent to a one-dimensional system. ((orig.)).
Stochastic quantization and gauge-fixing of the linearized gravitational field
Hueffel, H.; Rumpf, H.
1984-01-01
Due to the indefiniteness of the Euclidean gravitational action the Parisi-Wu stochastic quantization scheme fails in the case of the gravitational field. Therefore we apply a recently proposed modification of stochastic quantization that works in Minkowski space and preserves all the advantages of the original Parisi-Wu method; in particular no gauge-fixing is required. Additionally stochastic gauge-fixing may be introduced and is also studied in detail. The graviton propagators obtained with and without stochastic gauge-fixing all exhibit a noncausal contribution, but apart from this effect the gauge-invariant quantities are the same as those of standard quantization. (Author)
Canonical quantum theory of gravitational field with higher derivatives, 2
Kawasaki, Shoichiro; Kimura, Tadahiko
1982-01-01
The asymptotic fields in a canonically quantized graviational field with higher derivatives are analyzed. A possible mechanism of the recovery of the physical S-matrix unitarity is discussed. The constraint nabla sub(μ)(B sup(μν) + (Beta /α)g sup(μν)B) = 0 due to the Bianchi identity on R sub(μν) is treated by Dirac's method. (author)
Quantum fields on manifolds: PCT and gravitationally induced thermal states
Sewell, G.L.
1982-01-01
We formulate an axiomatic scheme, designed to provide a framework for a general, rigorous theory of relativistic quantum fields on a class of manifolds, that includes Kruskal's extension of Schwarzchild space-time, as well as Minkowski space-time. The scheme is an adaptation of Wightman's to this class of manifolds. We infer from it that, given an arbitrary field (in general, interacting) on a manifold X, the restriction of the field to a certain open submanifold X/sup( + ), whose boundaries are event horizons, satisfies the Kubo--Martin--Schwinger (KMS) thermal equilibrium conditions. This amounts to a rigorous, model-independent proof of a generalized Hawking--Unruh effect. Further, in cases where the field enjoys a certain PCT symmetry, the conjugation governing the KMS condition is just the PCT operator. The key to these results is an analogue, that we prove, of the Bisognano--Wichmann theorem [J. Math. Phys. 17, (1976), Theorem 1]. We also construct an alternative scheme by replacing a regularity condition at an event horizon by the assumption that the field in X/sup( + ) is in a ground, rather then a thermal, state. We show that, in this case, the observables in X/sup( + ) are uncorrelated to those in its causal complement, X/sup( - ), and thus that the event horizons act as physical barriers. Finally, we argue that the choice between the two schemes must be dictated by the prevailing conditions governing the state of the field
Geometrical Aspects of non-gravitational interactions
Roldan, Omar; Barros Jr, C. C.
2016-01-01
In this work we look for a geometric description of non-gravitational forces. The basic ideas are proposed studying the interaction between a punctual particle and an electromagnetic external field. For this purpose, we introduce the concept of proper space-time, that allow us to describe this interaction in a way analogous to the one that the general relativity theory does for gravitation. The field equations that define this geometry are similar to the Einstein's equations, where in general...
Conformally covariant massless spin-two field equations
Drew, M.S.; Gegenberg, J.D.
1980-01-01
An explicit proof is constructed to show that the field equations for a symmetric tensor field hsub(ab) describing massless spin-2 particles in Minkowski space-time are not covariant under the 15-parameter group SOsub(4,2); this group is usually associated with conformal transformations on flat space, and here it will be considered as a global gauge group which acts upon matter fields defined on space-time. Notwithstanding the above noncovariance, the equations governing the rank-4 tensor Ssub(abcd) constructed from hsub(ab) are shown to be covariant provided the contraction Ssub(ab) vanishes. Conformal covariance is proved by demonstrating the covariance of the equations for the equivalent 5-component complex field; in fact, covariance is proved for a general field equation applicable to massless particles of any spin >0. It is shown that the noncovariance of the hsub(ab) equations may be ascribed to the fact that the transformation behaviour of hsub(ab) is not the same as that of a field consisting of a gauge only. Since this is in contradistinction to the situation for the electromagnetic-field equations, the vector form of the electromagnetic equations is cast into a form which can be duplicated for the hsub(ab)-field. This procedure results in an alternative, covariant, field equation for hsub(ab). (author)
Ermakov-Pinney equation in scalar field cosmologies
Hawkins, Rachael M.; Lidsey, James E.
2002-01-01
It is shown that the dynamics of cosmologies sourced by a mixture of perfect fluids and self-interacting scalar fields are described by the nonlinear, Ermakov-Pinney equation. The general solution of this equation can be expressed in terms of particular solutions to a related, linear differential equation. This characteristic is employed to derive exact cosmologies in the inflationary and quintessential scenarios. The relevance of the Ermakov-Pinney equation to the braneworld scenario is discussed
Construction of alternative Hamiltonian structures for field equations
Herrera, Mauricio [Departamento de Fisica, Facultad de Ciencias Fisicas y Matematicas, Universidad de Chile, Santiago (Chile); Hojman, Sergio A. [Departamento de Fisica, Facultad de Ciencias, Universidad de Chile, Santiago (Chile); Facultad de Educacion, Universidad Nacional Andres Bello, Santiago (Chile); Centro de Recursos Educativos Avanzados, CREA, Santiago (Chile)
2001-08-10
We use symmetry vectors of nonlinear field equations to build alternative Hamiltonian structures. We construct such structures even for equations which are usually believed to be non-Hamiltonian such as heat, Burger and potential Burger equations. We improve on a previous version of the approach using recursion operators to increase the rank of the Poisson bracket matrices. Cole-Hopf and Miura-type transformations allow the mapping of these structures from one equation to another. (author)
LSZ asymptotic condition and dynamic equations in quantum field theory
Arkhipov, A.A.; Savrin, V.I.
1983-01-01
Some techniques that may be appropriate for the derivation of dynamic equations in quantum field theory are considered. A new method of deriving equations based on the use of LSZ asymptotic condition is described. It is proved that with the help of this method it becomes possible to obtain equations for wave functions both of scattering and bound states. Work is described in several papers under the dame title. The first paper is devoted to the Bethe-Salpeter equation
Functional equations and Green's functions for augmented scalar fields
Klauder, J.R.
1977-01-01
Certain noncanonical self-coupled scalar quantum field theories, previously formulated by means of functional integration, are herein recast into the form of functional differential equations for the Green's functional. From these expressions the set of coupled equations relating the Green's functions is obtained. The new equations are compared with those of the conventional formulation, and are proposed as alternatives, especially for nonrenormalizable models when the conventional equations fail
Charged Tori in Spherical Gravitational and Dipolar Magnetic Fields
Slaný, P.; Kovář, J.; Stuchlík, Z.; Karas, Vladimír
2013-01-01
Roč. 205, č. 1 (2013), 3/1-3/16 ISSN 0067-0049 R&D Projects: GA ČR(CZ) GC13-00070J Institutional support: RVO:67985815 Keywords : accretion * accretion disks * magnetic fields Subject RIV: BN - Astronomy, Celestial Mechanics, Astrophysics Impact factor: 14.137, year: 2013
Canonical quantum theory of gravitational field with higher derivatives, 3
Kawasaki, Shoichiro; Kimura, Tadahiko
1983-01-01
A formulation which is invariant under an additional BRS transformation with nilpotency of order two is presented for the canonical theory of the renormalizable quantum gravity with higher derivatives. The canonical quantization is carried out and various equal time (anti-) commutation relations are derived. The asymptotic fields are reanalyzed. The physical particle contents are just the same as those obtained in previous papers. (author)
Lugovenko, V.N.; Pronin, V.P.; Kosheleva, L.V.
1989-01-01
A method for the correlation analysis of anomalous geophysical fields at different survey altitudes is proposed. The joint correlation analysis is performed for anomalous magnetic and gravitational fields for regions with different types of the Earth's crust. (author)
Lagrangian vector field and Lagrangian formulation of partial differential equations
M.Chen
2005-01-01
Full Text Available In this paper we consider the Lagrangian formulation of a system of second order quasilinear partial differential equations. Specifically we construct a Lagrangian vector field such that the flows of the vector field satisfy the original system of partial differential equations.
Gravitational radiation quadrupole formula is valid for gravitationally interacting systems
Walker, M.; Will, C.M.
1980-01-01
An argument is presented for the validity of the quadrupole formula for gravitational radiation energy loss in the far field of nearly Newtonian (e.g., binary stellar) systems. This argument differs from earlier ones in that it determines beforehand the formal accuracy of approximation required to describe gravitationally self-interacting systems, uses the corresponding approximate equation of motion explicitly, and evaluate the appropriate asymptotic quantities by matching along the correct space-time light cones
Theory of a gauge gravitational field at localization of the Einstein group
Tunyak, V.N.
1985-01-01
Theory of a gauge gravitational field when localizing a group of movements of the Einstein homogeneous static Universe (the R x SO Einstein group (4)) has been formulated. Proceeding from tetrade components of the Einstein Universe the relation between the Riemann metrics and gauge fields of the Einstein group has been established. Metric coherence with torsion transforming to the Kristoffel coherence of the Einstein Universe has been found when switching out gauge fields. It is shown that within the limit of infinite radius of the Einstein Universe curvature the given Einstein-invariant gauge theory transforms to the tetrade gravitation theory with localized triade rotations. Exact solutions in the form of nonsingular cosmological models have been obtained
Linear interaction of gravitational waves
Ciubotariu, C.D.
1992-01-01
Starting with the linearized Einstein equations written in the same form as Maxwell equations, a damping term is found in the wave equation. The analogy with the propagation of the electromagnetic wave in ohmic media is obvious if we introduce an 'ohmic relation' for gravitational interaction. The possibility of the amplification of gravitational waves by a suitable choice of the velocity field of a dust ('dust with negative viscosity'), for example by the use of the free-electron laser principle, is indicated. (Author)
Particle content and degrees of freedom of a gravitational field in 4th order theories of gravity
Moebius, K.; Akademie der Wissenschaften der DDR, Potsdam-Babelsberg. Einstein-Laboratorium fuer Theoretische Physik)
1988-01-01
In gravitational theories of 4-th order, the influence of certain properties of the field equations (tracelessness, conformal invariance, scale invariance respectively their breaking) for the 'particle content' (number of degrees of freedom, mass, spin) is investigated. Using the plane-wave ansatz valid in linearized theory it is possible to determine the mass content of the theory, but one cannot get assertions about the number of degrees of freedom and the spin states corresponding to the field quanta. In the linearized theory, this can be done with a spin projection formalism. Using the Cauchy initial value problem and a counting method first developed by Einstein one can get, however, a useful definition of the concept of the degrees of freedom for the full nonlinear theory. This is due to the fact that this method allows to incorporate the concrete structure of the field equations (and thus their nonlinearities). Analysing different general-relativistic field theories via these approaches the influence of the various structures of nonlinearities is discussed. It is, in particular, shown that those results obtained by the spin projection formalism can be reproduced by 'nonlinear methods'. (author)
BRS symmetry in stochastic quantization of the gravitational field
Nakazawa, Naohito.
1989-12-01
We study stochastic quantization of gravity in terms of a BRS invariant canonical operator formalism. By introducing artificially canonical momentum variables for the original field variables, a canonical formulation of stochastic quantization is proposed in a sense that the Fokker-Planck hamiltonian is the generator of the fictitious time translation. Then we show that there exists a nilpotent BRS symmetry in an enlarged phase space for gravity (in general, for the first-class constrained systems). The stochastic action of gravity includes explicitly an unique De Witt's type superspace metric which leads to a geometrical interpretation of quantum gravity analogous to nonlinear σ-models. (author)
Montani, Giovanni; Ruffini, Remo; Zalaletdinov, Roustam
2003-01-01
A model for the static weak-field macroscopic medium is analysed and the equation for the macroscopic gravitational potential is derived. This is a biharmonic equation which is a non-trivial generalization of the Poisson equation of Newtonian gravity. In the case of strong gravitational quadrupole polarization, it essentially holds inside a macroscopic matter source. Outside the source the gravitational potential fades away exponentially. The equation is equivalent to a system of the Poisson equation and the non-homogeneous modified Helmholtz equations. The general solution to this system is obtained by using the Green function method and it is not limited to Newtonian gravity. In the case of insignificant gravitational quadrupole polarization, the equation for macroscopic gravitational potential becomes the Poisson equation with the matter density renormalized by a factor including the value of the quadrupole gravitational polarization of the source. The general solution to this equation obtained by using the Green function method is limited to Newtonian gravity
Bencivinni, Daniele
2011-01-01
The chapters about the propagation of the electromagnetic field, its properties in view of the propagation in space, the accompanying momentum, its kinetic energy and its mass-equivalent distribution of the total energy coupled to the relativistic mass represent today known and scientifically for a long time acknowledged as well as proved description of each phenomena. They are successively in a mathematically simple way formally listed and explained. The fundamental results of quantum mechanics, the quantum-mechanical momentum, Planck's action quantum etc. are also presented in a simplified way. Also the essential forms of special relativity theory concerning the propagation of energy and momentum are presented. In a last setpit is checked, whether a possible common entity between the listed scientific experiences can be established. Possible explanation approaches on the described connections and the subsequent results are presented. If the gravitational waves are interpreted as quantized electromagnetic quantum waves, as matter waves, which can be assigned to a mass in the sense of Louis de Broglie and are for instance detectable as electron waves, by means of the relativistic quantum-mechanical spatial radiation gravitation could be described. So the ''quantum-mechanical wave'' could be responsible for the generation of mass via the interaction of elementary quantum fields. The propagation of one of these as mass appearing interaction of bound quantum fields can carry a conventional momentum because of its kinetic energy. The interaction in the Bose-Einstein condensate shows that the cooled rest mass exhibits the picture of a standing wave, the wave front of which propagates into the space. Because of the massive superposition of interference pattern warns the gravitational respectively matter wave can no more be isolated. A spatial radiation is however possible. Matter can generate a radiation in front of the inertial mass (quantum waves). If it succeeds to
ODE/IM correspondence and modified affine Toda field equations
Ito, Katsushi; Locke, Christopher
2014-08-15
We study the two-dimensional affine Toda field equations for affine Lie algebra g{sup ^} modified by a conformal transformation and the associated linear equations. In the conformal limit, the associated linear problem reduces to a (pseudo-)differential equation. For classical affine Lie algebra g{sup ^}, we obtain a (pseudo-)differential equation corresponding to the Bethe equations for the Langlands dual of the Lie algebra g, which were found by Dorey et al. in study of the ODE/IM correspondence.
Fukushima, Toshio
2017-01-01
In order to obtain the gravitational field of a general finite body inside its Brillouin sphere, we developed a new method to compute the field accurately. First, the body is assumed to consist of some layers in a certain spherical polar coordinate system and the volume mass density of each layer is expanded as a Maclaurin series of the radial coordinate. Second, the line integral with respect to the radial coordinate is analytically evaluated in a closed form. Third, the resulting surface integrals are numerically integrated by the split quadrature method using the double exponential rule. Finally, the associated gravitational acceleration vector is obtained by numerically differentiating the numerically integrated potential. Numerical experiments confirmed that the new method is capable of computing the gravitational field independently of the location of the evaluation point, namely whether inside, on the surface of, or outside the body. It can also provide sufficiently precise field values, say of 14–15 digits for the potential and of 9–10 digits for the acceleration. Furthermore, its computational efficiency is better than that of the polyhedron approximation. This is because the computational error of the new method decreases much faster than that of the polyhedron models when the number of required transcendental function calls increases. As an application, we obtained the gravitational field of 433 Eros from its shape model expressed as the 24 × 24 spherical harmonic expansion by assuming homogeneity of the object.
Fukushima, Toshio, E-mail: Toshio.Fukushima@nao.ac.jp [National Astronomical Observatory/SOKENDAI, Ohsawa, Mitaka, Tokyo 181-8588 (Japan)
2017-10-01
In order to obtain the gravitational field of a general finite body inside its Brillouin sphere, we developed a new method to compute the field accurately. First, the body is assumed to consist of some layers in a certain spherical polar coordinate system and the volume mass density of each layer is expanded as a Maclaurin series of the radial coordinate. Second, the line integral with respect to the radial coordinate is analytically evaluated in a closed form. Third, the resulting surface integrals are numerically integrated by the split quadrature method using the double exponential rule. Finally, the associated gravitational acceleration vector is obtained by numerically differentiating the numerically integrated potential. Numerical experiments confirmed that the new method is capable of computing the gravitational field independently of the location of the evaluation point, namely whether inside, on the surface of, or outside the body. It can also provide sufficiently precise field values, say of 14–15 digits for the potential and of 9–10 digits for the acceleration. Furthermore, its computational efficiency is better than that of the polyhedron approximation. This is because the computational error of the new method decreases much faster than that of the polyhedron models when the number of required transcendental function calls increases. As an application, we obtained the gravitational field of 433 Eros from its shape model expressed as the 24 × 24 spherical harmonic expansion by assuming homogeneity of the object.
Dark sector impact on gravitational collapse of an electrically charged scalar field
Nakonieczna, Anna [Institute of Physics, Maria Curie-Skłodowska University,Plac Marii Curie-Skłodowskiej 1, 20-031 Lublin (Poland); Institute of Agrophysics, Polish Academy of Sciences,Doświadczalna 4, 20-290 Lublin (Poland); Rogatko, Marek [Institute of Physics, Maria Curie-Skłodowska University,Plac Marii Curie-Skłodowskiej 1, 20-031 Lublin (Poland); Nakonieczny, Łukasz [Institute of Theoretical Physics, Faculty of Physics, University of Warsaw,Pasteura 5, 02-093 Warszawa (Poland)
2015-11-04
Dark matter and dark energy are dominating components of the Universe. Their presence affects the course and results of processes, which are driven by the gravitational interaction. The objective of the paper was to examine the influence of the dark sector on the gravitational collapse of an electrically charged scalar field. A phantom scalar field was used as a model of dark energy in the system. Dark matter was modeled by a complex scalar field with a quartic potential, charged under a U(1)-gauge field. The dark components were coupled to the electrically charged scalar field via the exponential coupling and the gauge field-Maxwell field kinetic mixing, respectively. Complete non-linear simulations of the investigated process were performed. They were conducted from regular initial data to the end state, which was the matter dispersal or a singularity formation in a spacetime. During the collapse in the presence of dark energy dynamical wormholes and naked singularities were formed in emerging spacetimes. The wormhole throats were stabilized by the violation of the null energy condition, which occurred due to a significant increase of a value of the phantom scalar field function in its vicinity. The square of mass parameter of the dark matter scalar field potential controlled the formation of a Cauchy horizon or wormhole throats in the spacetime. The joint impact of dark energy and dark matter on the examined process indicated that the former decides what type of an object forms, while the latter controls the amount of time needed for the object to form. Additionally, the dark sector suppresses the natural tendency of an electrically charged scalar field to form a dynamical Reissner-Nordström spacetime during the gravitational collapse.
On the fundamental principles of the relativistic theory of gravitation
Logunov, A.A.; Mestvirishvili, M.A.
1990-01-01
This paper expounds consistently within the frames of the Special Relativity Theory the fundamental postulates of the Relativistic Theory of Gravitation (RTG) which make it possible to obtain the unique complete system of the equations for gravitational field. Major attention has been paid to the analysis of the gauge group and of the causality principle. Some results related to the evolution of the Friedmann Universe, to gravitational collapse, etc. being the consequences of the RTG equations are also presented. 7 refs
Exact gravitational quasinormal frequencies of topological black holes
Birmingham, Danny; Mokhtari, Susan
2006-01-01
We compute the exact gravitational quasinormal frequencies for massless topological black holes in d-dimensional anti-de Sitter space. Using the gauge invariant formalism for gravitational perturbations derived by Kodama and Ishibashi, we show that in all cases the scalar, vector, and tensor modes can be reduced to a simple scalar field equation. This equation is exactly solvable in terms of hypergeometric functions, thus allowing an exact analytic determination of the gravitational quasinormal frequencies
Rebreyend, D.; Pignol, G.; Baeßler, S.; Nesvizhevsky, V. V.; Protasov, K.; Voronin, A.
2014-01-01
Gravitational resonance spectroscopy consists in measuring the energy spectrum of bouncing ultracold neutrons above a mirror by inducing resonant transitions between different discrete quantum levels. We discuss how to induce the resonances with a flow through arrangement in the GRANIT spectrometer, excited by an oscillating magnetic field gradient. The spectroscopy could be realized in two distinct modes (so called DC and AC) using the same device to produce the magnetic excitation. We present calculations demonstrating the feasibility of the newly proposed AC mode
Unified theory of gravitation, electromagnetism, and the Yang-Mills field
Borchsenius, K.
1976-01-01
The recent modification and extension of Einstein's nonsymmetric unified field theory for gravitation and electromagnetism is generalized to include the Yang-Mills field theory. The generalization consists in assuming that the components of the linear connection and of the fundamental tensor are not ordinary c numbers but are matrices related to some unitary symmetry. As an example we consider the SU(2) case. The theory is applied to the gauge-covariant formulation of electrically and isotopically charged spin-1/2 field theories
Gravitational and electromagnetic fields near an anti-de Sitter-like infinity
Krtous, Pavel; Podolsky, Jiri
2004-01-01
We analyze the asymptotic structure of general gravitational and electromagnetic fields near an anti-de Sitter-like conformal infinity. The dependence of the radiative component of the fields on a null direction along which the infinity is approached is obtained. The directional pattern of outgoing and ingoing radiation, which supplements standard peeling property, is determined by the algebraic (Petrov) type of the fields and also by the orientation of the principal null directions with respect to timelike infinity. The dependence on the orientation is a new feature if compared to spacelike infinity
Field equations for gravity quadratic in the curvature
Rose, B.
1992-01-01
Vacuum field equations for gravity are studied having their origin in a Lagrangian quadratic in the curvature. The motivation for this choice of the Lagrangian-namely the treating of gravity in a strict analogy to gauge theories of Yang-Mills type-is criticized, especially the implied view of connections as gauge potentials with no dynamical relation to the metric. The correct field equations with respect to variation of the connections and the metric independently are given. We deduce field equations which differs from previous ones by variation of the metric, the torsion, and the nonmetricity from which the connections are built. 6 refs
Evaluation of abutment scour prediction equations with field data
Benedict, S.T.; Deshpande, N.; Aziz, N.M.
2007-01-01
The U.S. Geological Survey, in cooperation with FHWA, compared predicted abutment scour depths, computed with selected predictive equations, with field observations collected at 144 bridges in South Carolina and at eight bridges from the National Bridge Scour Database. Predictive equations published in the 4th edition of Evaluating Scour at Bridges (Hydraulic Engineering Circular 18) were used in this comparison, including the original Froehlich, the modified Froehlich, the Sturm, the Maryland, and the HIRE equations. The comparisons showed that most equations tended to provide conservative estimates of scour that at times were excessive (as large as 158 ft). Equations also produced underpredictions of scour, but with less frequency. Although the equations provide an important resource for evaluating abutment scour at bridges, the results of this investigation show the importance of using engineering judgment in conjunction with these equations.
Field Method for Integrating the First Order Differential Equation
JIA Li-qun; ZHENG Shi-wang; ZHANG Yao-yu
2007-01-01
An important modern method in analytical mechanics for finding the integral, which is called the field-method, is used to research the solution of a differential equation of the first order. First, by introducing an intermediate variable, a more complicated differential equation of the first order can be expressed by two simple differential equations of the first order, then the field-method in analytical mechanics is introduced for solving the two differential equations of the first order. The conclusion shows that the field-method in analytical mechanics can be fully used to find the solutions of a differential equation of the first order, thus a new method for finding the solutions of the first order is provided.
Exact solutions to the nonlinear spinor field equations in the Goedel universe
Herrera, A.
1996-01-01
The nonlinear spinor field in the external gravitational field of the Goedel universe is considered and exact static solutions to the field equations corresponding to the Lagrangians with the nonlinear terms L N =F(I S ) and L N =G(I P ) are obtained. Here F(I S ) and G(I P ) are arbitrary functions of the spinor invariants I S =S+Ψ bar Ψ and I P =P 2 =(iΨ bar γ 5 Ψ) 2 . The conditions under which one-dimensional soliton-like solutions exist are established and the role of gravity in the formation of these objects is determined. 9 refs., 1 fig
Relativistic wave equations for particles in electromagnetic fields
Good, R.H. Jr.
1989-01-01
A new type of generalization of the Dirac equation of higher spin particles and antiparticles is given, in case only the terms proportional to the external fields need to be retained. copyright 1989 Academic Press, Inc
A new solution of Einstein's vacuum field equations
The motivation for the new solution ensues ... terms of singularity, does not seem to work universally as there also exist other solutions of eq. ..... the field equations and not necessarily a contribution to the energy–stress tensor, rather just.
Linear spin-zero quantum fields in external gravitational and scalar fields
Kay, B.S.
1977-11-01
A general formalism for quantizing the covariant Klein Gordon equation in an arbitrary globally hyperbolic space-time is presented. It is argued that much of the conceptual confusion surrounding ''quantum field theory in curved space-time'' has been caused by the misapplication of a quantization procedure (the single representation formalism) which is really only suitable for quantizing stationary systems. Drawing on a close analogy with time-dependent external field problems in flat space-time, it is argued for the introduction of a new quantization procedure: the many vacuum formalism which accommodates non-stationary situations. In the many vacuum formalism, a whole family of different representations of the field algebra plays a role and dynamics is necessarily described in terms of isomorphisms between different algebras rather than automorphisms of a single algebra. It is shown how this many vacuum approach gives physically sensible results in the flat space-time case. In the curved space-time case, corresponding well defined formalism is obtained relying on rigorous results established in I. A principal feature is that a different vacuum state is obtained for each choice of Cauchy surface together with a choice of lapse and shift functions on that surface. Several questions-mathematical and interpretational- raised by the scheme are discussed
El-Nabulsi, Rami Ahmad
2018-03-01
Recently, the notion of non-standard Lagrangians was discussed widely in literature in an attempt to explore the inverse variational problem of nonlinear differential equations. Different forms of non-standard Lagrangians were introduced in literature and have revealed nice mathematical and physical properties. One interesting form related to the inverse variational problem is the logarithmic Lagrangian, which has a number of motivating features related to the Liénard-type and Emden nonlinear differential equations. Such types of Lagrangians lead to nonlinear dynamics based on non-standard Hamiltonians. In this communication, we show that some new dynamical properties are obtained in stellar dynamics if standard Lagrangians are replaced by Logarithmic Lagrangians and their corresponding non-standard Hamiltonians. One interesting consequence concerns the emergence of an extra pressure term, which is related to the gravitational field suggesting that gravitation may act as a pressure in a strong gravitational field. The case of the stellar halo of the Milky Way is considered.
Plocková, Jana; Matulík, František; Chmelík, Josef
2002-01-01
Roč. 955, č. 1 (2002), s. 95-103 ISSN 0021-9673 R&D Projects: GA AV ČR IAA4031805 Institutional research plan: CEZ:AV0Z4031919 Keywords : gravitational field-flow fractionation * field programming * hydrodynamic lift forces Subject RIV: CB - Analytical Chemistry, Separation Impact factor: 3.098, year: 2002
Teguh Budi Prayitno
2011-04-01
Full Text Available This paper studies the effect of higher order derivative tensor in the Einstein field equations for vacuum condition on the planet perihelion precession. This tensor was initially proposed as the space-time curvature tensor by Deser and Tekin on discussions about the energy effects caused by this tensor. However, they include this tensor to Einstein field equations as a new model in general relativity theory. This is very interesting since there are some questions in cosmology and astrophysics that have no answers. Thus, they hoped this model could solve those problems by finding analytical or perturbative solution and interpreting it. In this case, the perturbative solution was used to find the Schwarzschild solution and it was also applied to consider the planetary motion in the solar gravitational field. Furthermore, it was proven that the tensor is divergence-free in order to keep the Einstein field equations remain valid.
Relativistic covariant wave equations and acausality in external fields
Pijlgroms, R.B.J.
1980-01-01
The author considers linear, finite dimensional, first order relativistic wave equations: (βsup(μ)ideltasub(μ)-β)PSI(x) = 0 with βsup(μ) and β constant matrices. Firstly , the question of the relativistic covariance conditions on these equations is considered. Then the theory of these equations with β non-singular is summarized. Theories with βsup(μ), β square matrices and β singular are also discussed. Non-square systems of covariant relativistic wave equations for arbitrary spin > 1 are then considered. Finally, the interaction with external fields and the acausality problem are discussed. (G.T.H.)
Nesvizhevsky, V V; Protasov, K V
2005-01-01
An upper limit to non-Newtonian attractive forces is obtained from the measurement of quantum states of neutrons in the Earth's gravitational field. This limit improves the existing constraints in the nanometer range.
The magnetic field experiment onboard Equator-S and its scientific possibilities
K.-H. Fornacon
1999-12-01
Full Text Available The special feature of the ringcore fluxgate magnetometer on Equator-S is the high time and field resolution. The scientific aim of the experiment is the investigation of waves in the 10–100 picotesla range with a time resolution up to 64 Hz. The instrument characteristics and the influence of the spacecraft on the magnetic field measurement will be discussed. The work shows that the applied pre- and inflight calibration techniques are sufficient to suppress spacecraft interferences. The offset in spin axis direction was determined for the first time with an independent field measurement by the Equator-S Electron Drift Instrument. The data presented gives an impression of the accuracy of the measurement.Key words. Magnetospheric physics (instruments and techniques · Space plasma physics (instruments and techniques
The magnetic field experiment onboard Equator-S and its scientific possibilities
K.-H. Fornacon
Full Text Available The special feature of the ringcore fluxgate magnetometer on Equator-S is the high time and field resolution. The scientific aim of the experiment is the investigation of waves in the 10–100 picotesla range with a time resolution up to 64 Hz. The instrument characteristics and the influence of the spacecraft on the magnetic field measurement will be discussed. The work shows that the applied pre- and inflight calibration techniques are sufficient to suppress spacecraft interferences. The offset in spin axis direction was determined for the first time with an independent field measurement by the Equator-S Electron Drift Instrument. The data presented gives an impression of the accuracy of the measurement.
Key words. Magnetospheric physics (instruments and techniques · Space plasma physics (instruments and techniques
Gravitation SL(2,C) gauge theory and conservation laws
Carmeli, Moshe; Nissani, Noah
1990-01-01
This monograph gives a comprehensive presentation of the SL(2,C) Gauge Theory of Gravitation along with some recent developments in the problem of Conservation Laws in General Relativity. Emphasis is put on quadratic Lagrangians which yield the Einstein field equations, as compared with Hilbert's original linear Langrangian, thus gravitation follows the other Gauge Fields all of which are derived from nonlinear Lagrangians.
Three-dimensional loop quantum gravity: towards a self-gravitating quantum field theory
Noui, Karim
2007-01-01
In a companion paper, we have emphasized the role of the Drinfeld double DSU(2) in the context of three-dimensional Riemannian loop quantum gravity coupled to massive spinless point particles. We make use of this result to propose a model for a self-gravitating quantum field theory (massive spinless non-causal scalar field) in three-dimensional Riemannian space. We start by constructing the Fock space of the free self-gravitating field: the vacuum is the unique DSU(2) invariant state, one-particle states correspond to DSU(2) unitary irreducible simple representations and any multi-particles states are obtained as the symmetrized tensor product between simple representations. The associated quantum field is defined by the usual requirement of covariance under DSU(2). Then, we introduce a DSU(2)-invariant self-interacting potential (the obtained model is a group field theory) and explicitly compute the lowest order terms (in the self-interaction coupling constant λ) of the propagator and of the three-point function. Finally, we compute the lowest order quantum gravity corrections (in the Newton constant G) to the propagator and to the three-point function
The Dirac equation in external fields: Variable separation in Cartesian coordinates
Shishkin, G.V.; Cabos, W.D.
1991-01-01
The method of separation of variables in the Dirac equation proposed in an earlier work by one of the present authors [J. Math. Phys. 30, 2132 (1989)] is developed for the complete set of interactions of the Dirac particle. The essence of the method consists of the separation of the first-order matrix differential operators that define the dependence of the Dirac bispinor on the related variables, but commutation of such operators with or between the operator of the equation is not assumed. This approach, which is perfectly justified in the presence of gravitational [Theor. Math. Phys. 70, 204 (1987)] or vector fields [J. Math. Phys. 30, 2132 (1989)], permits one to find all the possibilities of separation of variables in the Dirac equation in the case of the most general set of external fields. The complete set of interactions of the Dirac particle is determined by the symmetry group of equations, namely, viz. the SU(4) group. The interactions are scalar, vector, tensor, pseudovector and pseudoscalar. The analysis in this article is limited to Cartesian coordinates. The corresponding results for the general curvilinear coordinates will be presented in a future paper
Effect of scalar field mass on gravitating charged scalar solitons and black holes in a cavity
Ponglertsakul, Supakchai, E-mail: supakchai.p@gmail.com; Winstanley, Elizabeth, E-mail: E.Winstanley@sheffield.ac.uk
2017-01-10
We study soliton and black hole solutions of Einstein charged scalar field theory in cavity. We examine the effect of introducing a scalar field mass on static, spherically symmetric solutions of the field equations. We focus particularly on the spaces of soliton and black hole solutions, as well as studying their stability under linear, spherically symmetric perturbations of the metric, electromagnetic field, and scalar field.
Ohanian, Hans C
2013-01-01
The third edition of this classic textbook is a quantitative introduction for advanced undergraduates and graduate students. It gently guides students from Newton's gravitational theory to special relativity, and then to the relativistic theory of gravitation. General relativity is approached from several perspectives: as a theory constructed by analogy with Maxwell's electrodynamics, as a relativistic generalization of Newton's theory, and as a theory of curved spacetime. The authors provide a concise overview of the important concepts and formulas, coupled with the experimental results underpinning the latest research in the field. Numerous exercises in Newtonian gravitational theory and Maxwell's equations help students master essential concepts for advanced work in general relativity, while detailed spacetime diagrams encourage them to think in terms of four-dimensional geometry. Featuring comprehensive reviews of recent experimental and observational data, the text concludes with chapters on cosmology an...
Relativistic theory of gravitation and the graviton rest mass
Logunsov, A.A.; Mestvirishvili, M.A.
1986-01-01
This paper examines a graviton rest mass (m) introduced in the framework of the relativistic theory of gravitation and obtains equations that describe a massive gravitational field. Under the assumption that the entire hidden mass of the matter in the Universe is due to the existence of a massive gravitational field, an upper bound on the rest mass is obtained: m ≤ 0.64 x 10 --65 g
Extended Thermodynamics: a Theory of Symmetric Hyperbolic Field Equations
Müller, Ingo
2008-12-01
Extended thermodynamics is based on a set of equations of balance which are supplemented by local and instantaneous constitutive equations so that the field equations are quasi-linear first order differential equations. If the constitutive functions are subject to the requirements of the entropy principle, one may write them in symmetric hyperbolic form by a suitable choice of fields. The kinetic theory of gases, or the moment theories based on the Boltzmann equation provide an explicit example for extended thermodynamics. The theory proves its usefulness and practicality in the successful treatment of light scattering in rarefied gases. This presentation is based upon the book [1] of which the author of this paper is a co-author. For more details about the motivation and exploitation of the basic principles the interested reader is referred to that reference. It would seem that extended thermodynamics is worthy of the attention of mathematicians. It may offer them a non-trivial field of study concerning hyperbolic equations, if ever they get tired of the Burgers equation. Physicists may prefer to appreciate the success of extended thermodynamics in light scattering and to work on the open problems concerning the modification of the Navier-Stokes-Fourier theory in rarefied gases as predicted by extended thermodynamics of 13, 14, and more moments.
Rivera, Susana
Throughout the last century, since the last decades of the XIX century, until present day, there had been many attempts to achieve the unification of the Forces of Nature. First unification was done by James Clerk Maxwell, with his Electromagnetic Theory. Then Max Plank developed his Quantum Theory. In 1905, Albert Einstein gave birth to the Special Relativity Theory, and in 1916 he came out with his General Relativity Theory. He noticed that there was an evident parallelism between the Gravitational Force, and the Electromagnetic Force. So, he tried to unify these forces of Nature. But Quantum Theory interposed on his way. On the 1940’s it had been developed the Quantum Electrodynamics (QED), and with it, the unified field theory had an arise interest. On the 60’s and 70’s there was developed the Quantum Chromodynamics (QCD). Along with these theories came the discovery of the strong interaction force and weak interaction force. And though there had been many attempts to unify all these forces of the nature, it could only be achieved the Unification of strong interaction, weak interaction and Electromagnetic Force. On the late 80”s and throughout the last two decades, theories such as “super-string theory”, “or the “M-theory”, among others, groups of Scientists, had been doing grand efforts and finally they came out with the unification of the forces of nature, being the only limitation the use of more than 11 dimensions. Using an ingenious mathematical tool known as the super symmetries, based on the Kaluza - Klein work, they achieve this goal. The strings of these theories are in the rank of 10-33 m. Which make them undetectable. There are many other string theories. The GEUFT theory is based on the existence of concentrated energy lines, which vibrates, expands and contracts, submitting and absorbing energy, matter and antimatter, and which yields a determined geometry, that gives as a result the formation of stars, galaxies, nebulae, clusters
Generalized force in classical field theory. [Euler-Lagrange equations
Krause, J [Universidad Central de Venezuela, Caracas
1976-02-01
The source strengths of the Euler-Lagrange equations, for a system of interacting fields, are heuristically interpreted as generalized forces. The canonical form of the energy-momentum tensor thus consistently appears, without recourse to space-time symmetry arguments. A concept of 'conservative' generalized force in classical field theory is also briefly discussed.
Rarita-Schwinger field and multicomponent wave equation
Kaloshin, A.E.; Lomov, V.P.
2011-01-01
We suggest a simple method to solve a wave equation for Rarita-Schwinger field without additional constraints. This method based on the use of off-shell projection operators allows one to diagonalize spin-1/2 sector of the field
Vacaru, Olivia [National College of Iasi (Romania); Vacaru, Sergiu I. [Quantum Gravity Research, Topanga, CA (United States); University ' ' Al.I. Cuza' ' Iasi, Project IDEI, Iasi (Romania); Werner-Heisenberg-Institute, Max-Planck-Institute for Physics, Munich (Germany); Leibniz University of Hannover, Institute for Theoretical Physics (Germany); Ruchin, Vyacheslav
2017-03-15
Using double 2 + 2 and 3 + 1 nonholonomic fibrations on Lorentz manifolds, we extend the concept of W-entropy for gravitational fields in general relativity (GR). Such F- and W-functionals were introduced in the Ricci flow theory of three dimensional (3-d) Riemannian metrics by Perelman (the entropy formula for the Ricci flow and its geometric applications. arXiv:math.DG/0211159). Non-relativistic 3-d Ricci flows are characterized by associated statistical thermodynamical values determined by W-entropy. Generalizations for geometric flows of 4-d pseudo-Riemannian metrics are considered for models with local thermodynamical equilibrium and separation of dissipative and non-dissipative processes in relativistic hydrodynamics. The approach is elaborated in the framework of classical field theories (relativistic continuum and hydrodynamic models) without an underlying kinetic description, which will be elaborated in other work. The 3 + 1 splitting allows us to provide a general relativistic definition of gravitational entropy in the Lyapunov-Perelman sense. It increases monotonically as structure forms in the Universe. We can formulate a thermodynamic description of exact solutions in GR depending, in general, on all spacetime coordinates. A corresponding 2 + 2 splitting with nonholonomic deformation of linear connection and frame structures is necessary for generating in very general form various classes of exact solutions of the Einstein and general relativistic geometric flow equations. Finally, we speculate on physical macrostates and microstate interpretations of the W-entropy in GR, geometric flow theories and possible connections to string theory (a second unsolved problem also contained in Perelman's work) in Polyakov's approach. (orig.)
CSR Fields: Direct Numerical Solution of the Maxwell's Equation
Novokhatski, Alexander
2011-01-01
We discuss the properties of the coherent electromagnetic fields of a very short, ultra-relativistic bunch in a rectangular vacuum chamber inside a bending magnet. The analysis is based on the results of a direct numerical solution of Maxwell's equations together with Newton's equations. We use a new dispersion-free time-domain algorithm which employs a more efficient use of finite element mesh techniques and hence produces self-consistent and stable solutions for very short bunches. We investigate the fine structure of the CSR fields including coherent edge radiation. This approach should be useful in the study of existing and future concepts of particle accelerators and ultrafast coherent light sources. The coherent synchrotron radiation (CSR) fields have a strong action on the beam dynamics of very short bunches, which are moving in the bends of all kinds of magnetic elements. They are responsible for additional energy loss and energy spread; micro bunching and beam emittance growth. These fields may bound the efficiency of damping rings, electron-positron colliders and ultrafast coherent light sources, where high peak currents and very short bunches are envisioned. This is relevant to most high-brightness beam applications. On the other hand these fields together with transition radiation fields can be used for beam diagnostics or even as a powerful resource of THz radiation. A history of the study of CSR and a good collection of references can be found in (1). Electromagnetic theory suggests several methods on how to calculate CSR fields. The most popular method is to use Lienard-Wiechert potentials. Other approach is to solve numerically the approximate equations, which are a Schrodinger type equation. These numerical methods are described in (2). We suggest that a direct solution of Maxwell's equations together with Newton's equations can describe the detailed structure of the CSR fields (3).
Vacuum-field solutions of Ross and Sen-Dunn theories of gravitation
Krori, K.D.; Nandy, D.
1978-01-01
Vacuum-field solutions of Ross (Phys. Rev.; D5:284 (1972)) and Sen-Dunn (J. Math. Phys.; 12:578 (1971)) theories of gravitation have been obtained with the aid of a Friedmann-type metric. Non-static solutions are found showing that the Birkhoff theorem holds for neither theory. It has been observed that the two theories have a limited scope for vacuum solution as against the Brans-Dicke theory. Mach's principle, however, holds for both the theories. (author)
Hanauske, Matthias; Steinheimer, Jan; Bovard, Luke; Mukherjee, Ayon; Schramm, Stefan; Takami, Kentaro; Papenfort, Jens; Wechselberger, Natascha; Rezzolla, Luciano; Stöcker, Horst
2017-07-01
The underlying open questions in the fields of general relativistic astrophysics and elementary particle and nuclear physics are strongly connected and their results are interdependent. Although the physical systems are quite different, the 4D-simulation of a merger of a binary system of two neutron stars and the properties of the hot and dense matter created in high energy heavy ion collisions, strongly depend on the equation of state of fundamental elementary matter. Neutron star mergers represent optimal astrophysical laboratories to investigate the QCD phase structure using a spectrogram of the post-merger phase of the emitted gravitational waves. These studies can be supplemented by observations from heavy ion collisions to possibly reach a conclusive picture on the QCD phase structure at high density and temperature. As gravitational waves (GWs) emitted from merging neutron star binaries are on the verge of their first detection, it is important to understand the main characteristics of the underlying merging system in order to predict the expected GW signal. Based on numerical-relativity simulations of merging neutron star binaries, the emitted GW and the interior structure of the generated hypermassive neutron stars (HMNS) have been analyzed in detail. This article will focus on the internal and rotational HMNS properties and their connection with the emitted GW signal. Especially, the appearance of the hadon-quark phase transition in the interior region of the HMNS and its conjunction with the spectral properties of the emitted GW will be addressed and confronted with the simulation results of high energy heavy ion collisions.
Twisting gravitational waves and eigenvector fields for SL(2,C on an infinite jet
J. D. Finley III
2000-07-01
Full Text Available A system of coupled vector-field-valued partial differential equations is presented, the solutions to which would determine two coupled, infinite-dimensional vector-field realizations of the group SL(2,C. While the general solution is (partially presented, the complicated nature of that solution is deplored, and the hope expressed that someone can replace it by something much more natural. The physical origins of the problem are briefly described. The problem arises out of searches for Backlund transforms of a system of PDE's that describe twisting, Petrov type N solutions of Einstein's vacuum field equations.
Konishi anomaly approach to gravitational F-terms
David, Justin R.; Gava, Edi; Narain, K.S.
2003-04-01
We study gravitational corrections to the effective superpotential in theories with a single adjoint chiral multiplet, using the generalized Konishi anomaly and the gravitationally deformed chiral ring. We show that the genus one correction to the loop equation in the corresponding matrix model agrees with the gravitational corrected anomaly equations in the gauge theory. An important ingredient in the proof is the lack of factorization of chiral gauge invariant operators in presence of a supergravity background. We also find a genus zero gravitational correction to the superpotential, which can be removed by a field redefinition. (author)
Gravitation and electromagnetism
Apsel, D
1979-01-01
Through an examination of the Bohm-Aharonov experiment, a new theory of gravitation and electromagnetism is proposed. The fundamental assumption of the theory is that the motion of a particle in a combination of gravitational and electromagnetic fields is determined from a variational principle of the form delta integral /sub A//sup B /d tau =0. The form of the physical time is determined from an examination of the Maxwell-Einstein action function. The field and motion equations are formally identical to those of Maxwell-Einstein theory. The theory predicts that even in a field-free region of space, electromagnetic potentials can alter the phase of a wave function and the lifetime of a charged particle. The phase alteration has been observed in the Bohm-Aharonov experiment. There is an indication that the lifetime alteration has shown up in a recent CERN storage ring experiment. Experimental tests are proposed. (11 refs).
Dirac's equation and the nature of quantum field theory
Plotnitsky, Arkady
2012-01-01
This paper re-examines the key aspects of Dirac's derivation of his relativistic equation for the electron in order advance our understanding of the nature of quantum field theory. Dirac's derivation, the paper argues, follows the key principles behind Heisenberg's discovery of quantum mechanics, which, the paper also argues, transformed the nature of both theoretical and experimental physics vis-à-vis classical physics and relativity. However, the limit theory (a crucial consideration for both Dirac and Heisenberg) in the case of Dirac's theory was quantum mechanics, specifically, Schrödinger's equation, while in the case of quantum mechanics, in Heisenberg's version, the limit theory was classical mechanics. Dirac had to find a new equation, Dirac's equation, along with a new type of quantum variables, while Heisenberg, to find new theory, was able to use the equations of classical physics, applied to different, quantum-mechanical variables. In this respect, Dirac's task was more similar to that of Schrödinger in his work on his version of quantum mechanics. Dirac's equation reflects a more complex character of quantum electrodynamics or quantum field theory in general and of the corresponding (high-energy) experimental quantum physics vis-à-vis that of quantum mechanics and the (low-energy) experimental quantum physics. The final section examines this greater complexity and its implications for fundamental physics.
On the linear conformal gravitation
Pal'chik, M.Ya.; Fradkin, E.S.
1984-01-01
Conformal gravitation is analyzed under the assumption that its solution possesses the property of conformal symmetry. This assumption has sense in the case of small distances and only for definite types of matter fields, namely: at special choice of matter fields and their interactions, providing a lack of conformal anomalies; or at definite magnitudes of binding constants, coinciding with the zeroes of the Gell-Mann-Low function. The field equations, of the group-theoretical natura are obtained
Diffusion phenomenon at the interface of Cu-brass under a strong gravitational field
Ogata, Yudai; Tokuda, Makoto; Januszko, Kamila; Khandaker, Jahirul Islam; Mashimo, Tsutomu, E-mail: mashimo@gpo.kumamoto-u.ac.jp [Institute of Pulsed Power Science, Kumamoto University, Kumamoto 860-8555 (Japan); Iguchi, Yusuke [Department of Solid State Physics, Debrecen University, 4032 Debrecen (Hungary); Ono, Masao [Advanced Science Research Center, Japan Atomic Energy Agency (JAEA), Ibaraki 319-1195 (Japan)
2015-03-28
To investigate diffusion phenomenon at the interface between Cu and brass under a strong gravitational field generated by ultracentrifuge apparatus, we performed gravity experiments on samples prepared by electroplating with interfaces normal and parallel to the direction of gravity. For the parallel-mode sample, for which sedimentation cannot occur thorough the interface, the concentration change was significant within the lower gravity region; many pores were observed in this region. Many vacancies arising from crystal strain due to the strong gravitational field moved into the lower gravity region, and enhanced the atoms mobilities. For the two normal-mode samples, which have interface normal to the direction of gravity, the composition gradient of the brass-on-Cu sample was steeper than that for Cu-on-brass. This showed that the atoms of denser Cu diffuse in the direction of gravity, whereas Zn atoms diffuse in the opposite direction by sedimentation. The interdiffusion coefficients became higher in the Cu-on-brass sample, and became lower in the brass-on-Cu sample. This rise may be related to the behavior of the vacancies.
Building Secure Public Key Encryption Scheme from Hidden Field Equations
Yuan Ping
2017-01-01
Full Text Available Multivariate public key cryptography is a set of cryptographic schemes built from the NP-hardness of solving quadratic equations over finite fields, amongst which the hidden field equations (HFE family of schemes remain the most famous. However, the original HFE scheme was insecure, and the follow-up modifications were shown to be still vulnerable to attacks. In this paper, we propose a new variant of the HFE scheme by considering the special equation x2=x defined over the finite field F3 when x=0,1. We observe that the equation can be used to further destroy the special structure of the underlying central map of the HFE scheme. It is shown that the proposed public key encryption scheme is secure against known attacks including the MinRank attack, the algebraic attacks, and the linearization equations attacks. The proposal gains some advantages over the original HFE scheme with respect to the encryption speed and public key size.
Remarks on an equation common to Weyl's gauge field, Yang-Mills field and Toda lattice
Nishioka, M.
1984-01-01
In this letter a remark is presented on an equation of a gauge-invariant Weyl's gauge field and it is shown that the equation is common to Yang's approach to the self-duality condition for SU 2 gauge field and the simplest Toda lattice
Chrusciel, P.T.
1985-01-01
It is shown, that the interpretation of the Einstein energy-momentum ''pseudo-tensor'',''covariantized'' with the help of a background metric, as the energy-momentum tensor of the gravitational field with respect to a background field, is consistent with a geometric hamiltonian analysis. It is also shown, that the von Freud superpotential and the Komar superpotential describe the dynamics of the gravitational field in different function spaces, subject to different boundary conditions. One can pass from one superpotential to the other by performing a Legendre transformation on the boundary. It is explained why the ADM and the von Freud energy expressions are the same, for asymptotically flat space-times
Chrusciel, P.T.
1983-09-01
It is shown that the interpretation of the Einstein energy-momentum ''pseudo-tensor'', ''covariantized'' with the help of a background metric, as the energy-momentum tensor of the gravitational field with respect to a background field is consistent with a geometric Hamiltonian analysis. It is also shown that the von Freud superpotential and the Komar superpotential describe the dynamics of the gravitational field in different function spaces, subject to different boundary conditions. One can pass from one superpotential to the other by performing a Legendre transformation on the boundary. (author)
Gravitational instability in isotropic MHD plasma waves
Cherkos, Alemayehu Mengesha
2018-04-01
The effect of compressive viscosity, thermal conductivity and radiative heat-loss functions on the gravitational instability of infinitely extended homogeneous MHD plasma has been investigated. By taking in account these parameters we developed the six-order dispersion relation for magnetohydrodynamic (MHD) waves propagating in a homogeneous and isotropic plasma. The general dispersion relation has been developed from set of linearized basic equations and solved analytically to analyse the conditions of instability and instability of self-gravitating plasma embedded in a constant magnetic field. Our result shows that the presence of viscosity and thermal conductivity in a strong magnetic field substantially modifies the fundamental Jeans criterion of gravitational instability.
Non-Euclidean Geometry and Gravitation
Stavroulakis N.
2006-04-01
Full Text Available A great deal of misunderstandings and mathematical errors are involved in the currently accepted theory of the gravitational field generated by an isotropic spherical mass. The purpose of the present paper is to provide a short account of the rigorous mathematical theory and exhibit a new formulation of the problem. The solution of the corresponding equations of gravitation points out several new and unusual features of the stationary gravitational field which are related to the non-Euclidean structure of the space. Moreover it precludes the black hole from being a mathematical and physical notion.
Parquet equations for numerical self-consistent-field theory
Bickers, N.E.
1991-01-01
In recent years increases in computational power have provided new motivation for the study of self-consistent-field theories for interacting electrons. In this set of notes, the so-called parquet equations for electron systems are derived pedagogically. The principal advantages of the parquet approach are outlined, and its relationship to simpler self-consistent-field methods, including the Baym-Kadanoff technique, is discussed in detail. (author). 14 refs, 9 figs
The deflection angle of a gravitational source with a global monopole in the strong field limit
Cheng Hongbo; Man Jingyun
2011-01-01
We investigate the gravitational lensing effect in the strong field background around the Schwarzschild black hole with extremely small mass and solid deficit angle subject to the global monopole by means of the strong field limit issue. We obtain the angular position and magnification of the relativistic images and show that they relate to the global monopole parameter η. We discuss that with the increase of the parameter η, the minimum impact parameter u m and angular separation s increase and the relative magnification r decreases. We also find that s grows extremely as the increasing parameter η becomes large enough. The deflection angle will become larger when the parameter η grows. The effect from the solid deficit angle is the dependence of angular position, angular separation, relative magnification and deflection angle on the parameter η, which may offer a way to characterize some possible distinct signatures of the Schwarzschild black hole with a solid deficit angle associated with the global monopole.
Energy-momentum tensor for a Casimir apparatus in a weak gravitational field
Bimonte, Giuseppe; Calloni, Enrico; Esposito, Giampiero; Rosa, Luigi
2006-01-01
The influence of the gravity acceleration on the regularized energy-momentum tensor of the quantized electromagnetic field between two plane-parallel conducting plates is derived. We use Fermi coordinates and work to first order in the constant acceleration parameter. A perturbative expansion, to this order, of the Green functions involved and of the energy-momentum tensor is derived by means of the covariant geodesic point-splitting procedure. In correspondence to the Green functions satisfying mixed and gauge-invariant boundary conditions, and Ward identities, the energy-momentum tensor is covariantly conserved and satisfies the expected relation between gauge-breaking and ghost parts, while a new simple formula for the trace anomaly is obtained to first order in the constant acceleration. A more systematic derivation is therefore obtained of the theoretical prediction according to which the Casimir device in a weak gravitational field will experience a tiny push in the upwards direction
A stochastic differential equation framework for the turbulent velocity field
Barndorff-Nielsen, Ole Eiler; Schmiegel, Jürgen
We discuss a stochastic differential equation, as a modelling framework for the turbulent velocity field, that is capable of capturing basic stylized facts of the statistics of velocity increments. In particular, we focus on the evolution of the probability density of velocity increments...
Grassmann expansion of the classical N=2 supergravity field equations
Embacher, F.
1984-01-01
The classical field equations of N=2 supergravity are expanded with respect to an infinite dimensional Grassmann algebra. The general freedom in constructing classical solution is exhibited. As an application, a uniqueness theorem for supersymmetric extreme black holes is given. (Author)
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.
Volkmann, D; Buchen, B; Hejnowicz, Z; Tewinkel, M; Sievers, A
1991-09-01
During five rocket flights (TEXUS 18, 19, 21, 23 and 25), experiments were performed to investigate the behaviour of statoliths in rhizoids of the green alga Chara globularia Thuill. and in statocytes of cress (Lepidium sativum L.) roots, when the gravitational field changed to approx. 10(-4) · g (i.e. microgravity) during the parabolic flight (lasting for 301-390 s) of the rockets. The position of statoliths was only slightly influenced by the conditions during launch, e.g. vibration, acceleration and rotation of the rocket. Within approx. 6 min of microgravity conditions the shape of the statolith complex in the rhizoids changed from a transversely oriented lens into a longitudinally oriented spindle. The center of the statolith complex moved approx. 14 μm and 3.6 μm in rhizoids and root statocytes, respectively, in the opposite direction to the originally acting gravity vector. The kinetics of statolith displacement in rhizoids demonstrate that the velocity was nearly constant under microgravity whereas it decreased remarkably after inversion of rhizoids on Earth. It can be concluded that on Earth the position of statoliths in both rhizoids and root statocytes depends on the balance of two forces, i.e. the gravitational force and the counteracting force mediated by microfilaments.
Mass loss due to gravitational waves with Λ > 0
Saw, Vee-Liem
2017-07-01
The theoretical basis for the energy carried away by gravitational waves that an isolated gravitating system emits was first formulated by Hermann Bondi during the ’60s. Recent findings from the observation of distant supernovae revealed that the rate of expansion of our universe is accelerating, which may be well explained by sticking a positive cosmological constant into the Einstein field equations for general relativity. By solving the Newman-Penrose equations (which are equivalent to the Einstein field equations), we generalize this notion of Bondi mass-energy and thereby provide a firm theoretical description of how an isolated gravitating system loses energy as it radiates gravitational waves, in a universe that expands at an accelerated rate. This is in line with the observational front of LIGO’s first announcement in February 2016 that gravitational waves from the merger of a binary black hole system have been detected.
Souza, Rafael S. de; Opher, Reuven
2011-01-01
The origin of magnetic fields in astrophysical objects is a challenging problem in astrophysics. Throughout the years, many scientists have suggested that non-minimal gravitational-electromagnetic coupling (NMGEC) could be the origin of the ubiquitous astrophysical magnetic fields. We investigate the possible origin of intense magnetic fields by NMGEC near rotating black holes, connected with quasars and gamma-ray bursts. Whereas these intense magnetic fields are difficult to explain astrophysically, we find that they are easily explained by NMGEC.
Classical field theory on electrodynamics, non-abelian gauge theories and gravitation
Scheck, Florian
2018-01-01
Scheck’s successful textbook presents a comprehensive treatment, ideally suited for a one-semester course. The textbook describes Maxwell's equations first in their integral, directly testable form, then moves on to their local formulation. The first two chapters cover all essential properties of Maxwell's equations, including their symmetries and their covariance in a modern notation. Chapter 3 is devoted to Maxwell's theory as a classical field theory and to solutions of the wave equation. Chapter 4 deals with important applications of Maxwell's theory. It includes topical subjects such as metamaterials with negative refraction index and solutions of Helmholtz' equation in paraxial approximation relevant for the description of laser beams. Chapter 5 describes non-Abelian gauge theories from a classical, geometric point of view, in analogy to Maxwell's theory as a prototype, and culminates in an application to the U(2) theory relevant for electroweak interactions. The last chapter 6 gives a concise summary...
T. Reubelt
2003-01-01
Full Text Available An algorithm for the (kinematic orbit analysis of a Low Earth Orbiting (LEO GPS tracked satellite to determine the spherical harmonic coefficients of the terrestrial gravitational field is presented. A contribution to existing long wavelength gravity field models is expected since the kinematic orbit of a LEO satellite can nowadays be determined with very high accuracy in the range of a few centimeters. To demonstrate the applicability of the proposed method, first results from the analysis of real CHAMP Rapid Science (dynamic Orbits (RSO and kinematic orbits are illustrated. In particular, we take advantage of Newton’s Law of Motion which balances the acceleration vector and the gradient of the gravitational potential with respect to an Inertial Frame of Reference (IRF. The satellite’s acceleration vector is determined by means of the second order functional of Newton’s Interpolation Formula from relative satellite ephemeris (baselines with respect to the IRF. Therefore the satellite ephemeris, which are normally given in a Body fixed Frame of Reference (BRF have to be transformed into the IRF. Subsequently the Newton interpolated accelerations have to be reduced for disturbing gravitational and non-gravitational accelerations in order to obtain the accelerations caused by the Earth’s gravitational field. For a first insight in real data processing these reductions have been neglected. The gradient of the gravitational potential, conventionally expressed in vector-valued spherical harmonics and given in a Body Fixed Frame of Reference, must be transformed from BRF to IRF by means of the polar motion matrix, the precession-nutation matrices and the Greenwich Siderial Time Angle (GAST. The resulting linear system of equations is solved by means of a least squares adjustment in terms of a Gauss-Markov model in order to estimate the spherical harmonics coefficients of the Earth’s gravitational field.Key words. space gravity spectroscopy
Magnetic field mapping of the UCNTau magneto-gravitational trap: design study
Libersky, Matthew Murray [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2014-09-04
The beta decay lifetime of the free neutron is an important input to the Standard Model of particle physics, but values measured using different methods have exhibited substantial disagreement. The UCN r experiment in development at Los Alamos National Laboratory (LANL) plans to explore better methods of measuring the neutron lifetime using ultracold neutrons (UCNs). In this experiment, UCNs are confined in a magneto-gravitational trap formed by a curved, asymmetric Halbach array placed inside a vacuum vessel and surrounded by holding field coils. If any defects present in the Halbach array are sufficient to reduce the local field near the surface below that needed to repel the desired energy level UCNs, loss by material interaction can occur at a rate similar to the loss by beta decay. A map of the magnetic field near the surface of the array is necessary to identify any such defects, but the array's curved geometry and placement in a vacuum vessel make conventional field mapping methods difficult. A system consisting of computer vision-based tracking and a rover holding a Hall probe has been designed to map the field near the surface of the array, and construction of an initial prototype has begun at LANL. The design of the system and initial results will be described here.
Creation of particles in the gravitational field and the boundary conditions for quantized fields
Khrustalev, O.A.; Silaev, P.K.
1995-01-01
We prove, that if one impose the linear constraints on the quantized fields that satisfy different boundary conditions, it can leads to such a transformation between creation-annihilation operators, that corresponds to particle creation. We also prove, that the correspondence between field, quantized in Minkowski space and the field, quantized in Rindler space has Rindler space can't be observed. 7 refs
Supersymmetric electroweak baryogenesis, nonequilibrium field theory and quantum Boltzmann equations
Riotto, Antonio
1998-01-01
The closed time-path (CPT) formalism is a powerful Green's function formulation to describe nonequilibrium phenomena in field theory and it leads to a complete nonequilibrium quantum kinetic theory. In this paper we make use of the CPT formalism to write down a set of quantum Boltzmann equations describing the local number density asymmetries of the particles involved in supersymmetric electroweak baryogenesis. These diffusion equations automatically and self-consistently incorporate the CP-violating sources which fuel baryogenesis when transport properties allow the CP-violating charges to diffuse in front of the bubble wall separating the broken from the unbroken phase at the electroweak phase transition. This is a significant improvement with respect to recent approaches where the CP-violating sources are inserted by hand into the diffusion equations. Furthermore, the CP-violating sources and the particle number changing interactions manifest ``memory'' effects which are typical of the quantum transp ort t...
Production of gravitation waves by electromagnetic radiation
Buchner, K.; Rosca, R.
1980-01-01
An exact solution of Einstein's equations is presented that corresponds to an axisymmetric bundle of electromagnetic waves with finite cross section. Outside this bundle, there is gravitational radiation parallel to the electromagnetic radiation. If no static electromagnetic fields are present, the frequency of the gravitational waves is twice the frequency of the electromagnetic waves. Einstein's energy complex vanishes identically. The covariant energy complex, however, yields also a radial momentum. (author)
Rigorous derivation of porous-media phase-field equations
Schmuck, Markus; Kalliadasis, Serafim
2017-11-01
The evolution of interfaces in Complex heterogeneous Multiphase Systems (CheMSs) plays a fundamental role in a wide range of scientific fields such as thermodynamic modelling of phase transitions, materials science, or as a computational tool for interfacial flow studies or material design. Here, we focus on phase-field equations in CheMSs such as porous media. To the best of our knowledge, we present the first rigorous derivation of error estimates for fourth order, upscaled, and nonlinear evolution equations. For CheMs with heterogeneity ɛ, we obtain the convergence rate ɛ 1 / 4 , which governs the error between the solution of the new upscaled formulation and the solution of the microscopic phase-field problem. This error behaviour has recently been validated computationally in. Due to the wide range of application of phase-field equations, we expect this upscaled formulation to allow for new modelling, analytic, and computational perspectives for interfacial transport and phase transformations in CheMSs. This work was supported by EPSRC, UK, through Grant Nos. EP/H034587/1, EP/L027186/1, EP/L025159/1, EP/L020564/1, EP/K008595/1, and EP/P011713/1 and from ERC via Advanced Grant No. 247031.
Reduction of static field equation of Faddeev model to first order PDE
Hirayama, Minoru; Shi Changguang
2007-01-01
A method to solve the static field equation of the Faddeev model is presented. For a special combination of the concerned field, we adopt a form which is compatible with the field equation and involves two arbitrary complex functions. As a result, the static field equation is reduced to a set of first order partial differential equations
Figueroa, Daniel G; Torrentí, Francisco
2016-01-01
During or towards the end of inflation, the Standard Model (SM) Higgs forms a condensate with a large amplitude. Following inflation, the condensate oscillates, decaying non-perturbatively into the rest of the SM species. The resulting out-of-equilibrium dynamics converts a fraction of the energy available into gravitational waves (GW). We study this process using classical lattice simulations in an expanding box, following the energetically dominant electroweak gauge bosons $W^\\pm$ and $Z$. We characterize the GW spectrum as a function of the running couplings, Higgs initial amplitude, and post-inflationary expansion rate. As long as the SM is decoupled from the inflationary sector, the generation of this background is universally expected, independently of the nature of inflation. Our study demonstrates the efficiency of GW emission by gauge fields undergoing parametric resonance. The initial energy of the Higgs condensate represents however, only a tiny fraction of the inflationary energy. Consequently, th...
Time of flight and range of the motion of a projectile in a constant gravitational field
P. A. Karkantzakos
2009-01-01
Full Text Available In this paper we study the classical problem of the motion of a projectile in a constant gravitational field under the influenceof a retarding force proportional to the velocity. Specifically, we express the time of flight, the time of fall and the range ofthe motion as a function of the constant of resistance per unit mass of the projectile. We also prove that the time of fall isgreater than the time of rise with the exception of the case of zero constant of resistance where we have equality. Finally weprove a formula from which we can compute the constant of resistance per unit mass of the projectile from time of flight andrange of the motion when the acceleration due to gravity and the initial velocity of the projectile are known.
Dynamics of Equilibrium Points in a Uniformly Rotating Second-Order and Degree Gravitational Field
Feng, Jinglang; Hou, Xiyun
2017-07-01
Using tools such as periodic orbits and invariant manifolds, the global dynamics around equilibrium points (EPs) in a rotating second-order and degree gravitational field are studied. For EPs on the long axis, planar and vertical periodic families are computed, and their stability properties are investigated. Invariant manifolds are also computed, and their relation to the first-order resonances is briefly discussed. For EPs on the short axis, planar and vertical periodic families are studied, with special emphasis on the genealogy of the planar periodic families. Our studies show that the global dynamics around EPs are highly similar to those around libration points in the circular restricted three-body problem, such as spatial halo orbits, invariant manifolds, and the genealogy of planar periodic families.
Dynamics of Equilibrium Points in a Uniformly Rotating Second-Order and Degree Gravitational Field
Feng, Jinglang; Hou, Xiyun
2017-01-01
Using tools such as periodic orbits and invariant manifolds, the global dynamics around equilibrium points (EPs) in a rotating second-order and degree gravitational field are studied. For EPs on the long axis, planar and vertical periodic families are computed, and their stability properties are investigated. Invariant manifolds are also computed, and their relation to the first-order resonances is briefly discussed. For EPs on the short axis, planar and vertical periodic families are studied, with special emphasis on the genealogy of the planar periodic families. Our studies show that the global dynamics around EPs are highly similar to those around libration points in the circular restricted three-body problem, such as spatial halo orbits, invariant manifolds, and the genealogy of planar periodic families.
Dynamics of Equilibrium Points in a Uniformly Rotating Second-Order and Degree Gravitational Field
Feng, Jinglang; Hou, Xiyun, E-mail: jinglang@nju.edu.cn, E-mail: silence@nju.edu.cn [School of Astronomy and Space Science, Nanjing University, 210093 (China)
2017-07-01
Using tools such as periodic orbits and invariant manifolds, the global dynamics around equilibrium points (EPs) in a rotating second-order and degree gravitational field are studied. For EPs on the long axis, planar and vertical periodic families are computed, and their stability properties are investigated. Invariant manifolds are also computed, and their relation to the first-order resonances is briefly discussed. For EPs on the short axis, planar and vertical periodic families are studied, with special emphasis on the genealogy of the planar periodic families. Our studies show that the global dynamics around EPs are highly similar to those around libration points in the circular restricted three-body problem, such as spatial halo orbits, invariant manifolds, and the genealogy of planar periodic families.
Improved model of the Earth's gravitational field: GEM-T1
Marsh, J.G.; Lerch, F.J.; Christodoulidis, D.C.
1987-07-01
Goddard Earth Model T1 (GEM-T1), which was developed from an analysis of direct satellite tracking observations, is the first in a new series of such models. GEM-T1 is complete to degree and order 36. It was developed using consistent reference parameters and extensive earth and ocean tidal models. It was simultaneously solved for gravitational and tidal terms, earth orientation parameters, and the orbital parameters of 580 individual satellite arcs. The solution used only satellite tracking data acquired on 17 different satellites and is predominantly based upon the precise laser data taken by third generation systems. In all, 800,000 observations were used. A major improvement in field accuracy was obtained. For marine geodetic applications, long wavelength geoidal modeling is twice as good as in earlier satellite-only GEM models. Orbit determination accuracy has also been substantially advanced over a wide range of satellites that have been tested
INFLUENCE OF THE GALACTIC GRAVITATIONAL FIELD ON THE POSITIONAL ACCURACY OF EXTRAGALACTIC SOURCES
Larchenkova, Tatiana I.; Lutovinov, Alexander A.; Lyskova, Natalya S.
2017-01-01
We investigate the influence of random variations of the Galactic gravitational field on the apparent celestial positions of extragalactic sources. The basic statistical characteristics of a stochastic process (first-order moments, an autocorrelation function and a power spectral density) are used to describe a light ray deflection in a gravitational field of randomly moving point masses as a function of the source coordinates. We map a 2D distribution of the standard deviation of the angular shifts in positions of distant sources (including reference sources of the International Celestial Reference Frame) with respect to their true positions. For different Galactic matter distributions the standard deviation of the offset angle can reach several tens of μ as (microarcsecond) toward the Galactic center, decreasing down to 4–6 μ as at high galactic latitudes. The conditional standard deviation (“jitter”) of 2.5 μ as is reached within 10 years at high galactic latitudes and within a few months toward the inner part of the Galaxy. The photometric microlensing events are not expected to be disturbed by astrometric random variations anywhere except the inner part of the Galaxy as the Einstein–Chvolson times are typically much shorter than the jittering timescale. While a jitter of a single reference source can be up to dozens of μ as over some reasonable observational time, using a sample of reference sources would reduce the error in relative astrometry. The obtained results can be used for estimating the physical upper limits on the time-dependent accuracy of astrometric measurements.
INFLUENCE OF THE GALACTIC GRAVITATIONAL FIELD ON THE POSITIONAL ACCURACY OF EXTRAGALACTIC SOURCES
Larchenkova, Tatiana I. [ASC of P.N.Lebedev Physical Institute, Leninskiy prospect 53, Moscow 119991 (Russian Federation); Lutovinov, Alexander A.; Lyskova, Natalya S. [Space Research Institute, Russian Academy of Sciences, Profsoyuznaya 84/32, 117997 Moscow (Russian Federation)
2017-01-20
We investigate the influence of random variations of the Galactic gravitational field on the apparent celestial positions of extragalactic sources. The basic statistical characteristics of a stochastic process (first-order moments, an autocorrelation function and a power spectral density) are used to describe a light ray deflection in a gravitational field of randomly moving point masses as a function of the source coordinates. We map a 2D distribution of the standard deviation of the angular shifts in positions of distant sources (including reference sources of the International Celestial Reference Frame) with respect to their true positions. For different Galactic matter distributions the standard deviation of the offset angle can reach several tens of μ as (microarcsecond) toward the Galactic center, decreasing down to 4–6 μ as at high galactic latitudes. The conditional standard deviation (“jitter”) of 2.5 μ as is reached within 10 years at high galactic latitudes and within a few months toward the inner part of the Galaxy. The photometric microlensing events are not expected to be disturbed by astrometric random variations anywhere except the inner part of the Galaxy as the Einstein–Chvolson times are typically much shorter than the jittering timescale. While a jitter of a single reference source can be up to dozens of μ as over some reasonable observational time, using a sample of reference sources would reduce the error in relative astrometry. The obtained results can be used for estimating the physical upper limits on the time-dependent accuracy of astrometric measurements.
Visualising magnetic fields numerical equation solvers in action
Beeteson, John Stuart
2001-01-01
Visualizing Magnetic Fields: Numerical Equation Solvers in Action provides a complete description of the theory behind a new technique, a detailed discussion of the ways of solving the equations (including a software visualization of the solution algorithms), the application software itself, and the full source code. Most importantly, there is a succinct, easy-to-follow description of each procedure in the code.The physicist Michael Faraday said that the study of magnetic lines of force was greatly influential in leading him to formulate many of those concepts that are now so fundamental to our modern world, proving to him their "great utility as well as fertility." Michael Faraday could only visualize these lines in his mind's eye and, even with modern computers to help us, it has been very expensive and time consuming to plot lines of force in magnetic fields
Cristea, Gh.
1975-01-01
In the first part of this paper, additional data are given concerning a gravimeter consisting in a pendulum-laser set proposed in a previous paper of the author (1). This gravimeter could have a sensitivity of 0.1 microgal or even 0.01 microgal in the case of statistical measurements. If processing by an on-line computer is used, the pendulum-laser can constitute a gravimeter which, used in statistical measurements on a long time interval, could reach a sensitivity of 10 -12 g. The second part of the paper points out the advantages resulting from determining the velocity of the gravitational reaction in an artificial satellite of the earth. The main advantage is the very fact that this measurement can be achieved by means of the existant gravimeters. The massive reduction of the time error is due to the increase of the ''sinusoid'' frequency resulting from the recording being made on the gravimeter set on an artificial satellite turning around the earth in about 90 minutes
Dodelson, Scott
2017-01-01
Gravitational lensing is a consequence of general relativity, where the gravitational force due to a massive object bends the paths of light originating from distant objects lying behind it. Using very little general relativity and no higher level mathematics, this text presents the basics of gravitational lensing, focusing on the equations needed to understand the phenomena. It then applies them to a diverse set of topics, including multiply imaged objects, time delays, extrasolar planets, microlensing, cluster masses, galaxy shape measurements, cosmic shear, and lensing of the cosmic microwave background. This approach allows undergraduate students and others to get quickly up to speed on the basics and the important issues. The text will be especially relevant as large surveys such as LSST and Euclid begin to dominate the astronomical landscape. Designed for a one semester course, it is accessible to anyone with two years of undergraduate physics background.
Scalar-metric and scalar-metric-torsion gravitational theories
Aldersley, S.J.
1977-01-01
The techniques of dimensional analysis and of the theory of tensorial concomitants are employed to study field equations in gravitational theories which incorporate scalar fields of the Brans-Dicke type. Within the context of scalar-metric gravitational theories, a uniqueness theorem for the geometric (or gravitational) part of the field equations is proven and a Lagrangian is determined which is uniquely specified by dimensional analysis. Within the context of scalar-metric-torsion gravitational theories a uniqueness theorem for field Lagrangians is presented and the corresponding Euler-Lagrange equations are given. Finally, an example of a scalar-metric-torsion theory is presented which is similar in many respects to the Brans-Dicke theory and the Einstein-Cartan theory
Hashino, Katsuya, E-mail: hashino@jodo.sci.u-toyama.ac.jp [Department of Physics, University of Toyama, 3190 Gofuku, Toyama 930-8555 (Japan); Kakizaki, Mitsuru, E-mail: kakizaki@sci.u-toyama.ac.jp [Department of Physics, University of Toyama, 3190 Gofuku, Toyama 930-8555 (Japan); Kanemura, Shinya, E-mail: kanemu@sci.u-toyama.ac.jp [Department of Physics, University of Toyama, 3190 Gofuku, Toyama 930-8555 (Japan); Ko, Pyungwon, E-mail: pko@kias.re.kr [School of Physics, KIAS, Seoul 02455 (Korea, Republic of); Matsui, Toshinori, E-mail: matsui@kias.re.kr [School of Physics, KIAS, Seoul 02455 (Korea, Republic of)
2017-03-10
We calculate the spectrum of gravitational waves originated from strongly first order electroweak phase transition in the extended Higgs model with a real singlet scalar field. In order to calculate the bubble nucleation rate, we perform a two-field analysis and evaluate bounce solutions connecting the true and the false vacua using the one-loop effective potential at finite temperatures. Imposing the Sakharov condition of the departure from thermal equilibrium for baryogenesis, we survey allowed regions of parameters of the model. We then investigate the gravitational waves produced at electroweak bubble collisions in the early Universe, such as the sound wave, the bubble wall collision and the plasma turbulence. We find that the strength at the peak frequency can be large enough to be detected at future space-based gravitational interferometers such as eLISA, DECIGO and BBO. Predicted deviations in the various Higgs boson couplings are also evaluated at the zero temperature, and are shown to be large enough too. Therefore, in this model strongly first order electroweak phase transition can be tested by the combination of the precision study of various Higgs boson couplings at the LHC, the measurement of the triple Higgs boson coupling at future lepton colliders and the shape of the spectrum of gravitational wave detectable at future gravitational interferometers.
Katsuya Hashino
2017-03-01
Full Text Available We calculate the spectrum of gravitational waves originated from strongly first order electroweak phase transition in the extended Higgs model with a real singlet scalar field. In order to calculate the bubble nucleation rate, we perform a two-field analysis and evaluate bounce solutions connecting the true and the false vacua using the one-loop effective potential at finite temperatures. Imposing the Sakharov condition of the departure from thermal equilibrium for baryogenesis, we survey allowed regions of parameters of the model. We then investigate the gravitational waves produced at electroweak bubble collisions in the early Universe, such as the sound wave, the bubble wall collision and the plasma turbulence. We find that the strength at the peak frequency can be large enough to be detected at future space-based gravitational interferometers such as eLISA, DECIGO and BBO. Predicted deviations in the various Higgs boson couplings are also evaluated at the zero temperature, and are shown to be large enough too. Therefore, in this model strongly first order electroweak phase transition can be tested by the combination of the precision study of various Higgs boson couplings at the LHC, the measurement of the triple Higgs boson coupling at future lepton colliders and the shape of the spectrum of gravitational wave detectable at future gravitational interferometers.
Direct Construction of Conservation Laws from Field Equations
Anco, S.C.; Bluman, G.
1997-01-01
This Letter presents an algorithm to obtain all local conservation laws for any system of field equations. The algorithm uses a formula which directly generates the conservation laws and does not depend on the system having a Lagrangian formulation, in contrast to Noether close-quote s theorem which requires a Lagrangian. Several examples are considered including dissipative systems inherently having no Lagrangian. copyright 1997 The American Physical Society
Levi, Michele [Université Pierre et Marie Curie, CNRS-UMR 7095, Institut d' Astrophysique de Paris, 98 bis Boulevard Arago, 75014 Paris (France); Steinhoff, Jan, E-mail: michele.levi@upmc.fr, E-mail: jan.steinhoff@aei.mpg.de [Max-Planck-Institute for Gravitational Physics (Albert-Einstein-Institute), Am Mühlenberg 1, 14476 Potsdam-Golm (Germany)
2016-01-01
The next-to-next-to-leading order spin-squared interaction potential for generic compact binaries is derived for the first time via the effective field theory for gravitating spinning objects in the post-Newtonian scheme. The spin-squared sector is an intricate one, as it requires the consideration of the point particle action beyond minimal coupling, and mainly involves the spin-squared worldline couplings, which are quite complex, compared to the worldline couplings from the minimal coupling part of the action. This sector also involves the linear in spin couplings, as we go up in the nonlinearity of the interaction, and in the loop order. Hence, there is an excessive increase in the number of Feynman diagrams, of which more are higher loop ones. We provide all the Feynman diagrams and their values. The beneficial ''nonrelativistic gravitational'' fields are employed in the computation. This spin-squared correction, which enters at the fourth post-Newtonian order for rapidly rotating compact objects, completes the conservative sector up to the fourth post-Newtonian accuracy. The robustness of the effective field theory for gravitating spinning objects is shown here once again, as demonstrated in a recent series of papers by the authors, which obtained all spin dependent sectors, required up to the fourth post-Newtonian accuracy. The effective field theory of spinning objects allows to directly obtain the equations of motion, and the Hamiltonians, and these will be derived for the potential obtained here in a forthcoming paper.
Finite field equation for asymptotically free phi4 theory
Brandt, R.A.; Wing-chiu, N.; Wai-Bong, Y.
1979-01-01
We consider the finite local field equation - (D 7 Alembertian + m 2 ) phi (x) = lim/sub xitsarrow-rightts/0[1/6gZ (xi 2 ):phi (x - xi) phi (x) phi (x + xi):- Δ (xi 2 ) phi (x) + sigma (xi 2 )(xi x partial/sub x/) 2 phi (x)], which rigorously describes gphi 4 scalar field theory, and the operator-product expansion phi (xi) phi (0) /sup approximately/ /sub xitsarrow-rightts0/F (xi 2 ) N[phi 2 ], where N[phi 2 ] denotes a normal product. For g 2 ), Δ (xi 2 ), sigma (xi 2 ), and F (xi 2 ). We perform the R transformation phi (x) → phi (x) + r on the finite field equation and obtain the operator part of the change to be proportional to lim/sub xitsarrow-rightts0/Z (xi 2 ) F (xi 2 ) N[phi 2 ] which vanishes by our knowledge of the functions Z (xi 2 ) and F (xi 2 ). We have therefore verified rigorously the partial R invariance of - vertical-bargvertical-barphi 4 theory. We discuss and solve the technical problem of finding the solution for renormalization-group equations with a matrix γ function where the lowest-order expansions of the various elements do not begin with the same powers of g
Many-Body Mean-Field Equations: Parallel implementation
Vallieres, M.; Umar, S.; Chinn, C.; Strayer, M.
1993-01-01
We describe the implementation of Hartree-Fock Many-Body Mean-Field Equations on a Parallel Intel iPSC/860 hypercube. We first discuss the Nuclear Mean-Field approach in physical terms. Then we describe our parallel implementation of this approach on the Intel iPSC/860 hypercube. We discuss and compare the advantages and disadvantages of the domain partition versus the Hilbert space partition for this problem. We conclude by discussing some timing experiments on various computing platforms
The large number hypothesis and Einstein's theory of gravitation
Yun-Kau Lau
1985-01-01
In an attempt to reconcile the large number hypothesis (LNH) with Einstein's theory of gravitation, a tentative generalization of Einstein's field equations with time-dependent cosmological and gravitational constants is proposed. A cosmological model consistent with the LNH is deduced. The coupling formula of the cosmological constant with matter is found, and as a consequence, the time-dependent formulae of the cosmological constant and the mean matter density of the Universe at the present epoch are then found. Einstein's theory of gravitation, whether with a zero or nonzero cosmological constant, becomes a limiting case of the new generalized field equations after the early epoch
Testing the gravitational instability hypothesis?
Babul, Arif; Weinberg, David H.; Dekel, Avishai; Ostriker, Jeremiah P.
1994-01-01
We challenge a widely accepted assumption of observational cosmology: that successful reconstruction of observed galaxy density fields from measured galaxy velocity fields (or vice versa), using the methods of gravitational instability theory, implies that the observed large-scale structures and large-scale flows were produced by the action of gravity. This assumption is false, in that there exist nongravitational theories that pass the reconstruction tests and gravitational theories with certain forms of biased galaxy formation that fail them. Gravitational instability theory predicts specific correlations between large-scale velocity and mass density fields, but the same correlations arise in any model where (a) structures in the galaxy distribution grow from homogeneous initial conditions in a way that satisfies the continuity equation, and (b) the present-day velocity field is irrotational and proportional to the time-averaged velocity field. We demonstrate these assertions using analytical arguments and N-body simulations. If large-scale structure is formed by gravitational instability, then the ratio of the galaxy density contrast to the divergence of the velocity field yields an estimate of the density parameter Omega (or, more generally, an estimate of beta identically equal to Omega(exp 0.6)/b, where b is an assumed constant of proportionality between galaxy and mass density fluctuations. In nongravitational scenarios, the values of Omega or beta estimated in this way may fail to represent the true cosmological values. However, even if nongravitational forces initiate and shape the growth of structure, gravitationally induced accelerations can dominate the velocity field at late times, long after the action of any nongravitational impulses. The estimated beta approaches the true value in such cases, and in our numerical simulations the estimated beta values are reasonably accurate for both gravitational and nongravitational models. Reconstruction tests
E. W. Grafarend
1997-06-01
Full Text Available The length of the gravitational field lines/of the orthogonal trajectories of a family of gravity equipotential surfaces/of the plumbline between a terrestrial topographic point and a point on a reference equipotential surface like the geoid í also known as the orthometric height í plays a central role in Satellite Geodesy as well as in Physical Geodesy. As soon as we determine the geometry of the Earth pointwise by means of a satellite GPS (Global Positioning System: «global problem solver» we are left with the problem of converting ellipsoidal heights (geometric heights into orthometric heights (physical heights. For the computation of the plumbline we derive its three differential equations of first order as well as the three geodesic equations of second order. The three differential equations of second order take the form of a Newton differential equation when we introduce the parameter time via the Marussi gauge on a conformally flat three-dimensional Riemann manifold and the generalized force field, the gradient of the superpotential, namely the modulus of gravity squared and taken half. In particular, we compute curvature and torsion of the plumbline and prove their functional relationship to the second and third derivatives of the gravity potential. For a spherically symmetric gravity field, curvature and torsion of the plumbline are zero, the plumbline is straight. Finally we derive the three Lagrangean as well as the six Hamiltonian differential equations of the plumbline, in particular in their star form with respect to Marussi gauge.
Unification of Gravitation and Electromagnetism in a Relativistic ...
A theory of gravitation is considered in a relativistic version of Finslerian geometry. It is found that both the geodesic equations and the Finslerian analogue of the Einstein\\'s field equations have terms that involve the electromagnetic field tensor, thereby pointing out to the geometrization of electrodynamics and hence to a ...
Interaction of gravitational waves with superconductors
Inan, N.A.; Thompson, J.J. [University of California, Schools of Natural Sciences, Merced, CA (United States); Chiao, R.Y. [University of California, Schools of Natural Sciences and Engineering, Merced, CA (United States)
2017-06-15
Applying the Helmholtz Decomposition theorem to linearized General Relativity leads to a gauge-invariant formulation where the transverse-traceless part of the metric perturbation describes gravitational waves in matter. Gravitational waves incident on a superconductor can be described by a linear London-like constituent equation characterized by a ''gravitational shear modulus'' and a corresponding plasma frequency and penetration depth. Electric-like and magnetic-like gravitational tensor fields are defined in terms of the strain field of a gravitational wave. It is shown that in the DC limit, the magnetic-like tensor field is expelled from the superconductor in a gravitational Meissner-like effect. The Cooper pair density is described by the Ginzburg-Landau theory embedded in curved space-time. The ionic lattice is modeled by quantum harmonic oscillators coupled to gravitational waves and characterized by quasi-energy eigenvalues for the phonon modes. The formulation predicts the possibility of a dynamical Casimir effect since the zero-point energy of the ionic lattice phonons is found to be modulated by the gravitational wave, in a quantum analog of a ''Weber-bar effect.'' Applying periodic thermodynamics and the Debye model in the low-temperature limit leads to a free energy density for the ionic lattice. Lastly, we relate the gravitational strain of space to the strain of matter to show that the response to a gravitational wave is far less for the Cooper pair density than for the ionic lattice. This predicts a charge separation effect in the superconductor as a result of the gravitational wave. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Nonlinear coupled Alfven and gravitational waves
Kaellberg, Andreas; Brodin, Gert; Bradley, Michael
2004-01-01
In this paper we consider nonlinear interaction between gravitational and electromagnetic waves in a strongly magnetized plasma. More specifically, we investigate the propagation of gravitational waves with the direction of propagation perpendicular to a background magnetic field and the coupling to compressional Alfven waves. The gravitational waves are considered in the high-frequency limit and the plasma is modeled by a multifluid description. We make a self-consistent, weakly nonlinear analysis of the Einstein-Maxwell system and derive a wave equation for the coupled gravitational and electromagnetic wave modes. A WKB-approximation is then applied and as a result we obtain the nonlinear Schroedinger equation for the slowly varying wave amplitudes. The analysis is extended to 3D wave pulses, and we discuss the applications to radiation generated from pulsar binary mergers. It turns out that the electromagnetic radiation from a binary merger should experience a focusing effect, that in principle could be detected
Mass loss due to gravitational waves with $\\Lambda>0$
Saw, Vee-Liem
2017-01-01
The theoretical basis for the energy carried away by gravitational waves that an isolated gravitating system emits was first formulated by Hermann Bondi during the 1960s. Recent findings from looking at distant supernovae revealed that the rate of expansion of our universe is accelerating, which may be well-explained by sticking in a positive cosmological constant into the Einstein field equations for general relativity. By solving the Newman-Penrose equations (which are equivalent to the Ein...
Dynamics of Fermat potentials in nonperturbative gravitational lensing
Frittelli, Simonetta; Newman, Ezra T.
2002-01-01
We present a framework, based on the null-surface formulation of general relativity, for discussing the dynamics of Fermat potentials for gravitational lensing in a generic situation without approximations of any kind. Additionally, we derive two lens equations: one for the case of thick compact lenses and the other one for lensing by gravitational waves. These equations in principle generalize the astrophysical scheme for lensing by removing the thin-lens approximation while retaining the weak fields
Colombo, Maria
2017-01-01
The first part of the book is devoted to the transport equation for a given vector field, exploiting the lagrangian structure of solutions. It also treats the regularity of solutions of some degenerate elliptic equations, which appear in the eulerian counterpart of some transport models with congestion. The second part of the book deals with the lagrangian structure of solutions of the Vlasov-Poisson system, which describes the evolution of a system of particles under the self-induced gravitational/electrostatic field, and the existence of solutions of the semigeostrophic system, used in meteorology to describe the motion of large-scale oceanic/atmospheric flows.
Gravitational instability of thermally anisotropic plasma
Singh, B.; Kalra, G.L.
1986-01-01
The equations of Chew, Goldberger, and Low (1956) modified to include the heat flux vector and self-gravitation are used to study the gravitational instability of unbounded plasma placed in a uniform static magnetic field. The linear stability analysis shows that some of the additional terms which arise as a result of higher moments are of the same order of magnitude as the terms in the original Chew, Goldberger, and Low theory. The influence of these terms on the gravitational instability has been specially examined. It is found that the gravitational instability sets in at a comparatively shorter wavelength and the growth rate is enhanced owing to the inclusion of these terms in the case where the propagation vector is along the magnetic field. The condition for instability is, however, unaltered when the direction of propagation is transverse to the direction of magnetic field. 19 references
Class of Exact Solutions for a Cosmological Model of Unified Gravitational and Quintessence Fields
Asenjo, Felipe A.; Hojman, Sergio A.
2017-07-01
A new approach to tackle Einstein equations for an isotropic and homogeneous Friedmann-Robertson-Walker Universe in the presence of a quintessence scalar field is devised. It provides a way to get a simple exact solution to these equations. This solution determines the quintessence potential uniquely and it differs from solutions which have been used to study inflation previously. It relays on a unification of geometry and dark matter implemented through the definition of a functional relation between the scale factor of the Universe and the quintessence field. For a positive curvature Universe, this solution produces perpetual accelerated expansion rate of the Universe, while the Hubble parameter increases abruptly, attains a maximum value and decreases thereafter. The behavior of this cosmological solution is discussed and its main features are displayed. The formalism is extended to include matter and radiation.
Extensions of the auxiliary field method to solve Schroedinger equations
Silvestre-Brac, Bernard; Semay, Claude; Buisseret, Fabien
2008-01-01
It has recently been shown that the auxiliary field method is an interesting tool to compute approximate analytical solutions of the Schroedinger equation. This technique can generate the spectrum associated with an arbitrary potential V(r) starting from the analytically known spectrum of a particular potential P(r). In the present work, general important properties of the auxiliary field method are proved, such as scaling laws and independence of the results on the choice of P(r). The method is extended in order to find accurate analytical energy formulae for radial potentials of the form aP(r) + V(r), and several explicit examples are studied. Connections existing between the perturbation theory and the auxiliary field method are also discussed
Extensions of the auxiliary field method to solve Schroedinger equations
Silvestre-Brac, Bernard [LPSC Universite Joseph Fourier, Grenoble 1, CNRS/IN2P3, Institut Polytechnique de Grenoble, Avenue des Martyrs 53, F-38026 Grenoble-Cedex (France); Semay, Claude; Buisseret, Fabien [Groupe de Physique Nucleaire Theorique, Universite de Mons-Hainaut, Academie universitaire Wallonie-Bruxelles, Place du Parc 20, B-7000 Mons (Belgium)], E-mail: silvestre@lpsc.in2p3.fr, E-mail: claude.semay@umh.ac.be, E-mail: fabien.buisseret@umh.ac.be
2008-10-24
It has recently been shown that the auxiliary field method is an interesting tool to compute approximate analytical solutions of the Schroedinger equation. This technique can generate the spectrum associated with an arbitrary potential V(r) starting from the analytically known spectrum of a particular potential P(r). In the present work, general important properties of the auxiliary field method are proved, such as scaling laws and independence of the results on the choice of P(r). The method is extended in order to find accurate analytical energy formulae for radial potentials of the form aP(r) + V(r), and several explicit examples are studied. Connections existing between the perturbation theory and the auxiliary field method are also discussed.
Black holes and fundamental fields: Hair, kicks, and a gravitational Magnus effect
Okawa, Hirotada; Cardoso, Vitor
2014-11-01
Scalar fields pervade theoretical physics and are a fundamental ingredient to solve the dark matter problem, to realize the Peccei-Quinn mechanism in QCD or the string-axiverse scenario. They are also a useful proxy for more complex matter interactions, such as accretion disks or matter in extreme conditions. Here, we study the collision between scalar "clouds" and rotating black holes. For the first time we are able to compare analytic estimates and strong field, nonlinear numerical calculations for this problem. As the black hole pierces through the cloud it accretes according to the Bondi-Hoyle prediction, but is deflected through a purely kinematic gravitational "anti-Magnus" effect, which we predict to be present also during the interaction of black holes with accretion disks. After the interaction is over, we find large recoil velocities in the transverse direction. The end-state of the process belongs to the vacuum Kerr family if the scalar is massless, but can be a hairy black hole when the scalar is massive.
Plocková, J; Chmelík, J
2001-05-25
Gravitational field-flow fractionation (GFFF) utilizes the Earth's gravitational field as an external force that causes the settlement of particles towards the channel accumulation wall. Hydrodynamic lift forces oppose this action by elevating particles away from the channel accumulation wall. These two counteracting forces enable modulation of the resulting force field acting on particles in GFFF. In this work, force-field programming based on modulating the magnitude of hydrodynamic lift forces was implemented via changes of flow-rate, which was accomplished by a programmable pump. Several flow-rate gradients (step gradients, linear gradients, parabolic, and combined gradients) were tested and evaluated as tools for optimization of the separation of a silica gel particle mixture. The influence of increasing amount of sample injected on the peak resolution under flow-rate gradient conditions was also investigated. This is the first time that flow-rate gradients have been implemented for programming of the resulting force field acting on particles in GFFF.
On classical solutions of SU(3) gauge field equations
Chakrabarti, A.
1975-01-01
Static classical solutions of SU(3) gauge field equations are studied. The roles of the O(3) subgroup and of the quadrupole generators are discussed systematically. The general form thus obtained leads, through-out, to a high degree of symmetry in the results. This brings in some simplifying features. An octet of scalar mesons is finally added. Certain classes of exact solutions are given that are singular at the origin. A generalized gauge condition is pointed out. The relation of the general form to known particular cases is discussed [fr
On the hydrodynamic limit of self-consistent field equations
Pauli, H.C.
1980-01-01
As an approximation to the nuclear many-body problem, the hydrodynamical limit of self-consistent field equations is worked out and applied to the treatment of vibrational and rotational motion. Its validity is coupled to the value of a smallness parameter, behaving as 20Asup(-2/3) with the number of nucleons. For finite nuclei, this number is not small enough as compared to 1, and indeed one observes a discrepancy of roughly a factor of 5 between the hydrodynamic frequencies and the relevant experimental numbers. (orig.)
Linear spin-zero quantum fields in external gravitational and scalar fields
Kay, B.S.
1977-10-01
Mathematically rigorous results are given on the quantization of the covariant Klein-Gordon field with an external stationary scalar interaction in a stationary curved space-time. It is shown how, following Segal, Weinless etc., the problem reduces to finding a ''one-particle structure'' for the corresponding classical system. The main result is an existence theorem for such a one-particle structure for a precisely specified class of stationary space-times. Byproducts of our approach are (1)a discussion of when the equal-time hypersurfaces in a given stationary space-time are Cauchy; (2)a proof that when a one-particle structure exists it is unique a result of general interest for the quantization of linear systems; (3)a modification and extension of the methods of Chernoff [3] for proving the essential self-adjointness of ceratin partial differential operators
Relativity theory and gravitation
Bondi, H.
1986-01-01
The paper on relativity theory and gravitation is presented as a preface to the first of the articles submitted to the Journal on general relativity. Newtonian gravitation and and observation, relativity, and the sources of the gravitational field, are all discussed. (UK)
The reduced basis method for the electric field integral equation
Fares, M.; Hesthaven, J.S.; Maday, Y.; Stamm, B.
2011-01-01
We introduce the reduced basis method (RBM) as an efficient tool for parametrized scattering problems in computational electromagnetics for problems where field solutions are computed using a standard Boundary Element Method (BEM) for the parametrized electric field integral equation (EFIE). This combination enables an algorithmic cooperation which results in a two step procedure. The first step consists of a computationally intense assembling of the reduced basis, that needs to be effected only once. In the second step, we compute output functionals of the solution, such as the Radar Cross Section (RCS), independently of the dimension of the discretization space, for many different parameter values in a many-query context at very little cost. Parameters include the wavenumber, the angle of the incident plane wave and its polarization.
Sine-Gordon breather form factors and quantum field equations
Babujian, H; Karowski, M
2002-01-01
Using the results of previous investigations on sine-Gordon form factors, exact expressions of all breather matrix elements are obtained for several operators: all powers of the fundamental Bose field, general exponentials of it, the energy-momentum tensor and all higher currents. Formulae for the asymptotic behaviour of bosonic form factors are presented which are motivated by Weinberg's power counting theorem in perturbation theory. It is found that the quantum sine-Gordon field equation holds, and an exact relation between the 'bare' mass and the renormalized mass is obtained. Also a quantum version of a classical relation for the trace of the energy-momentum is proved. The eigenvalue problem for all higher conserved charges is solved. All results are compared with perturbative Feynman graph expansions and full agreement is found
Snow load effect on earth's rotation and gravitational field, 1979-1985
Chao, B. Fong; O'Connor, William P.; Chang, Alfred T. C.; Hall, Dorothy K.; Foster, James L.
1987-01-01
A global, monthly snow depth data set has been generated from the Nimbus 7 satellite observations using passive microwave remote-sensing techniques. Seven years of data, 1979-1985, are analyzed to compute the snow load effects on the earth's rotation and low-degree zonal gravitational field. The resultant time series show dominant seasonal cycles. The annual peak-to-peak variation in J2 is found to be 2.3 x 10 to the -10th, that in J3 to be 1.1 x 10 to the -10th, and believed to decrease rapidly for higher degrees. The corresponding change in the length of day is 41 micro-s. The annual wobble excitation is (4.9 marc sec, -109 deg) for the prograde motion component and (4.8 marc sec, -28 deg) for the retrograde motion component. The excitation power of the Chandler wobble due to the snow load is estimated to be about 25 dB less than the power needed to maintain the observed Chandler wobble.
Ruffini, R.
2004-07-01
Recent developments in obtaining a detailed model for gamma-ray bursts have shown the need for a deeper understanding of phenomena described by solutions of the Einstein-Maxwell equations, reviving interest in the behavior of charges close to a black hole. In particular a drastic difference has been found between the lines of force of a charged test particle in the fields of Schwarzschild and Reissner-Nordström black holes. This difference characterizes a general relativistic effect for the electric field of a charged test particle around a (charged) Reissner-Nordström black hole similar to the “Meissner effect” for a magnetic field around a superconductor. These new results are related to earlier work by Fermi and Hanni-Ruffini-Wheeler.
Beraldo e Silva, Leandro; de Siqueira Pedra, Walter; Sodré, Laerte; Perico, Eder L. D.; Lima, Marcos
2017-09-01
The collapse of a collisionless self-gravitating system, with the fast achievement of a quasi-stationary state, is driven by violent relaxation, with a typical particle interacting with the time-changing collective potential. It is traditionally assumed that this evolution is governed by the Vlasov-Poisson equation, in which case entropy must be conserved. We run N-body simulations of isolated self-gravitating systems, using three simulation codes, NBODY-6 (direct summation without softening), NBODY-2 (direct summation with softening), and GADGET-2 (tree code with softening), for different numbers of particles and initial conditions. At each snapshot, we estimate the Shannon entropy of the distribution function with three different techniques: Kernel, Nearest Neighbor, and EnBiD. For all simulation codes and estimators, the entropy evolution converges to the same limit as N increases. During violent relaxation, the entropy has a fast increase followed by damping oscillations, indicating that violent relaxation must be described by a kinetic equation other than the Vlasov-Poisson equation, even for N as large as that of astronomical structures. This indicates that violent relaxation cannot be described by a time-reversible equation, shedding some light on the so-called “fundamental paradox of stellar dynamics.” The long-term evolution is well-described by the orbit-averaged Fokker-Planck model, with Coulomb logarithm values in the expected range 10{--}12. By means of NBODY-2, we also study the dependence of the two-body relaxation timescale on the softening length. The approach presented in the current work can potentially provide a general method for testing any kinetic equation intended to describe the macroscopic evolution of N-body systems.
The Newton constant and gravitational waves in some vector field adjusting mechanisms
Santillán, Osvaldo P. [IMAS (UBA-CONICET), Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Buenos Aires 1428 (Argentina); Scornavacche, Marina, E-mail: firenzecita@hotmail.com, E-mail: marina.scorna@hotmail.com [Departamento de Física, Universidad de Buenos Aires, Ciudad Universitaria, Buenos Aires 1428 (Argentina)
2017-10-01
At the present, there exist some Lorentz breaking scenarios which explain the smallness of the cosmological constant at the present era [1]–[2]. An important aspect to analyze is the propagation of gravitational waves and the screening or enhancement of the Newton constant G {sub N} in these models. The problem is that the Lorentz symmetry breaking terms may induce an unacceptable value of the Newton constant G {sub N} or introduce longitudinal modes in the gravitational wave propagation. Furthermore this breaking may spoil the standard dispersion relation ω= ck . In [3] the authors have presented a model suggesting that the behavior of the gravitational constant is correct for asymptotic times. In the present work, an explicit checking is made and we finally agree with these claims. Furthermore, it is suggested that the gravitational waves are also well behaved for large times. In the process, some new models with the same behavior are obtained, thus enlarging the list of possible adjustment mechanisms.
Daum, Jan-Eric
2011-01-01
Whereas the Standard Model of elementary particle physics represents a consistent, renormalizable quantum field theory of three of the four known interactions, the quantization of gravity still remains an unsolved problem. However, in recent years evidence for the asymptotic safety of gravity was provided. That means that also for gravity a quantum field theory can be constructed that is renormalizable in a generalized way which does not explicitly refer to perturbation theory. In addition, this approach, that is based on the Wilsonian renormalization group, predicts the correct microscopic action of the theory. In the classical framework, metric gravity is equivalent to the Einstein-Cartan theory on the level of the vacuum field equations. The latter uses the tetrad e and the spin connection ω as fundamental variables. However, this theory possesses more degrees of freedom, a larger gauge group, and its associated action is of first order. All these features make a treatment analogue to metric gravity much more difficult. In this thesis a three-dimensional truncation of the form of a generalized Hilbert-Palatini action is analyzed. Besides the running of Newton's constant G k and the cosmological constant Λ k , it also captures the renormalization of the Immirzi parameter γ k . In spite of the mentioned difficulties, the spectrum of the free Hilbert-Palatini propagator can be computed analytically. On its basis, a proper time-like flow equation is constructed. Furthermore, appropriate gauge conditions are chosen and analyzed in detail. This demands a covariantization of the gauge transformations. The resulting flow is analyzed for different regularization schemes and gauge parameters. The results provide convincing evidence for asymptotic safety within the (e,ω) approach as well and therefore for the possible existence of a mathematically consistent and predictive fundamental quantum theory of gravity. In particular, one finds a pair of non-Gaussian fixed
Bound states of spin-half particles in a static gravitational field close to the black hole field
Spencer-Smith, A. F.; Gossel, G. H.; Berengut, J. C.; Flambaum, V. V.
2013-03-01
We consider the bound-state energy levels of a spin-1/2 fermion in the gravitational field of a near-black hole object. In the limit that the metric of the body becomes singular, all binding energies tend to the rest-mass energy (i.e. total energy approaches zero). We present calculations of the ground state energy for three specific interior metrics (Florides, Soffel and Schwarzschild) for which the spectrum collapses and becomes quasi-continuous in the singular metric limit. The lack of zero or negative energy states prior to this limit being reached prevents particle pair production occurring. Therefore, in contrast to the Coulomb case, no pairs are produced in the non-singular static metric. For the Florides and Soffel metrics the singularity occurs in the black hole limit, while for the Schwarzschild interior metric it corresponds to infinite pressure at the centre. The behaviour of the energy level spectrum is discussed in the context of the semi-classical approximation and using general properties of the metric.
Finite field equation of Yang--Mills theory
Brandt, R.A.; Wing-Chiu, N.; Yeung, W.
1980-01-01
We consider the finite local field equation -][1+1/α (1+f 4 )]g/sup munu/D'Alembertian-partial/sup μ/partial/sup ν/]A/sup nua/ =-(1+f 3 ) g 2 N[A/sup c/νA/sup a/μA/sub ν//sup c/] +xxx+(1-s) 2 M 2 A/sup a/μ, introduced by Lowenstein to rigorously describe SU(2) Yang--Mills theory, which is written in terms of normal products. We also consider the operator product expansion A/sup c/ν(x+xi) A/sup a/μ(x) A/sup b/lambda(x-xi) approx.ΣM/sup c/abνμlambda/sub c/'a'b'ν'μ'lambda' (xi) N[A/sup nuprimec/'A/sup muprimea/'A/sup lambdaprimeb/'](x), and using asymptotic freedom, we compute the leading behavior of the Wilson coefficients M/sup ...//sub .../(xi) with the help of a computer, and express the normal products in the field equation in terms of products of the c-number Wilson coefficients and of operator products like A/sup c/ν(x+xi) A/sup a/μ(x) A/sup b/lambda(x-xi) at separated points. Our result is -][1+(1/α)(1+f 4 )]g/sup munu/D'Alembertian-partial/sup μ/partial/sup ν/]A/sup nua/ =-(1+f 3 ) g 2 lim/sub xiarrow-right0/] (lnxi)/sup -0.28/2b/[A/sup c/ν (x+xi) A/sup a/μ(x) A/sub ν//sup c/(x-xi) +epsilon/sup a/bcA/sup muc/(x+xi) partial/sup ν/A/sup b//sub ν/(x)+xxx] +xxx]+(1-s) 2 M 2 A/sup a/μ, where β (g) =-bg 3 , and so (lnxi)/sup -0.28/2b/ is the leading behavior of the c-number coefficient multiplying the operator products in the field equation
Robertson, Brant E.; Ellis, Richard S.; Dunlop, James S.; McLure, Ross J.; Stark, Dan P.; McLeod, Derek
2014-01-01
Strong gravitational lensing provides a powerful means for studying faint galaxies in the distant universe. By magnifying the apparent brightness of background sources, massive clusters enable the detection of galaxies fainter than the usual sensitivity limit for blank fields. However, this gain in effective sensitivity comes at the cost of a reduced survey volume and, in this Letter, we demonstrate that there is an associated increase in the cosmic variance uncertainty. As an example, we sho...
Solution of radial spin-1 field equation in Robertson-Walker space-time via Heun's equation
Zecca, A.
2010-01-01
The spin-1 field equation is considered in Robertson-Walker spacetime. The problem of the solution of the separated radial equations, previously discussed in the flat space-time case, is solved also for both the closed and open curvature case. The radial equation is reduced to Heun's differential equation that recently has been widely reconsidered. It is shown that the solution of the present Heun equation does not fall into the class of polynomial-like or hypergeometric functions. Heun's operator results also non-factorisable. The properties follow from application of general theorems and power series expansion. In the positive curvature case of the universe a discrete energy spectrum of the system is found. The result follows by requiring a polynomial-like behaviour of at least one component of the spinor field. Developments and applications of the theory suggest further study of the solution of Heun's equation.
Scully, M O
2008-01-01
The time dependent Schrodinger equation is frequently 'derived' by postulating the energy E → i h-bar (∂/∂t) and momentum p-vector → ( h-bar /i)∇ operator relations. In the present paper we review the quantum field theoretic route to the Schrodinger wave equation which treats time and space as parameters, not operators. Furthermore, we recall that a classical (nonlinear) wave equation can be derived from the classical action via Hamiltonian-Jacobi theory. By requiring the wave equation to be linear we again arrive at the Schrodinger equation, without postulating operator relations. The underlying philosophy is operational: namely 'a particle is what a particle detector detects.' This leads us to a useful physical picture combining the wave (field) and particle paradigms which points the way to the time-dependent Schrodinger equation
Infinite order quantum-gravitational correlations
Knorr, Benjamin
2018-06-01
A new approximation scheme for nonperturbative renormalisation group equations for quantum gravity is introduced. Correlation functions of arbitrarily high order can be studied by resolving the full dependence of the renormalisation group equations on the fluctuation field (graviton). This is reminiscent of a local potential approximation in O(N)-symmetric field theories. As a first proof of principle, we derive the flow equation for the ‘graviton potential’ induced by a conformal fluctuation and corrections induced by a gravitational wave fluctuation. Indications are found that quantum gravity might be in a non-metric phase in the deep ultraviolet. The present setup significantly improves the quality of previous fluctuation vertex studies by including infinitely many couplings, thereby testing the reliability of schemes to identify different couplings to close the equations, and represents an important step towards the resolution of the Nielsen identity. The setup further allows one, in principle, to address the question of putative gravitational condensates.
Backreaction effects on the matter side of Einstein's field equations
Floerchinger, Stefan; Wiedemann, Urs Achim
2015-01-01
Recently, we have derived a novel and compact expression for how perturbations in the matter fields of the cosmological fluid can lead to deviations from the standard Friedmann equations. Remarkably, the dissipative damping of velocity perturbations by bulk and shear viscosity in the dark sector can modify the expansion history of the universe on arbitrarily large scales. In universes in which this effect is sufficiently sizeable, it could account for the acceleration of the cosmological expansion. But even if dark matter should be less viscous and if the effect would be correspondingly smaller, it may have observable consequences in the era of precision cosmology. Here, we review the origin of this backreaction effect and possibilities to constrain it further.
Kowalska-Leszczynska, Izabela; Bulik, Tomasz; Bizouard, Marie-Anne; Robinet, Florent; Christensen, Nelson; Rohde, Maximilian; Coughlin, Michael; Gołkowski, Mark; Kubisz, Jerzy; Kulak, Andrzej; Mlynarczyk, Janusz
2017-01-01
It has been recognized that the magnetic fields from the Schumann resonances could affect the search for a stochastic gravitational-wave background by LIGO and Virgo. Presented here are the observations of short duration magnetic field transients that are coincident in the magnetometers at the LIGO and Virgo sites. Data from low-noise magnetometers in Poland and Colorado, USA, are also used and show short duration magnetic transients of global extent. We measure at least 2.3 coincident (between Poland and Colorado) magnetic transient events per day where one of the pulses exceeds 200 pT. Given the recently measured values of the magnetic coupling to differential arm motion for Advanced LIGO, there would be a few events per day that would appear simultaneously at the gravitational-wave detector sites and could move the test masses of order 10 −18 m. We confirm that in the advanced detector era short duration transient gravitational-wave searches must account for correlated magnetic field noise in the global detector network. (paper)
Consistent equations for interacting gauge fields of all spins in 3+1 dimensions
Vasiliev, M A [AN SSSR, Moscow. Inst. Teoreticheskoj Fiziki (USSR)
1990-07-05
Consistent equations of motion of interacting gauge fields of all spins in 3+1 dimensions are formulated in a closed form. These equations are explicitly general coordinate invariant, possess all necessary higher spin gauge symmetries and reduce to the usual equations of free massless fields of all spins s=0, 1/2, 1, ..., {infinity} at the linearized level. In the spin-2 sector, the proposed equations are equivalent to the Einstein equations with the cosmological term. (orig.).
Ciufolini, I; Moschella, U; Fre, P
2001-01-01
Gravitational waves (GWs) are a hot topic and promise to play a central role in astrophysics, cosmology, and theoretical physics. Technological developments have led us to the brink of their direct observation, which could become a reality in the coming years. The direct observation of GWs will open an entirely new field: GW astronomy. This is expected to bring a revolution in our knowledge of the universe by allowing the observation of previously unseen phenomena, such as the coalescence of compact objects (neutron stars and black holes), the fall of stars into supermassive black holes, stellar core collapses, big-bang relics, and the new and unexpected.With a wide range of contributions by leading scientists in the field, Gravitational Waves covers topics such as the basics of GWs, various advanced topics, GW detectors, astrophysics of GW sources, numerical applications, and several recent theoretical developments. The material is written at a level suitable for postgraduate students entering the field.
A new geometrical gravitational theory
Obata, T.; Chiba, J.; Oshima, H.
1981-01-01
A geometrical gravitational theory is developed. The field equations are uniquely determined apart from one unknown dimensionless parameter ω 2 . It is based on an extension of the Weyl geometry, and by the extension the gravitational coupling constant and the gravitational mass are made to be dynamical and geometrical. The fundamental geometrical objects in the theory are a metric gsub(μν) and two gauge scalars phi and psi. The theory satisfies the weak equivalence principle, but breaks the strong one generally. u(phi, psi) = phi is found out on the assumption that the strong one keeps holding good at least for bosons of low spins. Thus there is the simple correspondence between the geometrical objects and the gravitational objects. Since the theory satisfies the weak one, the inertial mass is also dynamical and geometrical in the same way as is the gravitational mass. Moreover, the cosmological term in the theory is a coscalar of power -4 algebraically made of psi and u(phi, psi), so it is dynamical, too. Finally spherically symmetric exact solutions are given. The permissible range of the unknown parameter ω 2 is experimentally determined by applying the solutions to the solar system. (author)
The energy-momentum problem and gravitation theory
Logunov, A.A.; Folomeshkin, V.N.
1977-01-01
General properties of geometrized gravitation theories are considered. A covariant formulation of conservation laws in an arbitrary Riemann space-time is presented. In the Einstein theory both symmetric and canonical energy-momentum tensors of the matter and gravitational field system and, in particular, energy-momentum of free gravitational waves prove to be equal to zero. Since gravitational waves carry the curvature and, consequently, affect the detector, this bears witness to an intrinsic contradiction of the Einstein theory. To realize the sources of difficulties concerning energy-momentum in the Einstein theory the gravitational field is treated in the same way as all the other physical fields, i.e. in terms of usual Lorentz-invariant field theory. Unification of this approach with the Einstein idea of geometrization enables to construct the geometrized theory, which is free from contradictions, has clearly defined the notions of gravitation field energy-momentum and satisfactorily describes all known experimental facts. To construct a logically consistent theory one should geometrize only the density of the matter Lagrangian. The gravitation field equations are formulated in terms of the Euclidean space-time with a metric tensor γsub(ik), while the matter motion may be completely described in terms of the non-Euclidean space-time with a metric tensor gsub(ik). For strong gravitational fields the predictions of the quasi-linear theory under consideration appriciably differ from those of the Einstein formulation of the gravitation theory. No black holes are present in the theory. The results of the calculation for the energy flow of gravitational waves are rigorously unambiguous and show that gravitational waves carry positively definite energy
Singh, Kangujam Priyokumar; Dewri, Mukunda; Singh, Koijam Manihar
2016-01-01
On studying some new models of Robertson-Walker universes with a Brans-Dicke scalar field, it is found that most of these universes contain a dark energy like fluid which confirms the present scenario of the expansion of the universe. In one of the cases, the exact solution of the field equations gives a universe with a false vacuum, while in another it reduces to that of dust distribution in the Brans-Dicke cosmology when the cosmological constant is not in the picture. In one particular model it is found that the universe may undergo a Big Rip in the future, and thus it will be very interesting to investigate such models further. (paper)
Reuss, J.D.
1967-08-01
We recall the algebraic statement that can be done for Petrov's classification. We determine Petrov's class in some points of the axial symmetric stationary solution given in 1953 by Papapetrou. We complete the determination of the Papapetrou non stationary cylindric solution. (author) [fr
Balakin, A.B.; Murzakhanov, Z.G.; Grunskaya, L.V.
1994-01-01
A proposal on the experimental detection of extremely low-frequency variations of the electromagnetic Earth field at the gravitational-wave frequency and method for correlation processing results of the experiments are described. 14 refs
Hoffmann, William F
1964-01-01
Remarks on the observational basis of general relativity ; Riemannian geometry ; gravitation as geometry ; gravitational waves ; Mach's principle and experiments on mass anisotropy ; the many faces of Mach ; the significance for the solar system of time-varying gravitation ; relativity principles and the role of coordinates in physics ; the superdense star and the critical nucleon number ; gravitation and light ; possible effects on the solar system of φ waves if they exist ; the Lyttleton-Bondi universe and charge equality ; quantization of general relativity ; Mach's principle as boundary condition for Einstein's equations.
Chen, Shao-Guang
According to f =d(mv)/dt=m(dv/dt)+ v(dm/dt), a same gravitational formula had been de-duced from the variance in physical mass of QFT and from the variance in mass of inductive energy-transfer of GR respectively: f QF T = f GR = -G (mM/r2 )((r/r)+(v/c)) when their interaction-constants are all taken the experimental values (H05-0029-08, E15-0039-08). f QF T is the quasi-Casimir pressure. f GR is equivalent to Einstein's equation, then more easy to solve it. The hypothesis of the equivalent principle is not used in f QF T , but required by f GR . The predictions of f QF T and f GR are identical except that f QF T has quantum effects but f GR has not and f GR has Lense-Thirring effect but f QF T has not. The quantum effects of gravitation had been verified by Nesvizhevsky et al with the ultracold neutrons falling in the earth's gravitational field in 2002. Yet Lense-Thirring effect had not been measured by GP-B. It shows that f QF T is essential but f GR is phenomenological. The macro-f QF T is the statistic average pressure collided by net virtual neutrinos ν 0 flux (after self-offset in opposite directions) and in direct proportion to the mass. But micro-f QF T is in direct proportion to the scattering section. The electric mass (in inverse proportion to de Broglie wavelength λ) far less than nucleonic mass and the electric scattering section (in direct proportion to λ2 ) far large than that of nucleon, then the net ν 0 flux pressure exerted to electron far large than that to nucleon and the electric displacement far large than that of nucleon, it causes the gravitational polarization of positive-negative charge center separation. Because the gravity far less than the electromagnetic binding force, in atoms the gravitational polarization only produces a little separation. But the net ν 0 flux can press a part freedom electrons in plasma of ionosphere into the earth's surface, the static electric force of redundant positive ions prevents electrons from further
Generalized Friedmann-Robertson-Walker metric and redundancy in the generalized Einstein equations
Kao, W.F.; Pen, U.
1991-01-01
A nontrivial redundancy relation, due to the differential structure of the gravitational Bianchi identity as well as the symmetry of the Friedmann-Robertson-Walker metric, in the gravitational field equation is clarified. A generalized Friedmann-Robertson-Walker metric is introduced in order to properly define a one-dimensional reduced problem which offers an alternative approach to obtain the gravitational field equations on Friedmann-Robertson-Walker spaces
Emmanuel Frenod
2002-01-01
Full Text Available We study the qualitative behavior of solutions to the Vlasov equation with strong external magnetic field and oscillating electric field. This model is relevant to the understanding of isotop resonant separation. We show that the effective equation is a kinetic equation with a memory term. This memory term involves a pseudo-differential operator whose kernel is characterized by an integral equation involving Bessel functions. The kernel is explicitly given in some particular cases.
Gravitational entropy and thermodynamics away from the horizon
Brustein, Ram, E-mail: ramyb@bgu.ac.il [Department of Physics, Ben-Gurion University, Beer-Sheva 84105 (Israel); CAS, Ludwig-Maximilians-Universitaet Muenchen, 80333 Muenchen (Germany); Medved, A.J.M., E-mail: j.medved@ru.ac.za [Department of Physics and Electronics, Rhodes University, Grahamstown 6140 (South Africa)
2012-08-29
We define, by an integral of geometric quantities over a spherical shell of arbitrary radius, an invariant gravitational entropy. This definition relies on defining a gravitational energy and pressure, and it reduces at the horizon of both black branes and black holes to Wald's Noether charge entropy. We support the thermodynamic interpretation of the proposed entropy by showing that, for some cases, the field theory duals of the entropy, energy and pressure are the same as the corresponding quantities in the field theory. In this context, the Einstein equations are equivalent to the field theory thermodynamic relation TdS=dE+PdV supplemented by an equation of state.
CERN. Geneva
2006-01-01
Gravitational wave astronomy is expected to become an observational field within the next decade. First direct detection of gravitational waves is possible with existing terrestrial-based detectors, and highly probable with proposed upgrades. In this three-part lecture series, we give an overview of the field, including material on gravitional wave sources, detection methods, some details of interferometric detectors, data analysis methods, and current results from observational data-taking runs of the LIGO and GEO projects.
Critical opalescence of neutrons in nonuniform liquid in the gravitation field
Sugakov, V.I.; Chalyj, A.V.; Chernenko, L.M.
1991-01-01
Single elastic scattering of neutrons has been investigated in a liquid near the critical point. Double differential cross sections of neutron scattering are obtained in such a system with allowance for the gravitational effect and in various approximation for the pair correlation function of density fluctuations
Extension of Gibbs-Duhem equation including influences of external fields
Guangze, Han; Jianjia, Meng
2018-03-01
Gibbs-Duhem equation is one of the fundamental equations in thermodynamics, which describes the relation among changes in temperature, pressure and chemical potential. Thermodynamic system can be affected by external field, and this effect should be revealed by thermodynamic equations. Based on energy postulate and the first law of thermodynamics, the differential equation of internal energy is extended to include the properties of external fields. Then, with homogeneous function theorem and a redefinition of Gibbs energy, a generalized Gibbs-Duhem equation with influences of external fields is derived. As a demonstration of the application of this generalized equation, the influences of temperature and external electric field on surface tension, surface adsorption controlled by external electric field, and the derivation of a generalized chemical potential expression are discussed, which show that the extended Gibbs-Duhem equation developed in this paper is capable to capture the influences of external fields on a thermodynamic system.
Karabut, P.V.; Chugreev, Yu.V.
1989-01-01
The relativistic theory of gravitation (RTG), which is constructed on the basis of Minkowski spacetime, the geometrization principle, and the notion of the gravitational field var-phi mn as a physical field in the spirit of Faraday and Maxwell, explains all known gravitational experiments and gives a new prediction for the evolution of the universe, collapse, etc. The RTG determines the structure of the gravitational field as a field possessing spins 2 and 0 and all conservation laws for energy, momentum, and angular momentum. An exact solution of the complete simultaneous system of equations of the relativistic theory of gravitation and Maxwell's equations is found in the axisymmetric case for an electrically charged rotating body. The uniqueness of this solution is proved
Functional renormalisation group equations for supersymmetric field theories
Synatschke-Czerwonka, Franziska
2011-01-11
This work is organised as follows: In chapter 2 the basic facts of quantum field theory are collected and the functional renormalisation group equations are derived. Chapter 3 gives a short introduction to the main concepts of supersymmetry that are used in the subsequent chapters. In chapter 4 the functional RG is employed for a study of supersymmetric quantum mechanics, a supersymmetric model which are studied intensively in the literature. A lot of results have previously been obtained with different methods and we compare these to the ones from the FRG. We investigate the N=1 Wess-Zumino model in two dimensions in chapter 5. This model shows spontaneous supersymmetry breaking and an interesting fixed-point structure. Chapter 6 deals with the three dimensional N=1 Wess-Zumino model. Here we discuss the zero temperature case as well as the behaviour at finite temperature. Moreover, this model shows spontaneous supersymmetry breaking, too. In chapter 7 the two-dimensional N=(2,2) Wess-Zumino model is investigated. For the superpotential a non-renormalisation theorem holds and thus guarantees that the model is finite. This allows for a direct comparison with results from lattice simulations. (orig.)
On integrability conditions of the equations of nonsymmetrical chiral field on SO(4)
Tskhakaya, D.D.
1990-01-01
Possibility of integrating the equations of nonsymmetrical chiral field on SO(4) by means of the inverse scattering method is investigated. Maximal number of the motion integrals is found for the corresponding system of ordinary differential equations
A calderón multiplicative preconditioner for the combined field integral equation
Bagci, Hakan; Andriulli, Francesco P.; Cools, Kristof; Olyslager, Femke; Michielssen, Eric
2009-01-01
A Calderón multiplicative preconditioner (CMP) for the combined field integral equation (CFIE) is developed. Just like with previously proposed Caldern-preconditioned CFIEs, a localization procedure is employed to ensure that the equation
Theory of gravitational interactions
Gasperini, Maurizio
2017-01-01
This is the second edition of a well-received book that is a modern, self-contained introduction to the theory of gravitational interactions. The new edition includes more details on gravitational waves of cosmological origin, the so-called brane world scenario, and gravitational time-delay effects. The first part of the book follows the traditional presentation of general relativity as a geometric theory of the macroscopic gravitational field, while the second, more advanced part discusses the deep analogies (and differences) between a geometric theory of gravity and the “gauge” theories of the other fundamental interactions. This fills a gap within the traditional approach to general relativity which usually leaves students puzzled about the role of gravity. The required notions of differential geometry are reduced to the minimum, allowing room for aspects of gravitational physics of current phenomenological and theoretical interest, such as the properties of gravitational waves, the gravitational inter...
On geometrized gravitation theories
Logunov, A.A.; Folomeshkin, V.N.
1977-01-01
General properties of the geometrized gravitation theories have been considered. Geometrization of the theory is realized only to the extent that by necessity follows from an experiment (geometrization of the density of the matter Lagrangian only). Aor a general case the gravitation field equations and the equations of motion for matter are formulated in the different Riemann spaces. A covariant formulation of the energy-momentum conservation laws is given in an arbitrary geometrized theory. The noncovariant notion of ''pseudotensor'' is not required in formulating the conservation laws. It is shown that in the general case (i.e., when there is an explicit dependence of the matter Lagrangian density on the covariant derivatives) a symmetric energy-momentum tensor of the matter is explicitly dependent on the curvature tensor. There are enlisted different geometrized theories that describe a known set of the experimental facts. The properties of one of the versions of the quasilinear geometrized theory that describes the experimental facts are considered. In such a theory the fundamental static spherically symmetrical solution has a singularity only in the coordinate origin. The theory permits to create a satisfactory model of the homogeneous nonstationary Universe
New exact solutions of the Einstein—Maxwell equations for magnetostatic fields
Goyal, Nisha; Gupta, R.K.
2012-01-01
The symmetry reduction method based on the Fréchet derivative of differential operators is applied to investigate symmetries of the Einstein—Maxwell field equations for magnetostatic fields, which is a coupled system of nonlinear partial differential equations of the second order. The technique yields invariant transformations that reduce the given system of partial differential equations to a system of nonlinear ordinary differential equations. Some of the reduced systems are further studied to obtain the exact solutions
Light rays and the tidal gravitational pendulum
Farley, A. N. St J.
2018-05-01
Null geodesic deviation in classical general relativity is expressed in terms of a scalar function, defined as the invariant magnitude of the connecting vector between neighbouring light rays in a null geodesic congruence projected onto a two-dimensional screen space orthogonal to the rays, where λ is an affine parameter along the rays. We demonstrate that η satisfies a harmonic oscillator-like equation with a λ-dependent frequency, which comprises terms accounting for local matter affecting the congruence and tidal gravitational effects from distant matter or gravitational waves passing through the congruence, represented by the amplitude, of a complex Weyl driving term. Oscillating solutions for η imply the presence of conjugate or focal points along the rays. A polarisation angle, is introduced comprising the orientation of the connecting vector on the screen space and the phase, of the Weyl driving term. Interpreting β as the polarisation of a gravitational wave encountering the light rays, we consider linearly polarised waves in the first instance. A highly non-linear, second-order ordinary differential equation, (the tidal pendulum equation), is then derived, so-called due to its analogy with the equation describing a non-linear, variable-length pendulum oscillating under gravity. The variable pendulum length is represented by the connecting vector magnitude, whilst the acceleration due to gravity in the familiar pendulum formulation is effectively replaced by . A tidal torque interpretation is also developed, where the torque is expressed as a coupling between the moment of inertia of the pendulum and the tidal gravitational field. Precessional effects are briefly discussed. A solution to the tidal pendulum equation in terms of familiar gravitational lensing variables is presented. The potential emergence of chaos in general relativity is discussed in the context of circularly, elliptically or randomly polarised gravitational waves encountering the null
Relativistic gravitation theory
Logunov, A.A.; Mestvirishvili, M.A.
1984-01-01
On the basis of the special relativity and geometrization principle a relativistic gravitation theory (RGT) is unambiguously constructed with the help of a notion of a gravitational field as a physical field in Faraday-Maxwell spirit, which posesses energy momentum and spins 2 and 0. The source of gravitation field is a total conserved energy-momentum tensor for matter and for gravitation field in Minkowski space. In the RGT conservation laws for the energy momentum and angular momentum of matter and gravitational field hold rigorously. The theory explains the whole set of gravitation experiments. Here, due to the geometrization principle the Riemannian space is of a field origin since this space arises effectively as a result of the gravitation field origin since this space arises effectively as a result of the gravitation field action on the matter. The RGT astonishing prediction is that the Universe is not closed but ''flat''. It means that in the Universe there should exist a ''missing'' mass in some form of matter
Theoretical approaches to laser spectroscopy in the presence of gravitational fields
Borde, C.J.; Sharma, J.; Tourrenc, P.; Damour, T.
1983-01-01
We present a general framework in which non-linear optical phenomena for an ensemble of accelerated atoms can be studied. We show the equivalence of various approaches through frame transformations. This equivalence is understood within the context of a covariant formalism which is briefly sketched. The choice of the frame, in which the atoms are not accelerated but where the light spectrum and the atomic source term are correspondingly modified, leads to the simplest calculated. It enables one to use the usual density matrix diagrams and associated rules. Explicit examples are given in the case of a sinusoidal gravitational wave. Finally a brief discussion of the signal-to-noise of the sidebands induced by gravitational waves on saturation resonances is outlined
Robertson, Brant E.; Ellis, Richard S.; Dunlop, James S.; McLure, Ross J.; Stark, Dan P.; McLeod, Derek
2014-12-01
Strong gravitational lensing provides a powerful means for studying faint galaxies in the distant universe. By magnifying the apparent brightness of background sources, massive clusters enable the detection of galaxies fainter than the usual sensitivity limit for blank fields. However, this gain in effective sensitivity comes at the cost of a reduced survey volume and, in this Letter, we demonstrate that there is an associated increase in the cosmic variance uncertainty. As an example, we show that the cosmic variance uncertainty of the high-redshift population viewed through the Hubble Space Telescope Frontier Field cluster Abell 2744 increases from ~35% at redshift z ~ 7 to >~ 65% at z ~ 10. Previous studies of high-redshift galaxies identified in the Frontier Fields have underestimated the cosmic variance uncertainty that will affect the ultimate constraints on both the faint-end slope of the high-redshift luminosity function and the cosmic star formation rate density, key goals of the Frontier Field program.