Degenerate pseudo-Riemannian metrics
Hervik, Sigbjorn; Yamamoto, Kei
2014-01-01
In this paper we study pseudo-Riemannian spaces with a degenerate curvature structure i.e. there exists a continuous family of metrics having identical polynomial curvature invariants. We approach this problem by utilising an idea coming from invariant theory. This involves the existence of a boost, the existence of this boost is assumed to extend to a neighbourhood. This approach proves to be very fruitful: It produces a class of metrics containing all known examples of degenerate metrics. To date, only Kundt and Walker metrics have been given, however, our study gives a plethora of examples showing that degenerate metrics extend beyond the Kundt and Walker examples. The approach also gives a useful criterion for a metric to be degenerate. Specifically, we use this to study the subclass of VSI and CSI metrics (i.e., spaces where polynomial curvature invariants are all vanishing or constants, respectively).
A New Family of Curvature Homogeneous Pseudo-Riemannian Manifolds
Dunn, Corey
2009-01-01
We construct a new family of curvature homogeneous pseudo-Riemannian manifolds modeled on $\\mathbb{R}^{3k+2}$ for integers $k \\geq 1$. In contrast to previously known examples, the signature may be chosen to be $(k+1+a, k+1+b)$ where $a,b \\in \\mathbb{N} \\bigcup \\{0\\}$ and $a+b = k$. The structure group of the 0-model of this family is studied, and is shown to be indecomposable. Several invariants that are not of Weyl type are found which will show that, in general, the members of this family ...
Examples of Sol-Solitons in the Pseudo-Riemannian case
Onda, Kensuke
2011-01-01
This paper provides a study of sol-solitons in the pseudo-Riemannian case. In the Riemannian case, all nontrivial homogeneous sol-soliton are expanding sol-solitons. In this paper, we obtain steady sol-solitons and shrinking sol-solitons in the Lorentzian setting.
Modified Einstein-Gauss-Bonnet gravity: Riemann-Cartan and Pseudo-Riemannian cases
Özer, Hatice; Delice, Özgür
2016-01-01
A modified Einstein-Gauss-Bonnet gravity in four dimensions where the quadratic Gauss-Bonnet term is coupled to a scalar field is considered. The field equations of the model are obtained by variational methods by making use of the constrained-first order formalism covering both pseudo-Riemannian and non-Riemannian cases. In the pseudo-Riemannian case, the Lagrange multiplier forms, which impose the vanishing torsion constraint, are eliminated in favor of the remaining fields and the resulting metric field equations are expressed in terms of the double-dual curvature 2-form. In the non-Riemannian case with torsion, the field equations are expressed in terms of the pseudo-Riemannian quantities by a perturbative scheme valid for a weak coupling constant. It is shown that, for both cases, the model admits a maximally symmetric de-Sitter solution with nontrivial scalar field. Minimal coupling of a Dirac spinor to the Gauss-Bonnet modified gravity is also discussed briefly.
Eikonal slant helices and eikonal Darboux helices in 3-dimensional pseudo-Riemannian manifolds
Önder, Mehmet; Ziplar, Evren
2013-01-01
In this study, we give definitions and characterizations of eikonal slant helices, eikonal Darboux helices and non-normed eikonal Darboux helices in 3-dimensional pseudo- Riemannian manifold M . We show that every eikonal slant helix is also an eikonal Darboux helix for timelike and spacelike curves. Furthermore, we obtain that if the non-null curve a is a non-normed eikonal Darboux helix, then a is an eikonal slant helix if and only if 2 2 e 3k +e1t = constant, where k and t are curvature an...
Wafaa Batat
2010-02-01
Full Text Available In this note we prove that the Heisenberg group with a left-invariant pseudo-Riemannian metric admits a completely integrable totally geodesic distribution of codimension 1. This is on the contrary to the Riemannian case, as it was proved by T. Hangan.
Statistics on Lie groups: A need to go beyond the pseudo-Riemannian framework
Miolane, Nina; Pennec, Xavier
2015-01-01
Lie groups appear in many fields from Medical Imaging to Robotics. In Medical Imaging and particularly in Computational Anatomy, an organ's shape is often modeled as the deformation of a reference shape, in other words: as an element of a Lie group. In this framework, if one wants to model the variability of the human anatomy, e.g. in order to help diagnosis of diseases, one needs to perform statistics on Lie groups. A Lie group G is a manifold that carries an additional group structure. Statistics on Riemannian manifolds have been well studied with the pioneer work of Fréchet, Karcher and Kendall [1, 2, 3, 4] followed by others [5, 6, 7, 8, 9]. In order to use such a Riemannian structure for statistics on Lie groups, one needs to define a Riemannian metric that is compatible with the group structure, i.e a bi-invariant metric. However, it is well known that general Lie groups which cannot be decomposed into the direct product of compact and abelian groups do not admit a bi-invariant metric. One may wonder if removing the positivity of the metric, thus asking only for a bi-invariant pseudo-Riemannian metric, would be sufficient for most of the groups used in Computational Anatomy. In this paper, we provide an algorithmic procedure that constructs bi-invariant pseudo-metrics on a given Lie group G. The procedure relies on a classification theorem of Medina and Revoy. However in doing so, we prove that most Lie groups do not admit any bi-invariant (pseudo-) metric. We conclude that the (pseudo-) Riemannian setting is not the richest setting if one wants to perform statistics on Lie groups. One may have to rely on another framework, such as affine connection space.
Spacelike Graphs with Parallel Mean Curvature in Pseudo-Riemannian Product Manifolds
Zicheng ZHAO
2012-01-01
The author introduces the w-function defined on the considered spacelike graph M.Under the growth conditions w =o(log z) and w =o(r),two Bernstein type theorems for M in Rmn+m are got,where z and r are the pseudo-Euclidean distance and the distance function on M to some fixed point respectively.As the ambient space is a curved pseudoRiemannian product of two Riemannian manifolds (∑1,g1) and (∑2,g2) of dimensions n and m,a Bernstein type result for n =2 under some curvature conditions on ∑1 and ∑2 and the growth condition w =o(r) is also got.As more general cases,under some curvature conditions on the ambient space and the growth condition w =o(Υ) or w =o(√Υ),the author concludes that if M has parallel mean curvature,then M is maximal.
Seiberg-Witten Like Equations on Pseudo-Riemannian Spinc Manifolds with G2(2∗ Structure
Nülifer Özdemir
2016-01-01
Full Text Available We consider 7-dimensional pseudo-Riemannian spinc manifolds with structure group G2(2∗. On such manifolds, the space of 2-forms splits orthogonally into components Λ2M=Λ72⊕Λ142. We define self-duality of a 2-form by considering the part Λ72 as the bundle of self-dual 2-forms. We express the spinor bundle and the Dirac operator and write down Seiberg-Witten like equations on such manifolds. Finally we get explicit forms of these equations on R4,3 and give some solutions.
Global existence of harmonic maps on Minkowski space time M/sub 3/
Choquet-Bruhat, Y.; Chao Hao, G.
1989-02-01
We prove the existence of global solutions of the Cauchy problem for harmonic maps from three dimensional Minkowski space time M/sub 3/ into some pseudo riemannian manifolds, including spaces with constant curvature, when the Cauchy data are small in appropriate norms.
Relative Locality in Curved Space-time
Kowalski-Glikman, Jerzy
2013-01-01
In this paper we construct the action describing dynamics of the particle moving in curved spacetime, with a non-trivial momentum space geometry. Curved momentum space is the core feature of theories where relative locality effects are presents. So far aspects of nonlinearities in momentum space have been studied only for flat or constantly expanding (De Sitter) spacetimes, relying on the their maximally symmetric nature. The extension of curved momentum space frameworks to arbitrary spacetime geometries could be relevant for the opportunities to test Planck-scale curvature/deformation of particles momentum space. As a first example of this construction we describe the particle with kappa-Poincar\\'e momentum space on a circular orbit in Schwarzschild spacetime, where the contributes of momentum space curvature turn out to be negligible. The analysis of this problem relies crucially on the solution of the soccer ball problem.
Expanding General Relativity's Space by S-Denying
Rabounski, Dmitri; Smarandache, Florentins; Borissova, Larissa
2016-05-01
Applying the S-denying procedure to signature conditions in a four-dimensional pseudo-Riemannian space - i.e. changing one (or even all) of the conditions to be partially true and partially false. Obtaining five kinds of expanded space-time for General Relativity. Kind I permits the space-time to be in collapse. Kind II permits the space-time to change its own signature. Kind III has peculiarities, linked to the third signature condition. Kind IV permits regions where the metric fully degenerates: there may be non-quantum teleportation, and a home for virtual photons. Kind V is common for kinds I, II, III, and IV.
A Mathematicians' View of Geometrical Unification of General Relativity and Quantum Physics
Vaugon, Michel
2015-01-01
This document contains a description of physics entirely based on a geometric presentation: all of the theory is described giving only a pseudo-riemannian manifold (M, g) of dimension n > 5 for which the g tensor is, in studied domains, almost everywhere of signature (-, -, +, ..., +). No object is added to this space-time, no general principle is supposed. The properties we impose to some domains of (M, g) are only simple geometric constraints, essentially based on the concept of "curvature". These geometric properties allow to define, depending on considered cases, some objects (frequently depicted by tensors) that are similar to the classical physics ones, they are however built here only from the g tensor. The links between these objects, coming from their natural definitions, give, applying standard theorems from the pseudo-riemannian geometry, all equations governing physical phenomena usually described by classical theories, including general relativity and quantum physics. The purely geometric approac...
Relativity for everyone how space-time bends
Fischer, Kurt
2015-01-01
This book, now in a revised and updated second edition, explains the theory of special and general relativity in detail without approaching Einstein's life or the historical background. The text is formulated in such a way that the reader will be able to understand the essence intuitively, and new sections have been added on time machines, the twin paradoxes, and tensors. The first part of the book focuses on the essentials of special relativity. It explains the famous equivalence between mass and energy and tells why Einstein was able to use the theory of electrodynamics as a template for his "electrodynamics of moving bodies". General relativity is then addressed, mainly with the help of thought experiments. Reference is made to the previously introduced special relativity and the equivalence principle and, using many figures, it is explained how space-time is bending under gravity. The climax of the book is the Einstein equation of gravity, which describes the way in which matter bends space-time. The read...
Relativity as the quantum mechanics of space-time measurements
Lieu, Richard
2016-01-01
Can a simple microscopic model of space and time demonstrate Special Relativity as the macroscopic (aggregate) behavior of an ensemble ? The question will be investigated in three parts. First, it is shown that the Lorentz transformation formally stems from the First Relativity Postulate (FRP) {\\it alone} if space-time quantization is a fundamental law of physics which must be included as part of the Postulate. An important corollary, however, is that when measuring devices which carry the basic units of lengths and time (e.g. a clock ticking every time quantum) are `moving' uniformly, they appear to be measuring with larger units. Secondly, such an apparent increase in the sizes of the quanta can be attributed to extra fluctuations associated with motion, which are precisely described in terms of a thermally agitated harmonic oscillator by using a temperature parameter. This provides a stringent constraint on the microscopic properties of flat space-time: it is an array of quantized oscillators. Thirdly, sin...
Scale relativity and fractal space-time: theory and applications
Nottale, Laurent
2008-01-01
In the first part of this contribution, we review the development of the theory of scale relativity and its geometric framework constructed in terms of a fractal and nondifferentiable continuous space-time. This theory leads (i) to a generalization of possible physically relevant fractal laws, written as partial differential equation acting in the space of scales, and (ii) to a new geometric foundation of quantum mechanics and gauge field theories and their possible generalisations. In the second part, we discuss some examples of application of the theory to various sciences, in particular in cases when the theoretical predictions have been validated by new or updated observational and experimental data. This includes predictions in physics and cosmology (value of the QCD coupling and of the cosmological constant), to astrophysics and gravitational structure formation (distances of extrasolar planets to their stars, of Kuiper belt objects, value of solar and solar-like star cycles), to sciences of life (log-p...
Papadopoulos, Georgios O
2014-01-01
A classic, double problem with intriguing implications at the level of both applied differential geometry and theoretical physics is dealt with in this short work: Is there any criterion in order to decide whether a pseudo-Riemannian space can be locally described using curvature scalars solely? Also: In the case where such a description is impossible, does the Cartan-Karlhede algorithm constitute the only refuge? Surprisingly enough, the first question is susceptible of a very simple and elegant answer, while a naive scheme carries the ambition of providing (modulo specific restrictions) a negative answer to the second question. In order to avoid unnecessary complexity, the analysis is restricted to local rather than global considerations, without any loss of not only the generality but also the insights to the initial problem.
Relativity Based on Physical Processes Rather Than Space-Time
Giese, Albrecht
2013-09-01
Physicists' understanding of relativity and the way it is handled is at present dominated by the interpretation of Albert Einstein, who related relativity to specific properties of space and time. The principal alternative to Einstein's interpretation is based on a concept proposed by Hendrik A. Lorentz, which uses knowledge of classical physics to explain relativistic phenomena. In this paper, we will show that on the one hand the Lorentz-based interpretation provides a simpler mathematical way of arriving at the known results for both Special and General Relativity. On the other hand, it is able to solve problems which have remained open to this day. Furthermore, a particle model will be presented, based on Lorentzian relativity, which explains the origin of mass without the use of the Higgs mechanism, based on the finiteness of the speed of light, and which provides the classical results for particle properties that are currently only accessible through quantum mechanics.
Snyder's quantized space-time and de Sitter special relativity
GUO Han-ying; HUANG Chao-guang; TIAN Yu; XU Zhan; ZHOU Bin
2007-01-01
There is a one-to-one correspondence between Snyder's model in de Sitter space of momenta and the dS-invariant special relativity as well as a minimum uncertaintylike relation.This indicates that physics at the Planck length lp and the scale R =(3/Λ)1/2 should be dual to each other and there is in-between gravity of local dS-invariance characterized by a dimensionless coupling constant g= lp/R～10-61.
Physical relativity space-time structure from a dynamical perspective
Brown, Harvey R
2005-01-01
Physical Relativity explores the nature of the distinction at the heart of Einstein's 1905 formulation of his special theory of relativity: that between kinematics and dynamics. Einstein himself became increasingly uncomfortable with this distinction, and with the limitations of what he called the 'principle theory' approach inspired by the logic of thermodynamics. A handful of physicists and philosophers have over the last century likewise expressed doubts about Einstein'streatment of the relativistic behaviour of rigid bodies and clocks in motion in the kinematical part of his great paper, a
S-Denying of the Signature Conditions Expands General Relativity's Space
Rabounski D.
2006-07-01
Full Text Available We apply the S-denying procedure to signature conditions in a four-dimensional pseudo-Riemannian space — i. e. we change one (or even all of the conditions to be partially true and partially false. We obtain five kinds of expanded space-time for General Relativity. Kind I permits the space-time to be in collapse. Kind II permits the space-time to change its own signature. Kind III has peculiarities, linked to the third signature condition. Kind IV permits regions where the metric fully degenerates: there may be non-quantum teleportation, and a home for virtual photons. Kind V is common for kinds I, II, III, and IV.
Chudecki, Adam
2016-01-01
4-dimensional spaces equipped with 2-dimensional (complex holomorphic or real smooth) completely integrable distributions are considered. The integral manifolds of such distributions are totally null and totally geodesics 2-dimensional surfaces which are called the null strings. Properties of congruences (foliations) of such 2-surfaces are studied. Relation between properties of congruences of null strings and Petrov-Penrose type of SD Weyl spinor and algebraic types of traceless Ricci tensor is analyzed.
Scale relativity and fractal space-time a new approach to unifying relativity and quantum mechanics
Nottale, Laurent
2011-01-01
This book provides a comprehensive survey of the development of the theory of scale relativity and fractal space-time. It suggests an original solution to the disunified nature of the classical-quantum transition in physical systems, enabling the basis of quantum mechanics on the principle of relativity, provided this principle is extended to scale transformations of the reference system. In the framework of such a newly generalized relativity theory (including position, orientation, motion and now scale transformations), the fundamental laws of physics may be given a general form that unifies
Brownian Motion and General Relativity
O'Hara, Paul
2013-01-01
We construct a model of Brownian Motion on a pseudo-Riemannian manifold associated with general relativity. There are two aspects of the problem: The first is to define a sequence of stopping times associated with the Brownian "kicks" or impulses. The second is to define the dynamics of the particle along geodesics in between the Brownian kicks. When these two aspects are taken together, we can associate various distributions with the motion. We will find that the statistics of space-time events will obey a temperature dependent four dimensional Gaussian distribution defined over the quaternions which locally can be identified with Minkowski space. Analogously, the statistics of the 4-velocities will obey a kind of Maxwell-Juttner distribution. In contrast to previous work, our processes are characterized by two independent proper time variables defined with respect to the laboratory frame: a discrete one corresponding to the stopping times when the impulses take place and a continuous one corresponding to th...
Supporting abstract relational space-time as fundamental without doctrinism against emergence
Vongehr, Sascha
2009-01-01
The present paper aims to contribute to the substantivalism versus relationalism debate and to defend general relativity (GR) against pseudoscientific attacks in a novel, especially inclusive way. This work was initially motivated by the desire to establish the incompatibility of any ether theories with accelerated cosmic expansion and inflation (motto: where would a hypothetical medium supposedly come from so fast?). The failure of this program is of interest for emergent GR concepts in high energy particle physics. However, it becomes increasingly important to guard scientific results against their misrepresentation by fundamentally anti-scientific agendas. We therefore argue that although it is not known whether the perceived space-time is fundamental (rather than a condensed state or a particular membrane), in a fundamental theory, space-time must be abstract relational: fundamental space-time is the consistent spatial-temporal arrangement of events. To pursue its own goals, this work should be accessible...
On the Possibility of Instant Displacements in the Space-Time of General Relativity
Borissova L.
2005-04-01
Full Text Available Employing the mathematical apparatus of chronometric invariants (physical observable quantities, this study finds a theoretical possibility for the instant displacement of particles in the space-time of the General Theory of Relativity. This is to date the sole theoretical explanation of the well-known phenomenon of photon teleportation, given by the purely geometrical methods of Einstein’s theory.
Superluminal Neutrinos from Special Relativity with de Sitter Space-time Symmetry
Yan, Mu-Lin; Xiao, Neng-Chao; Huang, Wei; Hu, Sen
2011-01-01
We explore the recent OPERA experiment of superluminal neutrinos in the framework of Special Relativity with de Sitter space-time symmetry (dS-SR). According to Einstein a photon is treated as a massless particle in the framework of Special Relativity. In Special Relativity (SR) we have the universal parameter $c$, the photon velocity $c_{photon}$ and the phase velocity of a light wave in vacuum $c_{wave}=\\lambda\
Superluminal Neutrinos from Special Relativity with de Sitter Space-time Symmetry
Yan, Mu-Lin; Huang, Wei
2011-01-01
We explore the recent OPERA experiment of superluminal neutrinos in the framework of Special Relativity with de Sitter space-time symmetry (dS-SR). According to Einstein, the photon is treated as the massless particle in the SR mechanics. The meanings of the universal parameter $c$ and the photon velocity $c_{photon}$ in SR have been analyzed. $c$ can be determined by means of the velocity-composition law in SR kinematically. And $c_{photon}$ is determined by the dispersion relations of SR. It is revealed that $c=c_{photon}$ in Einstein's Special Relativity (E-SR), but $c\
Cosmological special relativity the large scale structure of space, time and velocity
Carmeli, Moshe
1997-01-01
This book deals with special relativity theory and its application to cosmology. It presents Einstein's theory of space and time in detail, and describes the large scale structure of space, time and velocity as a new cosmological special relativity. A cosmological Lorentz-like transformation, which relates events at different cosmic times, is derived and applied. A new law of addition of cosmic times is obtained, and the inflation of the space at the early universe is derived, both from the cosmological transformation. The book will be of interest to cosmologists, astrophysicists, theoretical
Cosmological special relativity the large scale structure of space, time and velocity
Carmeli, Moshe
2002-01-01
This book presents Einstein's theory of space and time in detail, and describes the large-scale structure of space, time and velocity as a new cosmological special relativity. A cosmological Lorentz-like transformation, which relates events at different cosmic times, is derived and applied. A new law of addition of cosmic times is obtained, and the inflation of the space at the early universe is derived, both from the cosmological transformation. The relationship between cosmic velocity, acceleration and distances is given. In the appendices gravitation is added in the form of a cosmological g
Realization of Cohen-Glashow very special relativity on noncommutative space-time.
Sheikh-Jabbari, M M; Tureanu, A
2008-12-31
We show that the Cohen-Glashow very special relativity (VSR) theory [A. G. Cohen and S. L. Glashow, Phys. Rev. Lett. 97, 021601 (2006)] can be realized as the part of the Poincaré symmetry preserved on a noncommutative Moyal plane with lightlike noncommutativity. Moreover, we show that the three subgroups relevant to VSR can also be realized in the noncommutative space-time setting. For all of these three cases, the noncommutativity parameter theta(mu upsilon) should be lightlike (theta(mu upsilon) theta mu upsilon = 0). We discuss some physical implications of this realization of the Cohen-Glashow VSR.
Numerical relativity for D dimensional axially symmetric space-times: Formalism and code tests
Zilhão, Miguel; Witek, Helvi; Sperhake, Ulrich; Cardoso, Vitor; Gualtieri, Leonardo; Herdeiro, Carlos; Nerozzi, Andrea
2010-04-01
The numerical evolution of Einstein’s field equations in a generic background has the potential to answer a variety of important questions in physics: from applications to the gauge-gravity duality, to modeling black hole production in TeV gravity scenarios, to analysis of the stability of exact solutions, and to tests of cosmic censorship. In order to investigate these questions, we extend numerical relativity to more general space-times than those investigated hitherto, by developing a framework to study the numerical evolution of D dimensional vacuum space-times with an SO(D-2) isometry group for D≥5, or SO(D-3) for D≥6. Performing a dimensional reduction on a (D-4) sphere, the D dimensional vacuum Einstein equations are rewritten as a 3+1 dimensional system with source terms, and presented in the Baumgarte, Shapiro, Shibata, and Nakamura formulation. This allows the use of existing 3+1 dimensional numerical codes with small adaptations. Brill-Lindquist initial data are constructed in D dimensions and a procedure to match them to our 3+1 dimensional evolution equations is given. We have implemented our framework by adapting the Lean code and perform a variety of simulations of nonspinning black hole space-times. Specifically, we present a modified moving puncture gauge, which facilitates long-term stable simulations in D=5. We further demonstrate the internal consistency of the code by studying convergence and comparing numerical versus analytic results in the case of geodesic slicing for D=5, 6.
BIPM/IAU Joint Committee on relativity for space-time reference systems and metrology
Petit, G.
At the Kyoto General Assembly, the IAU endorsed, by its Resolution B3 (1997), the creation of the Joint Committee on Relativity for space-time reference systems and metrology (JCR), which was also approved by the Comité International des Poids et Mesures (CIPM) at its 86th meeting in September 1997. Its tasks are ``to establish definitions and conventions to provide a coherent relativistic frame ....... and to develop the adopted definitions and conventions for practical application by the user." The web site of the JCR (www.bipm.fr/WG/CCTF/JCR) contains the headlines of the JCR work. The BIPM/IAU JCR has worked in collaboration with the IAU Working Group on relativity for celestial mechanics and astrometry (RCMA) on the problems of astronomical relativistic space-time reference frames. A document was established in common (document jcrissue.html on the JCR web site) discussing as much as possible all topics that may be addressed by the two groups. The RCMA has specified a consistent framework for defining the barycentric and geocentric celestial reference systems at the first post-Newtonian level. Because new clock technology and space missions will necessitate the application of this framework for time and frequency measurements in the solar system, the JCR focused on these applications. The paper outlines the conclusions of the work and the proposed IAU resolutions, that were discussed at IAU Colloquium 180 in March 2000.
Evidence for special relativity with de Sitter space-time symmetry
YAN Mu-Lin
2011-01-01
I show the formulation of de Sitter Special Relativity (dS-SR) based on Dirac-Lu-Zou-Guo's discussions, dS-SR quantum mechanics is formulated, and the dS-SR Dirac equation for hydrogen is suggested. The equation in the earth-QSO framework reference is solved by means of the adiabatic approach. It's found that the fine-structure "constant" α in dS-SR varies with time. By means of the t-z relation of the ACDM model, α's time-dependency becomes redshift z-dependent. The dS-SR's predictions of △α/α agree with data of spectra of 143 quasar absorption systems, the dS-space-time symmetry is SO(3,2) (i.e., anti-dS group) and the universal parameter R (de Sitter ratio) in dS-SR is estimated to be R ≈ 2.73 x 10 ly. The effects of dS-SR become visible at the cosmic space-time scale (i.e., the distance≥ 10 ly). At that scale, dS-SR is more reliable than Einstein SR. The α-variation with time is evidence of SR with de Sitter symmetry.
On the relative energy associated with space-times of diagonal metrics
Murat Korunur; Mustafa Salti; Ali havare
2007-05-01
In order to evaluate the energy distribution (due to matter and ﬁelds including gravitation) associated with a space-time model of generalized diagonal metric, we consider the Einstein, Bergmann–Thomson and Landau–Lifshitz energy and/or momentum deﬁnitions both in Einstein's theory of general relativity and the teleparallel gravity (the tetrad theory of gravitation). We ﬁnd same energy distribution using Einstein and Bergmann–Thomson formulations, but we also ﬁnd that the energy–momentum prescription of Landau–Lifshitz disagree in general with these deﬁnitions. We also give eight different well-known space-time models as examples, and considering these models and using our results, we calculate the energy distributions associated with them. Furthermore, we show that for the Bianchi Type-I models all the formulations give the same result. This result agrees with the previous works of Cooperstock–Israelit, Rosen, Johri et al, Banerjee–Sen, Xulu, Vargas and Saltı et al and supports the viewpoints of Albrow and Tryon.
Dirac-Kahler equation in curved space-time, relation between spinor and tensor formulations
Red'kov, V M
2011-01-01
A common view is that generalization of a wave equation on Riemannian space-time is substantially determined by what a particle is - boson or fermion. As a rule, they say that tensor equations for bosons are extended in a simpler way then spinor equations for fermions. In that context, a very interesting problem is of extension a wave equation for Dirac--K\\"{a}hler field (Ivanenko--Landau field was historically first term, also the term a vector field of general type was used). The article relates a generally covariant tensor formalism to a spinor one when these both are applied to description of the Dirac-K\\"ahler field in a Rimannian space-time. Both methods are taken to be equivalent and the tensor equations are derived from spinor ones. It is shown that, for characterization of Dirac-K\\"ahler's tensor components, two alternative approaches are suitable: these are whether a tetrad-based pseudo tensor classification or a generally coordinate pseudo tensor one. By imposing definite restrictions on the the Di...
Numerical relativity for D dimensional axially symmetric space-times: formalism and code tests
Zilhao, Miguel; Sperhake, Ulrich; Cardoso, Vitor; Gualtieri, Leonardo; Herdeiro, Carlos; Nerozzi, Andrea
2010-01-01
The numerical evolution of Einstein's field equations in a generic background has the potential to answer a variety of important questions in physics: from applications to the gauge-gravity duality, to modelling black hole production in TeV gravity scenarios, analysis of the stability of exact solutions and tests of Cosmic Censorship. In order to investigate these questions, we extend numerical relativity to more general space-times than those investigated hitherto, by developing a framework to study the numerical evolution of D dimensional vacuum space-times with an SO(D-2) isometry group for D\\ge 5, or SO(D-3) for D\\ge 6. Performing a dimensional reduction on a (D-4)-sphere, the D dimensional vacuum Einstein equations are rewritten as a 3+1 dimensional system with source terms, and presented in the Baumgarte, Shapiro, Shibata and Nakamura (BSSN) formulation. This allows the use of existing 3+1 dimensional numerical codes with small adaptations. Brill-Lindquist initial data are constructed in D dimensions an...
Rica, Sergio
2016-01-01
The recent observation of gravitational waves, stimulates the question of the longtime evolution of the space-time fluctuations. Gravitational waves interact themselves through the nonlinear character of Einstein's equations of general relativity. This nonlinear wave interaction allows the spectral energy transfer from mode to mode. According to the wave turbulence theory, the weakly nonlinear interaction of gravitational waves leads to the existence of an irreversible kinetic regime that dominates the longtime evolution. The resulting kinetic equation suggests the existence of an equilibrium wave spectrum and the existence of a non-equilibrium Kolmogorov-Zakharov spectrum for spatio-temporal fluctuations. Evidence of these solutions extracted in the fluctuating signal of the recent observations will be discussed in the paper. Probably, the present results would be pertinent in the new age of development of gravitational astronomy, as well as, in new tests of General Relativity.
K-causal structure of space-time in general relativity
Sujatha Janardhan; R V Saraykar
2008-04-01
Using K-causal relation introduced by Sorkin and Woolgar [1], we generalize results of Garcia-Parrado and Senovilla [2,3] on causal maps. We also introduce causality conditions with respect to K-causality which are analogous to those in classical causality theory and prove their inter-relationships. We introduce a new causality condition following the work of Bombelli and Noldus [4] and show that this condition lies in between global hyperbolicity and causal simplicity. This approach is simpler and more general as compared to traditional causal approach [5,6] and it has been used by Penrose et al [7] in giving a new proof of positivity of mass theorem. 0-space-time structures arise in many mathematical and physical situations like conical singularities, discontinuous matter distributions, phenomena of topology-change in quantum field theory etc.
One Electron Atom in Special Relativity with de Sitter Space-Time Symmetry
闫沐露
2012-01-01
The de Sitter invariant Special Relativity （dS-SR） is SR with constant curvature, and a natural extension of usual Einstein SR （E-SR）. In this paper, we solve the dS-SR Dirac equation of Hydrogen by means of the adiabatic approach and the quasi-stationary perturbation calculations of QM. Hydrogen atom is located in the light cone of the Universe. FRW metric and ACDM cosmological model are used to discuss this issue. To the atom, effects of de Sitter space-time geometry described by Beltrami metric are taken into account. The dS-SR Dirac equation turns out to be a time dependent quantum Hamiltonian system. We reveal that： （i） The fundamental physics constants me, h, e variate adiabatically along with cosmologic time in dS-SR QM framework. But the fine-structure constant α≡ - e^2/（hc） keeps to be invariant; （ii） （2s^1/2 - 2p^1/2）-splitting due to dS-SR QM effects： By means of perturbation theory, that splitting △E（z） are calculated analytically, which belongs to O（1/R^2）-physics of dS-SR QM. Numerically, we find that when ｜R｜ = {103 Gly, 104 Gly, 105 Gly}, and z = {1, or 2}, the AE（z） 〉〉 1 （Lamb shift）. This indicates that for these cases the hyperfine structure effects due to QED could be ignored, and the dS-SR fine structure effects are dominant. This effect could be used to determine the universal constant R in dS-SR, and be thought as a new physics beyond E-SR.
Numerical Relativity in D dimensional space-times: Collisions of unequal mass black holes
Witek, Helvi; Cardoso, Vitor; Sperhake, Ulrich [CENTRA, Departamento de Fisica, Instituto Superior Tecnico, Universidade Tecnica de Lisboa - UTL, Av. Rovisco Pais 1, 1049 Lisboa (Portugal); Gualtieri, Leonardo [Dipartimento di Fisica, Universita di Roma ' Sapienza' and Sezione INFN Roma1, P.A. Moro 5, 00185, Roma (Italy); Herdeiro, Carlos [Departamento de Fisica da Universidade de Aveiro, Campus de Santiago, 3810-183 Aveiro (Portugal); Zilhao, Miguel, E-mail: helvi.witek@ist.utl.pt [Centro de Fisica do Porto - CFP, Departamento de Fisica e Astronomia, Faculdade de Ciencias da Universidade do Porto - FCUP, Rua do Campo Alegre, 4169-007 Porto (Portugal)
2011-09-22
We present unequal mass head-on collisions of black holes in D = 5 dimensional space-times. We have simulated BH systems with mass ratios q 1,1/2, 1/3, 1/4. We extract the total energy radiated throughout the collision and compute the linear momentum flux and the recoil velocity of the final black hole. The numerical results show very good agreement with point particle calculations when extrapolated to this limit.
On Yang's Noncommutative Space Time Algebra, Holography, Area Quantization and C-space Relativity
Castro, C
2004-01-01
An isomorphism between Yang's Noncommutative space-time algebra (involving two length scales) and the holographic-area-coordinates algebra of C-spaces (Clifford spaces) is constructed via an AdS_5 space-time which is instrumental in explaining the origins of an extra (infrared) scale R in conjunction to the (ultraviolet) Planck scale lambda characteristic of C-spaces. Yang's space-time algebra allowed Tanaka to explain the origins behind the discrete nature of the spectrum for the spatial coordinates and spatial momenta which yields a minimum length-scale lambda (ultraviolet cutoff) and a minimum momentum p = (\\hbar / R) (maximal length R, infrared cutoff). The double-scaling limit of Yang's algebra : lambda goes to 0, and R goes to infinity, in conjunction with the large n infinity limit, leads naturally to the area quantization condition : lambda R = L^2 = n lambda^2 (in Planck area units) given in terms of the discrete angular-momentum eigenvalues n . The generalized Weyl-Heisenberg algebra in C-spaces is ...
Space-time dependence between energy sources and climate related energy production
Engeland, Kolbjorn; Borga, Marco; Creutin, Jean-Dominique; Ramos, Maria-Helena; Tøfte, Lena; Warland, Geir
2014-05-01
The European Renewable Energy Directive adopted in 2009 focuses on achieving a 20% share of renewable energy in the EU overall energy mix by 2020. A major part of renewable energy production is related to climate, called "climate related energy" (CRE) production. CRE production systems (wind, solar, and hydropower) are characterized by a large degree of intermittency and variability on both short and long time scales due to the natural variability of climate variables. The main strategies to handle the variability of CRE production include energy-storage, -transport, -diversity and -information (smart grids). The three first strategies aim to smooth out the intermittency and variability of CRE production in time and space whereas the last strategy aims to provide a more optimal interaction between energy production and demand, i.e. to smooth out the residual load (the difference between demand and production). In order to increase the CRE share in the electricity system, it is essential to understand the space-time co-variability between the weather variables and CRE production under both current and future climates. This study presents a review of the literature that searches to tackle these problems. It reveals that the majority of studies deals with either a single CRE source or with the combination of two CREs, mostly wind and solar. This may be due to the fact that the most advanced countries in terms of wind equipment have also very little hydropower potential (Denmark, Ireland or UK, for instance). Hydropower is characterized by both a large storage capacity and flexibility in electricity production, and has therefore a large potential for both balancing and storing energy from wind- and solar-power. Several studies look at how to better connect regions with large share of hydropower (e.g., Scandinavia and the Alps) to regions with high shares of wind- and solar-power (e.g., green battery North-Sea net). Considering time scales, various studies consider wind
Spaans, M.
2013-01-01
General Relativity is extended into the quantum domain. A thought experiment is ex- plored to derive a specific topological build-up for Planckian space-time. The presented arguments are inspired by Feynman’s path integral for superposition andWheeler’s quan- tum foam of Planck mass mini black holes
Pseudo-Riemannian Universe from Euclidean bulk
Vasilić, Milovan
2015-01-01
I develop the idea that our world is a brane-like object embedded in Euclidean bulk. In its ground state, the brane constituent matter is assumed to be homogeneous and isotropic, and of negligible influence on the bulk geometry. No action functional is initially specified. Instead, the brane dynamics is derived from the universally valid stress-energy conservation equations. The present work studies the cosmology of a $3$-sphere in the $5$-dimensional Euclidean bulk. It is shown that the conventional equation of state $p=\\alpha\\rho$ is universal in the sector of small energy densities, and so is the resulting brane dynamics. The inequality $\\alpha<0$ is found to be a necessary condition for the existence of a stable ground state of the Universe. It is demonstrated that the generic braneworld physics rules out the Big Bang cosmology, and in that matter, any cosmology of finite lifetime. I also demonstrate that stable brane vibrations satisfy Klein-Gordon-like equation with an effective metric of Minkowski s...
El Naschie's {epsilon} {sup ({infinity})} space-time and new results in scale relativity theories
Gottlieb, I. [' Al.I.Cuza' University, Faculty of Physics, Department of Theoretical Physics, Blvd. Carol No. 1, Iasi 700506 (Romania)]. E-mail: gottlieb@uaic.ro; Agop, M. [' Gh. Asachi' Technical University, Department of Physics, Blvd. Mangeron, No. 64, Iasi 700050 (Romania); Ciobanu, Gabriela [' Al.I.Cuza' University, Faculty of Physics, Department of Theoretical Physics, Blvd. Carol No. 1, Iasi 700506 (Romania); Stroe, Aurelia [' Al.I.Cuza' University, Faculty of Physics, Department of Theoretical Physics, Blvd. Carol No. 1, Iasi 700506 (Romania)
2006-10-15
New results in fractal space-time theory are established: the fractal operator for the fractal dimension D = 2 implies a generalized Schroedinger equation in the Nottale's scale relativity theory, while the fractal operator for the fractal dimension D = 3 implies the Korteweg-de Vries equation in the one-dimensional case. The connection with El Naschie's {epsilon} {sup ({infinity})} theory result by means of the Cooper-type pairs or through wave-particle duality.
Spaans, Marco
2013-01-01
General Relativity is extended into the quantum domain. A thought experiment is explored to derive a specific topological build-up for Planckian space-time. The presented arguments are inspired by Feynman's path integral for superposition and Wheeler's quantum foam of Planck mass mini black holes/wormholes. Paths are fundamental and prime 3-manifolds like T^3, S^1xS^2 and S^3 are used to construct quantum space-time. A physical principle is formulated that causes observed paths to multiply: It takes one to know one. So topological fluctuations on the Planck scale take the form of multiple copies of any homeomorphically distinct path through quantum space-time. The discrete time equation of motion for this topological quantum gravity is derived by counting distinct paths globally. The equation of motion is solved to derive some properties of dark energy and inflation. The dark energy density depends linearly on the number of macroscopic black holes in the universe and is time dependent in a manner consistent w...
Ashtekar, Abhay
In general relativity space-time ends at singularities. The big bang is considered as the Beginning and the big crunch, the End. However these conclusions are arrived at by using general relativity in regimes which lie well beyond its physical domain of validity. Examples where detailed analysis is possible show that these singularities are naturally resolved by quantum geometry effects. Quantum space-times can be vastly larger than what Einstein had us believe. These non-trivial space-time extensions enable us to answer of some long standing questions and resolve of some puzzles in fundamental physics. Thus, a century after Minkowski's revolutionary ideas on the nature of space and time, yet another paradigm shift appears to await us in the wings.
Semiclassical relations and IR effects in de Sitter and slow-roll space-times
B. Giddings, Steven; Sloth, Martin Snoager
2010-01-01
We calculate IR divergent graviton one-loop corrections to scalar correlators in de Sitter space, and show that the leading IR contribution may be reproduced via simple semiclassical consistency relations. One can likewise use such semiclassical relations to calculate leading IR corrections to co...
Algebraically special space-time in relativity, black holes, and pulsar models
Adler, R. J.; Sheffield, C.
1973-01-01
The entire field of astronomy is in very rapid flux, and at the center of interest are problems relating to the very dense, rotating, neutron stars observed as pulsars. the hypothesized collapsed remains of stars known as black holes, and quasars. Degenerate metric form, or Kerr-Schild metric form, was used to study several problems related to intense gravitational fields.
Semiclassical relations and IR effects in de Sitter and slow-roll space-times
Giddings, Steven B. [Department of Physics, University of California, Santa Barbara, CA 93106 (United States); Sloth, Martin S., E-mail: giddings@physics.ucsb.edu, E-mail: sloth@cern.ch [CERN, Physics Department, Theory Unit, CH-1211 Geneva 23 (Switzerland)
2011-01-01
We calculate IR divergent graviton one-loop corrections to scalar correlators in de Sitter space, and show that the leading IR contribution may be reproduced via simple semiclassical consistency relations. One can likewise use such semiclassical relations to calculate leading IR corrections to correlators in slow-roll inflation. The regulated corrections shift the tensor/scalar ratio and consistency relation of single field inflation, and non-gaussianity parameters averaged over very large distances. For inflation of sufficient duration, for example arising from a chaotic inflationary scenario, these corrections become of order unity. First-order corrections of this size indicate a breakdown of the perturbative expansion, and suggest the need for a non-perturbative description of the corresponding regime. This is analogous to a situation argued to arise in black hole evolution, and to interfere with a sharp perturbative calculation of ''missing information'' in Hawking radiation.
Semiclassical relations and IR effects in de Sitter and slow-roll space-times
Giddings, Steven B
2011-01-01
We calculate IR divergent graviton one-loop corrections to scalar correlators in de Sitter space, and show that the leading IR contribution may be reproduced via simple semiclassical consistency relations. One can likewise use such semiclassical relations to calculate leading IR corrections to correlators in slow-roll inflation. The regulated corrections shift the tensor/scalar ratio and consistency relation of single field inflation, and non-gaussianity parameters averaged over very large distances. For inflation of sufficient duration, for example arising from a chaotic inflationary scenario, these corrections become of order unity. First-order corrections of this size indicate a breakdown of the perturbative expansion, and suggest the need for a non-perturbative description of the corresponding regime. This is analogous to a situation argued to arise in black hole evolution, and to interfere with a sharp perturbative calculation of "missing information" in Hawking radiation.
Six Not-So-Easy Pieces Einstein's Relativity, Symmetry, and Space-Time
Feynman, Richard P; Sands, Matthew
2011-01-01
Six lectures, all regarding the most revolutionary discovery in twentieth-century physics: Einstein's Theory of Relativity. No one--not even Einstein himself--explained these difficult, anti-intuitive concepts more clearly, or with more verve and gusto, than Feynman.
Evidence for special relativity with de Sitter space-time symmetry
闫沐霖
2011-01-01
I show the formulation of de Sitter Special Relativity （dS-SR） based on Dirac-Lu-Zou-Guo’s discussions. dS-SR quantum mechanics is formulated, and the dS-SR Dirac equation for hydrogen is suggested. The equation in the earth-QSO framework reference is sol
Crouse, David T
2016-01-01
In this work, resolutions will be given for commonly stated problems associated with a model that assumes that space and time are discretized (i.e., atomized). This model is in contrast to the continuous space-time model that is used in all common physical theories and equations -- a model that assumes that spatial coordinates and time are continuous variables. The resolutions to the problems are arrived at, not by proposing any new theories or postulates, but by strictly adhering to: Ernst Mach's principle of non-absolute space, the tenets of logical positivism, quantum mechanics and general relativity. The problems associated with discrete space-time addressed in this paper include: Lorentz contraction (time dilation) of the ostensibly smallest spatial (temporal) interval, maintaining isotropy, violations of causality, and conservation of energy and momentum. Importantly, this work yields modifications to the standard formulae for time dilation and length contraction, with these modifications preserving the...
2016-01-01
A new technique is used to study a family of time-dependent null horizons, called “Evolving Null Horizons” (ENHs), of generalized Robertson-Walker (GRW) space-time (M¯,g¯) such that the metric g¯ satisfies a kinematic condition. This work is different from our early papers on the same issue where we used (1 + n)-splitting space-time but only some special subcases of GRW space-time have this formalism. Also, in contrast to previous work, we have proved that each member of ENHs is totally umbilical in (M¯,g¯). Finally, we show that there exists an ENH which is always a null horizon evolving into a black hole event horizon and suggest some open problems. PMID:27722202
Akcay, A R
1999-01-01
This paper describes two new formulas: "formula A" and the Enhanced Einstein's Famous Formula (EEFF). The "formula A" has been experimentally proved and justified by using the High-Tc Superconductors, and provides the transmission of infinite (theoretically) frequencies. The EEFF has been mathematically derived from the Einstein's Famous Formula (EFF) by using the concept of the "formula A". The EEFF has been developed in place of EFF towards the prediction of the space-time singularities. The EEFF can predict and describe the space-time singularities without the distribution of mass and energy.
Soo, Chopin; Yu, Hoi-Lai
2013-12-01
Covariance of space and time in General Relativity (GR) entails a number of technical and conceptual difficulties. Remarkably, these can be resolved by a paradigm shift from full 4-dimensional general coordinate invariance to invariance only with respect to spatial diffeomorphisms. The framework for a theory of gravity with this paradigm shift, from quantum to classical regimes, is presented; GR is contained as a special case. Appositely formulated as a master constraint, the Hamiltonian constraint now determines only dynamics; and is relieved of its dual role of generating symmetry transformations. The Dirac algebra, in which 4-dimensional diffeomorphism symmetry is only realized on-shell, is replaced by the master constraint algebra which possesses only spatial diffeomorphism gauge symmetry, both on- and off-shell. Decomposition of the spatial metric into unimodular and determinant, q, factors results in mutually commuting pairs of canonical variables. The classical content of GR can be captured with a Hamiltonian constraint linear in the trace of the momentum. This implies a theory of quantum gravity can be described by a Schrodinger equation first order in intrinsic time ln q accompanied with positive semi-definite probability density. The semi-classical Hamilton-Jacobi equation is also first order in intrinsic time, with the implication of being complete; and gauge-invariant physical observables can be constructed from integration constants of its complete integral solution. Classical space-time, with direct correlation of its proper times and intrinsic time intervals, emerges from constructive interference; and the physical content of GR can be regained from a theory with a true Hamiltonian generating intrinsic time translations, but with only spatial diffeomorphism symmetry. The framework also prompts natural extensions towards a well-behaved quantum theory of gravity.
Nearly pseudo-Kähler manifolds and related special holonomies
Schäfer, Lars
2017-01-01
Developing and providing an overview of recent results on nearly Kähler geometry on pseudo-Riemannian manifolds, this monograph emphasizes the differences with the classical Riemannian geometry setting. The focal objects of the text are related to special holonomy and Killing spinors and have applications in high energy physics, such as supergravity and string theory. Before starting into the field, a self-contained introduction to the subject is given, aimed at students with a solid background in differential geometry. The book will therefore be accessible to masters and Ph.D. students who are beginning work on nearly Kähler geometry in pseudo-Riemannian signature, and also to non-experts interested in gaining an overview of the subject. Moreover, a number of results and techniques are provided which will be helpful for differential geometers as well as for high energy physicists interested in the mathematical background of the geometric objects they need.
Prather B.
2013-07-01
Full Text Available This paper considers the possibility of a teleparallel approximation of general relativity where the underlying space-time of a compact massive source is related to the isotropic coordinate chart rather than the geometric chart. This results in a 20 percent reduction of the expected shadow radius of compact objects. The observation of the shadow radius of Sagittarius A* should be possible in the near future using VLBI. The theoretical reduction is within the uncertainty of the expected shadow radius, however any observation less than a critical radius would indicate that gravity is not the result of space-time curvature alone. If space-time curvature does not act alone it is simpler to adopt the teleparallel view, with the tetrad ﬁeld representing the index of refraction of the required material ﬁeld in a ﬂat space-time.
Agop, M. [Department of Physics, Technical ' Gh. Asachi' University, Blvd. Mangeron, No. 64, Iasi 700029 (Romania)]. E-mail: magop@phys.tuiasi.ro; Murgulet, C. [Department of Physics, Technical ' Gh. Asachi' University, Blvd. Mangeron, No. 64, Iasi 700029 (Romania)
2007-05-15
In the topological dimension D = 4 of the scale relativity theory, the self-structuring of a coherent quantum fluid implies the Golden mean renormalization group. Then, the transfinite set of El Naschie's {epsilon} {sup ({infinity})} space-time becomes the background of a new physics (the transfinite physics)
无
2007-01-01
On the basis of our predecessors' research, we study the distribution and the space-time evolution characteristics of the seismic apparent strain field in Yunnan since the 1970's using the seismic data of Yunnan and its surrounding areas. The result shows that there is arather strong corresponding relationship between the anomaly region of seismic apparent strain and strong earthquakes. In the nine earthquakes studied, anomaly areas of seismic apparent strain had appeared before eight earthquakes, including five occurring in the anomaly region and three on the edge. Finally, the investigative result is demonstrated primarily.
Beal, Jacob; Viroli, Mirko
2015-01-01
... in terms of individual devices. This paper aims to provide a unified approach for the investigation and engineering of computations programmed with the aid of space-time abstractions, by bringing together a number of recent results...
Witek, Helvi; Gualtieri, Leonardo; Cardoso, Vitor; Herdeiro, Carlos; Nerozzi, Andrea; Sperhake, Ulrich
2010-01-01
Black objects in higher dimensional space-times have a remarkably richer structure than their four dimensional counterparts. They appear in a variety of configurations (e.g. black holes, black branes, black rings, black Saturns), and display complex stability phase diagrams. They might also play a key role in high energy physics: for energies above the fundamental Planck scale, gravity is the dominant interaction which, together with the hoop-conjecture, implies that the trans-Planckian scattering of point particles should be well described by black hole scattering. Higher dimensional scenarios with a fundamental Planck scale of the order of TeV predict, therefore, black hole production at the LHC, as well as in future colliders with yet higher energies. In this setting, accurate predictions for the production cross-section and energy loss (through gravitational radiation) in the formation of black holes in parton-parton collisions is crucial for accurate phenomenological modelling in Monte Carlo event genera...
Schrödinger, Erwin
1985-01-01
In response to repeated requests this classic book on space-time structure by Professor Erwin Schrödinger is now available in the Cambridge Science Classics series. First published in 1950, and reprinted in 1954 and 1960, this lucid and profound exposition of Einstein's 1915 theory of gravitation still provides valuable reading for students and research workers in the field.
Blum, Alexander; Lalli, Roberto; Renn, M Jürgen
2015-09-01
The history of the theory of general relativity presents unique features. After its discovery, the theory was immediately confirmed and rapidly changed established notions of space and time. The further implications of general relativity, however, remained largely unexplored until the mid 1950s, when it came into focus as a physical theory and gradually returned to the mainstream of physics. This essay presents a historiographical framework for assessing the history of general relativity by taking into account in an integrated narrative intellectual developments, epistemological problems, and technological advances; the characteristics of post-World War II and Cold War science; and newly emerging institutional settings. It argues that such a framework can help us understand this renaissance of general relativity as a result of two main factors: the recognition of the untapped potential of general relativity and an explicit effort at community building, which allowed this formerly disparate and dispersed field to benefit from the postwar changes in the scientific landscape.
Darling, D.
1980-10-01
A discussion of Einstein's General Relativity and how it can explain black holes is included. The key idea of general relativity being that gravitational forces are a direct outcome of local curvature of space-time. The more mass something has the deeper the depression or well it causes in space-time. Black holes are supermassive objects, hence their gravity well is so steep even light can't escape. The three properties associated with a black hole are mass angular momentum, and electric charge. Non-rotating, Schwarzchild, and rotating, Kerr, black holes are studied. A Kruskal-Szekeres diagram for each type is given and explained. (SC)
Soo, Chopin
2014-01-01
Covariance of space and time in General Relativity (GR) entails a number of technical and conceptual difficulties. These can be resolved by a paradigm shift from full 4-dimensional general coordinate invariance to invariance only with respect to spatial diffeomorphisms. A theory of gravity with this paradigm shift, from quantum to classical regimes, is presented; GR is contained as a special case. Appositely formulated as a master constraint, the Hamiltonian constraint now determines only dynamics; and is relieved of its dual role of generating symmetry transformations, and the consequent baggage of multi-fingered evolution with arbitrary lapse functions is absent. The Dirac algebra, with 4-dimensional diffeomorphism symmetry on-shell, is replaced by the master constraint algebra which possesses only spatial diffeomorphism gauge symmetry, both on- and off-shell. Decomposition of the spatial metric into unimodular and determinant, q, factors results in clean separation of the canonical variables. The classical...
Chapline, George
It has been shown that a nonlinear Schrödinger equation in 2+1 dimensions equipped with an SU(N) Chern-Simons gauge field can provide an exact description of certain self-dual Einstein spaces in the limit N-=∞. Ricci flat Einstein spaces can then be viewed as arising from a quantum pairing of the classical self-dual and anti-self-dual solutions. In this chapter, we will outline how this theory of empty space-time might be generalized to include matter and vacuum energy by transplanting the nonlinear Schrödinger equation used to construct Einstein spaces to the 25+1-dimensional Lorentzian Leech lattice. If the distinguished 2 spatial dimensions underlying the construction of Einstein spaces are identified with a hexagonal lattice section of the Leech lattice, the wave-function becomes an 11 × 11 matrix that can represent fermion and boson degrees of freedom (DOF) associated with 2-form and Yang-Mills gauge symmetries. The resulting theory of gravity and matter in 3+1 dimensions is not supersymmetric, which provides an entry for a vacuum energy. Indeed, in the case of a Lemaitre cosmological model, the emergent space-time will naturally have a vacuum energy on the order of the observed cosmological constant.
Exact Philosophy of Space-Time
Vucetich, Héctor
2011-01-01
Starting from Bunge's (1977) scientific ontology, we expose a materialistic relational theory of space-time, that carries out the program initiated by Leibniz, and provides a protophysical basis consistent with any rigorous formulation of General Relativity. Space-time is constructed from general concepts which are common to any consistent scientific theory and they are interpreted as emergent properties of the greatest assembly of things, namely, the world.
Field, J H
2016-01-01
Space-time intervals corresponding to different events on the worldline of any ponderable object (for example a clock) are time-like. In consequence, in the analysis of any space-time experiment involving clocks only the region for $c\\Delta t \\ge 0$ between the line $\\Delta x = 0$ and the light cone projection $c\\Delta t = \\Delta x$ of the $c\\Delta t$ versus $\\Delta x$ Minkowski plot is physically relevant. This breaks the manifest space-time symmetry of the plot. A further consequence is the unphysical nature of the `relativity of simultaneity' and `length contraction' effects of conventional special relativity theory. The only modification of space-time transformation laws in passing from Galilean to special relativity is then the replacement of universal Newtonian time by a universal (position independent) time dilation effect for moving clocks.
Weyl, Hermann
1999-01-01
Excellent introduction probes deeply into Euclidean space, Riemann's space, Einstein's general relativity, gravitational waves and energy, and laws of conservation. "A classic of physics." - British Journal for Philosophy and Science.
Space-time singularities in Weyl manifolds
Lobo, I.P. [CAPES Foundation, Ministry of Education of Brazil, Brasilia (Brazil); Sapienza Universita di Roma, Dipartimento di Fisica, Rome (Italy); Barreto, A.B.; Romero, C. [Universidade Federal da Paraiba, Departamento de Fisica, C. Postal 5008, Joao Pessoa, PB (Brazil)
2015-09-15
We extend one of the Hawking-Penrose singularity theorems in general relativity to the case of some scalar-tensor gravity theories in which the scalar field has a geometrical character and space-time has the mathematical structure of a Weyl integrable space-time. We adopt an invariant formalism, so that the extended version of the theorem does not depend on a particular frame. (orig.)
Dynamical Space-Time and Gravitational Waves
van Holten, J W
2016-01-01
According to General Relativity gravity is the result of the interaction between matter and space-time geometry. In this interaction space-time geometry itself is dynamical: it can store and transport energy and momentum in the form of gravitational waves. We give an introductory account of this phenomenon and discuss how the observation of gravitational waves may open up a fundamentally new window on the universe.
Annila, Arto
2009-01-01
The 2nd law of thermodynamics sheds light on present-day puzzles in cosmology. The universal law, as an equation of motion, describes diverse systems consuming free energy via various mechanisms to attain stationary states in their respective surroundings. Increasing rate of expansion of the Universe, galactic rotation and lensing as well as clustering of red-shifted spectral lines are found as natural consequences of the maximal energy dispersal that satisfies the conservation of energy, in the forms of kinetic, potential and dissipation. The Universe in its entirety is pictured as a giant Riemannian resonator in evolution via step-by-step spontaneous breaking of one stationary-state symmetry to another to diminish the energy density difference relative to its zero-density surroundings. The continuum equation of evolution is proven equivalent to the Navier-Stokes equation. The ubiquitous flow equation has no solution because the forces and flows are inseparable when the dissipative process has three or more ...
Hestenes, David
2015-01-01
This small book started a profound revolution in the development of mathematical physics, one which has reached many working physicists already, and which stands poised to bring about far-reaching change in the future. At its heart is the use of Clifford algebra to unify otherwise disparate mathematical languages, particularly those of spinors, quaternions, tensors and differential forms. It provides a unified approach covering all these areas and thus leads to a very efficient ‘toolkit’ for use in physical problems including quantum mechanics, classical mechanics, electromagnetism and relativity (both special and general) – only one mathematical system needs to be learned and understood, and one can use it at levels which extend right through to current research topics in each of these areas. These same techniques, in the form of the ‘Geometric Algebra’, can be applied in many areas of engineering, robotics and computer science, with no changes necessary – it is the same underlying mathematics, a...
Fermions without Vierbeins in Curved Space-Time
Weldon, H A
2001-01-01
A general formulation of spinor fields in Riemannian space-time is given without using vierbeins. The space-time dependence of the Dirac matrices required by the anticommutation relation {\\gamma_{\\mu},\\gamma_{\
Ronald E Meyers; Keith S Deacon
2015-01-01
.... The ghost imaging experiments are performed both with and without turbulence. A discussion of the physics of the space-time imaging is presented in terms of quantum nonlocal two-photon analysis to support the experimental results...
Space-time topology (II) - Causality, the fourth Stiefel-Whitney class and space-time as a boundary
Flagga, MSN; Antonsen, F
We show that stable causality is related to the vanishing of the top Stiefel - Whitney class of a space-time manifold M, and that if M is a stably causal space-time manifold, then it is the boundary of a five-dimensional space-time. We then propose a scheme for making it both a necessary and
Pair creation in noncommutative space-time
Hamil, B.; Chetouani, L.
2016-09-01
By taking two interactions, the Volkov plane wave and a constant electromagnetic field, the probability related to the process of pair creation from the vacuum is exactly and analytically determined via the Schwinger method in noncommutative space-time. For the plane wave, it is shown that the probability is simply null and for the electromagnetic wave it is found that the expression of the probability has a similar form to that obtained by Schwinger in a commutative space-time. For a certain critical value of H, the probability is simply equal to 1.
Energy Distribution in LTB Space-time
Salti, M; Salti, Mustafa; Havare, Ali
2005-01-01
Using general relativity analogs of Bergmann-Thomson, Papapetrou, Landau-Lifshitz and Einstein energy and momentum definitions, we find the energy distribution (due to matter plus fields) in the LTB Space-time. The energy distribution is found well defined and the same in all of these energy-momentum complexes.
Jing, Yindi
2014-01-01
Distributed Space-Time Coding (DSTC) is a cooperative relaying scheme that enables high reliability in wireless networks. This brief presents the basic concept of DSTC, its achievable performance, generalizations, code design, and differential use. Recent results on training design and channel estimation for DSTC and the performance of training-based DSTC are also discussed.
Geometry of Minkowski Space-Time
Catoni, Francesco; Cannata, Roberto; Catoni, Vincenzo; Zampetti, Paolo
2011-01-01
This book provides an original introduction to the geometry of Minkowski space-time. A hundred years after the space-time formulation of special relativity by Hermann Minkowski, it is shown that the kinematical consequences of special relativity are merely a manifestation of space-time geometry. The book is written with the intention of providing students (and teachers) of the first years of University courses with a tool which is easy to be applied and allows the solution of any problem of relativistic kinematics at the same time. The book treats in a rigorous way, but using a non-sophisticated mathematics, the Kinematics of Special Relativity. As an example, the famous "Twin Paradox" is completely solved for all kinds of motions. The novelty of the presentation in this book consists in the extensive use of hyperbolic numbers, the simplest extension of complex numbers, for a complete formalization of the kinematics in the Minkowski space-time. Moreover, from this formalization the understanding of gravity co...
Quantum Space-Time and Reference Frames in Gravity and Flat Space-Time
Mayburov, S
2000-01-01
The quantum space-time model which accounts material Reference Frames (RF) quantum effects considered for flat space-time and ADM canonical gravity. As was shown by Aharonov for RF - free material object its c.m. nonrelativistic motion in vacuum described by Schrodinger wave packet evolution which modify space coordinate operator of test particle in this RF and changes its Heisenberg uncertainty relations. In the relativistic case we show that Lorentz transformations between two RFs include the quantum corrections for RFs momentum uncertainty and in general can be formulated as the quantum space-time transformations. As the result for moving RF its Lorentz time boost acquires quantum fluctuations which calculated solving relativistic Heisenberg equations for the quantum clocks models. It permits to calculate RF proper time for the arbitrary RF quantum motion including quantum gravity metrics fluctuations. Space-time structure of canonical Quantum Gravity and its observables evolution for RF proper time discus...
Space-time framework of internal measurement
Matsuno, Koichiro
1998-07-01
Measurement internal to material bodies is ubiquitous. The internal observer has its own local space-time framework that enables the observer to distinguish, even to a slightest degree, those material bodies fallen into that framework. Internal measurement proceeding among the internal observers come to negotiate a construction of more encompassing local framework of space and time. The construction takes place through friction among the internal observers. Emergent phenomena are related to an occurrence of enlarging the local space-time framework through the frictional negotiation among the material participants serving as the internal observers. Unless such a negotiation is obtained, the internal observers would have to move around in the local space-time frameworks of their own that are mutually incommensurable. Enhancement of material organization as demonstrated in biological evolutionary processes manifests an inexhaustible negotiation for enlarging the local space-time framework available to the internal observers. In contrast, Newtonian space-time framework, that remains absolute and all encompassing, is an asymptote at which no further emergent phenomena could be expected. It is thus ironical to expect something to emerge within the framework of Newtonian absolute space and time. Instead of being a complex and organized configuration of interaction to appear within the global space-time framework, emergent phenomena are a consequence of negotiation among the local space-time frameworks available to internal measurement. Most indicative of the negotiation of local space-time frameworks is emergence of a conscious self grounding upon the reflexive nature of perceptions, that is, a self-consciousness in short, that certainly goes beyond the Kantian transcendental subject. Accordingly, a synthetic discourse on securing consciousness upon the ground of self-consciousness can be developed, though linguistic exposition of consciousness upon self
Ronald E. Meyers
2015-03-01
Full Text Available We report on an experimental and theoretical investigation of quantum imaging where the images are stored in both space and time. Ghost images of remote objects are produced with either one or two beams of chaotic laser light generated by a rotating ground glass and two sensors measuring the reference field and bucket field at different space-time points. We further observe that the ghost images translate depending on the time delay between the sensor measurements. The ghost imaging experiments are performed both with and without turbulence. A discussion of the physics of the space-time imaging is presented in terms of quantum nonlocal two-photon analysis to support the experimental results. The theoretical model includes certain phase factors of the rotating ground glass. These experiments demonstrated a means to investigate the time and space aspects of ghost imaging and showed that ghost imaging contains more information per measured photon than was previously recognized where multiple ghost images are stored within the same ghost imaging data sets. This suggests new pathways to explore quantum information stored not only in multi-photon coincidence information but also in time delayed multi-photon interference. The research is applicable to making enhanced space-time quantum images and videos of moving objects where the images are stored in both space and time.
Quantized Fractal Space Time and Stochastic Holism
Sidharth, B G
2000-01-01
The space time that is used in relativistic Quantum Mechanics and Quantum Field Theory is the Minkowski space time. Yet, as pointed out by several scholars this classical space time is incompatible with the Heisenberg Uncertainity Principle: We cannot go down to arbitrarily small space time intervals, let alone space time points. Infact this classical space time is at best an approximation, and this has been criticised by several scholars. We investigate, what exactly this approximation entails.
Asymptotically flat space-times: an enigma
Newman, Ezra T.
2016-07-01
We begin by emphasizing that we are dealing with standard Einstein or Einstein-Maxwell theory—absolutely no new physics has been inserted. The fresh item is that the well-known asymptotically flat solutions of the Einstein-Maxwell theory are transformed to a new coordinate system with surprising and (seemingly) inexplicable results. We begin with the standard description of (Null) asymptotically flat space-times described in conventional Bondi-coordinates. After transforming the variables (mainly the asymptotic Weyl tensor components) to a very special set of Newman-Unti (NU) coordinates, we find a series of relations totally mimicking standard Newtonian classical mechanics and Maxwell theory. The surprising and troubling aspect of these relations is that the associated motion and radiation does not take place in physical space-time. Instead these relations takes place in an unusual inherited complex four-dimensional manifold referred to as H-space that has no immediate relationship with space-time. In fact these relations appear in two such spaces, H-space and its dual space \\bar{H}.
Fine structure constant variation or space-time anisotropy?
Chang, Zhe; Li, Xin
2011-01-01
Recent observations on quasar absorption spectra supply evidences for variation of fine structure constant $\\alpha$. In this paper, we propose another interpretation of the observational data on quasar absorption spectra: a scenario with space-time inhomogeneity and anisotropy but uniform fine structure constant. Maybe the space-time is characterized by Finsler geometry instead of Riemann one. Finsler geometry admits less symmetries than Riemann geometry does. We investigate the Finslerian geodesic equations in Randers space-time (a special Finsler space-time). It is found that the cosmological redshift in this space-time is deviated from the one in general relativity. The modification term to redshift could be generally revealed as a monopole plus dipole function about space-time locations and directions. We suggest that this modification corresponds to the observed spatial monopole and Australian Dipole in quasar absorption spectra.
The theory of space, time and gravitation
Fock, V
2015-01-01
The Theory of Space, Time, and Gravitation, 2nd Revised Edition focuses on Relativity Theory and Einstein's Theory of Gravitation and correction of the misinterpretation of the Einsteinian Gravitation Theory. The book first offers information on the theory of relativity and the theory of relativity in tensor form. Discussions focus on comparison of distances and lengths in moving reference frames; comparison of time differences in moving reference frames; position of a body in space at a given instant in a fixed reference frame; and proof of the linearity of the transformation linking two iner
Shi, Shuai; Zhou, Zhi-Yuan; Li, Yan; Zhang, Wei; Shi, Bao-Sen; Guo, Guang-Can
2016-01-01
Light with phase front carrying an orbital angular momentum (OAM) is useful in many fields, such as optical tweezers, astronomy. In optical communication, light encoded information in its OAM degrees of freedom enables networks to carry significantly more information and increase their capacity significantly. However, light with OAM has a difficulty in propagating in commercial optical fibers, while light in Gaussian mode encoded with time-bin is most suitable for transmission in fiber. Therefore it is crucially important to build up a bridge for interfacing lights with OAM and time-bin. Here, we report the realization of a photonic space-time transcoder, by which light with an arbitrary OAM superposition is experimentally converted into a time-bin Gaussian pulse and vice versa in principle. Furthermore, we clearly demonstrate that the coherence is conserved very well and there is no crosstalk between orthogonal modes. Such a photonic device is simple and theoretically can be built up in a scalable architectu...
The Variational Principle for the Uniform Acceleration and Quasi-Spin in Two Dimensional Space-Time
Matsyuk, Roman Ya.
2008-02-01
The variational principle and the corresponding differential equation for geodesic circles in two dimensional (pseudo)-Riemannian space are being discovered. The relationship with the physical notion of uniformly accelerated relativistic particle is emphasized. The known form of spin-curvature interaction emerges due to the presence of second order derivatives in the expression for the Lagrange function. The variational equation itself reduces to the unique invariant variational equation of constant Frenet curvature in two dimensional (pseudo)-Euclidean geometry.
The Variational Principle for the Uniform Acceleration and Quasi-Spin in Two Dimensional Space-Time
Matsyuk, Roman Ya
2008-01-01
The variational principle and the corresponding differential equation for geodesic circles in two dimensional (pseudo)-Riemannian space are being discovered. The relationship with the physical notion of uniformly accelerated relativistic particle is emphasized. The known form of spin-curvature interaction emerges due to the presence of second order derivatives in the expression for the Lagrange function. The variational equation itself reduces to the unique invariant variational equation of constant Frenet curvature in two dimensional (pseudo)-Euclidean geometry.
The Variational Principle for the Uniform Acceleration and Quasi-Spin in Two Dimensional Space-Time
Roman Ya. Matsyuk
2008-02-01
Full Text Available The variational principle and the corresponding differential equation for geodesic circles in two dimensional (pseudo-Riemannian space are being discovered. The relationship with the physical notion of uniformly accelerated relativistic particle is emphasized. The known form of spin-curvature interaction emerges due to the presence of second order derivatives in the expression for the Lagrange function. The variational equation itself reduces to the unique invariant variational equation of constant Frenet curvature in two dimensional (pseudo-Euclidean geometry.
Electromagnetic and gravitational fields in a Schwarzschild space-time
Porrill, J.; Stewart, J.M. (Cambridge Univ. (UK). Dept. of Applied Mathematics and Theoretical Physics)
1981-05-19
The propagation of electromagnetic fields and linearized perturbations of the vacuum Einstein equations on a Schwarzchild background space-time are discussed, and relations between the asymptotic form of the fields at null infinity and the data are established. Without suitable restrictions on the data, perturbations of a Schwarzschild space-time need not be weakly asymptotically simple.
Eisenstaedt, J
2002-07-01
In this book, the author presents in an accessible language the context of the birth and evolution of the general relativity theory since the beginning of the 20. century. He details the history of the mathematical, physical and observation techniques which have led to the evolution of physics. (J.S.)
Michelle Lopes
Full Text Available This work describes the spatial-temporal variation of the relative abundance and size of Limnoperna fortunei (Dunker, 1857 collected in São Gonçalo Channel through bottom trawl with a 0.5 cm mesh, at depths between 3 and 6 m. The estimative of mean relative abundance (CPUE ranged from 2,425.3 individuals per drag (ind./drag in the spring to 21,715.0 ind./drag in the fall, with an average of 9,515.3 ind./drag throughout the year. The estimated mean density of L. fortunei for the deep region of São Gonçalo Channel ranged from 1.2 to 10.3 ind./m², and it was recorded a maximum density of 84.9 ind./m² in the fall of 2008. The method of sampling using bottom trawl enabled the capture of L. fortunei under the soft muddy bottom of the channel, in different sizes ranging from 0.4 to 3.2 cm. This shows that the structure of the L. fortunei adult population under the bottom of the São Gonçalo Channel is composed mostly of small individuals (<1.4 cm, which represent up to 74% of the population collected.
Agents in branching space-times
Nuel; Belnap
2003-01-01
The aim of this essay Is to make some brief suggestions on the beginnings of a theory of agentsand agency In branching spacetlmes.foe thought Is to combine the ideas of agency as developed agalnst the relatively simple background of branching time with the richer notions of Indetermlnlsm asstructured In the theory of branching space-times.My plan Is to say a little about agency In branchingtime and a little about branchlg spacetlmes,and then ask how the two can be brought together.Atthe end there Is an ...
Entropy of Movement Outcome in Space-Time.
Lai, Shih-Chiung; Hsieh, Tsung-Yu; Newell, Karl M
2015-07-01
Information entropy of the joint spatial and temporal (space-time) probability of discrete movement outcome was investigated in two experiments as a function of different movement strategies (space-time, space, and time instructional emphases), task goals (point-aiming and target-aiming) and movement speed-accuracy constraints. The variance of the movement spatial and temporal errors was reduced by instructional emphasis on the respective spatial or temporal dimension, but increased on the other dimension. The space-time entropy was lower in targetaiming task than the point aiming task but did not differ between instructional emphases. However, the joint probabilistic measure of spatial and temporal entropy showed that spatial error is traded for timing error in tasks with space-time criteria and that the pattern of movement error depends on the dimension of the measurement process. The unified entropy measure of movement outcome in space-time reveals a new relation for the speed-accuracy.
Hypersurface-deformation algebroids and effective space-time models
Bojowald, Martin; Buyukcam, Umut; D'Ambrosio, Fabio
2016-01-01
In canonical gravity, covariance is implemented by brackets of hypersurface-deformation generators forming a Lie algebroid. Lie algebroid morphisms therefore allow one to relate different versions of the brackets that correspond to the same space-time structure. An application to examples of modified brackets found mainly in models of loop quantum gravity can in some cases map the space-time structure back to the classical Riemannian form after a field redefinition. For one type of quantum corrections (holonomies), signature change appears to be a generic feature of effective space-time, and is shown here to be a new quantum space-time phenomenon which cannot be mapped to an equivalent classical structure. In low-curvature regimes, our constructions prove the existence of classical space-time structures assumed elsewhere in models of loop quantum cosmology, but also shows the existence of additional quantum corrections that have not always been included.
Semiletov, I. P.; Shakhova, N. E.; Pipko, I. I.; Pugach, S. P.; Charkin, A. N.; Dudarev, O. V.; Kosmach, D. A.; Nishino, S.
2013-09-01
This study aims to improve understanding of carbon cycling in the Buor-Khaya Bay (BKB) and adjacent part of the Laptev Sea by studying the inter-annual, seasonal, and meso-scale variability of carbon and related hydrological and biogeochemical parameters in the water, as well as factors controlling carbon dioxide (CO2) emission. Here we present data sets obtained on summer cruises and winter expeditions during 12 yr of investigation. Based on data analysis, we suggest that in the heterotrophic BKB area, input of terrestrially borne organic carbon (OC) varies seasonally and inter-annually and is largely determined by rates of coastal erosion and river discharge. Two different BKB sedimentation regimes were revealed: Type 1 (erosion accumulation) and Type 2 (accumulation). A Type 1 sedimentation regime occurs more often and is believed to be the quantitatively most important mechanism for suspended particular matter (SPM) and particulate organic carbon (POC) delivery to the BKB. The mean SPM concentration observed in the BKB under a Type 1 regime was one order of magnitude greater than the mean concentration of SPM (~ 20 mg L-1) observed along the Lena River stream in summer 2003. Loadings of the BKB water column with particulate material vary by more than a factor of two between the two regimes. Higher partial pressure of CO2 (pCO2), higher concentrations of nutrients, and lower levels of oxygen saturation were observed in the bottom water near the eroded coasts, implying that coastal erosion and subsequent oxidation of eroded organic matter (OM) rather than the Lena River serves as the predominant source of nutrients to the BKB. Atmospheric CO2 fluxes from the sea surface in the BKB vary from 1 to 95 mmol m-2 day-1 and are determined by specific features of hydrology and wind conditions, which change spatially, seasonally, and inter-annually. Mean values of CO2 emission from the shallow Laptev Sea were similar in September 1999 and 2005 (7.2 and 7.8 mmol m-2 day-1
Affine conformal vectors in space-time
Coley, A. A.; Tupper, B. O. J.
1992-05-01
All space-times admitting a proper affine conformal vector (ACV) are found. By using a theorem of Hall and da Costa, it is shown that such space-times either (i) admit a covariantly constant vector (timelike, spacelike, or null) and the ACV is the sum of a proper affine vector and a conformal Killing vector or (ii) the space-time is 2+2 decomposable, in which case it is shown that no ACV can exist (unless the space-time decomposes further). Furthermore, it is proved that all space-times admitting an ACV and a null covariantly constant vector (which are necessarily generalized pp-wave space-times) must have Ricci tensor of Segré type {2,(1,1)}. It follows that, among space-times admitting proper ACV, the Einstein static universe is the only perfect fluid space-time, there are no non-null Einstein-Maxwell space-times, and only the pp-wave space-times are representative of null Einstein-Maxwell solutions. Otherwise, the space-times can represent anisotropic fluids and viscous heat-conducting fluids, but only with restricted equations of state in each case.
Steps towards an axiomatic pregeometry of space-time
Bergliaffa, S E P; Vucetich, H; Bergliaffa, Santiago E. Perez; Romero, Gustavo E.; Vucetich, Hector
1998-01-01
We present a deductive theory of space-time which is realistic, objective, and relational. It is realistic because it assumes the existence of physical things endowed with concrete properties. It is objective because it can be formulated without any reference to cognoscent subjects or sensorial fields. Finally, it is relational because it assumes that space-time is not a thing but a complex of relations among things. In this way, the original program of Leibniz is consummated, in the sense that space is ultimately an order of coexistents, and time is an order of succesives. In this context, we show that the metric and topological properties of Minkowskian space-time are reduced to relational properties of concrete things. We also sketch how our theory can be extended to encompass a Riemmanian space-time.
Space-Time Geometry of Quark and Strange Quark Matter
无
2007-01-01
We study quark and strange quark matter in the context of general relativity. For this purpose, we solve Einstein's field equations for quark and strange quark matter in spherical symmetric space-times. We analyze strange quark matter for the different equations of state (EOS) in the spherical symmetric space-times, thus we are able to obtain the space-time geometries of quark and strange quark matter. Also, we discuss die features of the obtained solutions. The obtained solutions are consistent with the results of Brookhaven Laboratory, i.e. the quark-gluon plasma has a vanishing shear (i.e. quark-gluon plasma is perfect).
Hyperbolic statics in space-time
Pavlov, Dmitry
2015-01-01
Based on the concept of material event as an elementary material source that is concentrated on metric sphere of zero radius --- light-cone of Minkowski space-time, we deduce the analog of Coulomb's law for hyperbolic space-time field universally acting between the events of space-time. Collective field that enables interaction of world lines of a pair of particles at rest contains a standard 3-dimensional Coulomb's part and logarithmic addendum. We've found that the Coulomb's part depends on a fine balance between causal and geometric space-time characteristics (the two regularizations concordance).
Predictions of noncommutative space-time
Viet, Nguyen Ai
1994-01-01
An unified structure of noncommutative space-time for both gravity and particle physics is presented. This gives possibilities of testing the idea of noncommutative space-time at the currently available energy scale. There are several arguments indicating that noncommutative space-time is visible already at the electroweak scale. This noncommutative space-time predicts the top quark mass m_t \\sim 172 GeV, the Higgs mass M_H \\sim 241 GeV and the existence of a vector meson and a scalar, which ...
Generalised hyperbolicity in conical space-times
Vickers, J A
2000-01-01
Solutions of the wave equation in a space-time containing a thin cosmic string are examined in the context of non-linear generalised functions. Existence and uniqueness of solutions to the wave equation in the Colombeau algebra G is established for a conical space-time and this solution is shown to be associated to a distributional solution. A concept of generalised hyperbolicity, based on test fields, can be defined for such singular space-times and it is shown that a conical space-time is G-hyperbolic.
Measuring Space-Time Geometry over the Ages
Stebbins, Albert
2012-01-01
Theorists are often told to express things in the "observational plane". One can do this for space-time geometry, considering "visual" observations of matter in our universe by a single observer over time, with no assumptions about isometries, initial conditions, nor any particular relation between matter and geometry, such as Einstein's equations. Using observables as coordinates naturally leads to a parametrization of space-time geometry in terms of other observables, which in turn prescrib...
Fermions without vierbeins in curved space-time
Weldon, H. Arthur
2001-05-01
A general formulation of spinor fields in Riemannian space-time is given without using vierbeins. The space-time dependence of the Dirac matrices required by the anticommutation relation \\{γμ,γν\\}=2gμν determines the spin connection. The action is invariant under any local spin base transformations in the 32 parameter group Gl(4,c) and not just under local Lorentz transformations. The Dirac equation and the energy-momentum tensor are computed from the action.
Circular motion in NUT space-time
Jefremov, Paul
2016-01-01
We consider circular motion in the NUT (Newman-Unti-Tamburino) space-time. Among other things, we determine the location of circular time-like geodesic orbits, in particular of the innermost stable circular orbit (ISCO) and of the marginally bound circular orbit. Moreover, we discuss the von Zeipel cylinders with respect to the stationary observers and with respect to the Zero Angular Momentum Observers (ZAMOs). We also investigate the relation of von Zeipel cylinders to inertial forces, in particular in the ultra-relativistic limit. Finally, we generalise the construction of thick accretion tori ("Polish doughnuts") which are well known on the Schwarzschild or Kerr background to the case of the NUT metric. We argue that, in principle, a NUT source could be distinguished from a Schwarzschild or Kerr source by observing the features of circular matter flows in its neighbourhood.
Double conformal space-time algebra
Easter, Robert Benjamin; Hitzer, Eckhard
2017-01-01
The Double Conformal Space-Time Algebra (DCSTA) is a high-dimensional 12D Geometric Algebra G 4,8that extends the concepts introduced with the Double Conformal / Darboux Cyclide Geometric Algebra (DCGA) G 8,2 with entities for Darboux cyclides (incl. parabolic and Dupin cyclides, general quadrics, and ring torus) in spacetime with a new boost operator. The base algebra in which spacetime geometry is modeled is the Space-Time Algebra (STA) G 1,3. Two Conformal Space-Time subalgebras (CSTA) G 2,4 provide spacetime entities for points, flats (incl. worldlines), and hyperbolics, and a complete set of versors for their spacetime transformations that includes rotation, translation, isotropic dilation, hyperbolic rotation (boost), planar reflection, and (pseudo)spherical inversion in rounds or hyperbolics. The DCSTA G 4,8 is a doubling product of two G 2,4 CSTA subalgebras that inherits doubled CSTA entities and versors from CSTA and adds new bivector entities for (pseudo)quadrics and Darboux (pseudo)cyclides in spacetime that are also transformed by the doubled versors. The "pseudo" surface entities are spacetime hyperbolics or other surface entities using the time axis as a pseudospatial dimension. The (pseudo)cyclides are the inversions of (pseudo)quadrics in rounds or hyperbolics. An operation for the directed non-uniform scaling (anisotropic dilation) of the bivector general quadric entities is defined using the boost operator and a spatial projection. DCSTA allows general quadric surfaces to be transformed in spacetime by the same complete set of doubled CSTA versor (i.e., DCSTA versor) operations that are also valid on the doubled CSTA point entity (i.e., DCSTA point) and the other doubled CSTA entities. The new DCSTA bivector entities are formed by extracting values from the DCSTA point entity using specifically defined inner product extraction operators. Quadric surface entities can be boosted into moving surfaces with constant velocities that display the length
Pseudo-Z symmetric space-times
Mantica, Carlo Alberto, E-mail: carloalberto.mantica@libero.it [Physics Department, Università degli Studi di Milano, Via Celoria 16, 20133 Milano (Italy); Suh, Young Jin, E-mail: yjsuh@knu.ac.kr [Department of Mathematics, Kyungpook National University, Taegu 702-701 (Korea, Republic of)
2014-04-15
In this paper, we investigate Pseudo-Z symmetric space-time manifolds. First, we deal with elementary properties showing that the associated form A{sub k} is closed: in the case the Ricci tensor results to be Weyl compatible. This notion was recently introduced by one of the present authors. The consequences of the Weyl compatibility on the magnetic part of the Weyl tensor are pointed out. This determines the Petrov types of such space times. Finally, we investigate some interesting properties of (PZS){sub 4} space-time; in particular, we take into consideration perfect fluid and scalar field space-time, and interesting properties are pointed out, including the Petrov classification. In the case of scalar field space-time, it is shown that the scalar field satisfies a generalized eikonal equation. Further, it is shown that the integral curves of the gradient field are geodesics. A classical method to find a general integral is presented.
Soffel, Michael
2013-01-01
The high accuracy of modern astronomical spatial-temporal reference systems has made them considerably complex. This book offers a comprehensive overview of such systems. It begins with a discussion of ‘The Problem of Time’, including recent developments in the art of clock making (e.g., optical clocks) and various time scales. The authors address the definitions and realization of spatial coordinates by reference to remote celestial objects such as quasars. After an extensive treatment of classical equinox-based coordinates, new paradigms for setting up a celestial reference system are introduced that no longer refer to the translational and rotational motion of the Earth. The role of relativity in the definition and realization of such systems is clarified. The topics presented in this book are complemented by exercises (with solutions). The authors offer a series of files, written in Maple, a standard computer algebra system, to help readers get a feel for the various models and orders of magnitude. ...
Effect of Noncommutativity of Space-time on Zitterbewegung
Verma, Ravikant
2016-01-01
In this paper, we present the result of our investigation on the modification of Zitterbewegung due to the noncommutativity of the space-time. First, we study the effect of noncommutativity of Moyal space-time on Zitterbewegung to find that the noncommutativity of Moyal space-time does not affect the Zitterbewegung. Secondly, we see the effect of $\\kappa$-deformation of the space-time on Zitterbewegung. For this, we start with the $\\kappa$-deformed Dirac theory and using $\\kappa$-deformed Dirac equation valid upto first order in deformation parameter $a$, we find the modified Zitterbewegung due to $\\kappa$-deformation of space-time valid upto first order in the deformation parameter $a$. In the limit $a\\rightarrow 0$, we get back the commutative result. And finally, we find the modification of the Zitterbewegung due to the Magueijo-Smolin approach of doubly special relativity(DSR) and in the limit $E_p \\rightarrow \\infty$, we get back the result in the commutative space-time.
On Certain Conceptual Anomalies in Einstein's Theory of Relativity
Crothers S. J.
2008-01-01
Full Text Available There are a number of conceptual anomalies occurring in the Standard exposition of Einstein’s Theory of Relativity. These anomalies relate to issues in both mathematics and in physics and penetrate to the very heart of Einstein’s theory. This paper reveals and amplifies a few such anomalies, including the fact that Einstein’s field equations for the so-called static vacuum configuration, R = 0 , violates his Principle of Equiv- alence, and is therefore erroneous. This has a direct bearing on the usual concept of conservation of energy for the gravitational field and the conventional formulation for localisation of energy using Einstein’s pseudo-tensor. Misconceptions as to the relationship between Minkowski spacetime and Special Relativity are also discussed, along with their relationships to the pseudo-Riemannian metric manifold of Einstein’s gravitational field, and their fundamental geometric structures pertaining to spherical symmetry.
On Certain Conceptual Anomalies in Einstein's Theory of Relativity
Crothers S. J.
2008-01-01
Full Text Available There are a number of conceptual anomalies occurring in the Standard exposition of Einstein's Theory of Relativity. These anomalies relate to issues in both mathematics and in physics and penetrate to the very heart of Einstein's theory. This paper reveals and amplifies a few such anomalies, including the fact that Einstein's field equations for the so-called static vacuum configuration, $R_{mu u} = 0$, violates his Principle of Equivalence, and is therefore erroneous. This has a direct bearing on the usual concept of conservation of energy for the gravitational field and the conventional formulation for localisation of energy using Einstein's pseudo-tensor. Misconceptions as to the relationship between Minkowski spacetime and Special Relativity are also discussed, along with their relationships to the pseudo-Riemannian metric manifold of Einstein's gravitational field, and their fundamental geometric structures pertaining to spherical symmetry.
Tensors the mathematics of relativity and continuum mechanics
Das, A J
2007-01-01
Tensors: The Mathematics of Relativity Theory and Continuum Mechanics, by Anadijiban Das, emerged from courses taught over the years at the University College of Dublin, Carnegie-Mellon University and Simon Fraser University. This book will serve readers well as a modern introduction to the theories of tensor algebra and tensor analysis. Throughout Tensors, examples and worked-out problems are furnished from the theory of relativity and continuum mechanics. Topics covered in this book include, but are not limited to: -tensor algebra -differential manifold -tensor analysis -differential forms -connection forms -curvature tensors -Riemannian and pseudo-Riemannian manifolds The extensive presentation of the mathematical tools, examples and problems make the book a unique text for the pursuit of both the mathematical relativity theory and continuum mechanics.
Space Time Codes from Permutation Codes
Henkel, Oliver
2006-01-01
A new class of space time codes with high performance is presented. The code design utilizes tailor-made permutation codes, which are known to have large minimal distances as spherical codes. A geometric connection between spherical and space time codes has been used to translate them into the final space time codes. Simulations demonstrate that the performance increases with the block lengths, a result that has been conjectured already in previous work. Further, the connection to permutation codes allows for moderate complex en-/decoding algorithms.
Hawking evaporation and space-time structure
Balbinot, R.; Bergamini, R. (Consiglio Nazionale delle Ricerche, Bologna (Italy). Lab. di Radioastronomia); Giorgini, B. (Bologna Univ. (Italy). Ist. di Fisica)
1982-08-11
The Vaidya radiating metric is used to model an evaporating black-hole space-time. It is shown that, thus, a wormhole is produced in analogy with the Einstein-Rosen bridge. Its physical consequences are discussed.
Space-time crystals of trapped ions.
Li, Tongcang; Gong, Zhe-Xuan; Yin, Zhang-Qi; Quan, H T; Yin, Xiaobo; Zhang, Peng; Duan, L-M; Zhang, Xiang
2012-10-19
Spontaneous symmetry breaking can lead to the formation of time crystals, as well as spatial crystals. Here we propose a space-time crystal of trapped ions and a method to realize it experimentally by confining ions in a ring-shaped trapping potential with a static magnetic field. The ions spontaneously form a spatial ring crystal due to Coulomb repulsion. This ion crystal can rotate persistently at the lowest quantum energy state in magnetic fields with fractional fluxes. The persistent rotation of trapped ions produces the temporal order, leading to the formation of a space-time crystal. We show that these space-time crystals are robust for direct experimental observation. We also study the effects of finite temperatures on the persistent rotation. The proposed space-time crystals of trapped ions provide a new dimension for exploring many-body physics and emerging properties of matter.
Space-Time Disarray and Visual Awareness
Jan Koenderink
2012-04-01
Full Text Available Local space-time scrambling of optical data leads to violent jerks and dislocations. On masking these, visual awareness of the scene becomes cohesive, with dislocations discounted as amodally occluding foreground. Such cohesive space-time of awareness is technically illusory because ground truth is jumbled whereas awareness is coherent. Apparently the visual field is a construction rather than a (veridical perception.
Space-time as strongly bent plate
Kokarev, S S
1999-01-01
Futher development is made of a consept of space-time as multidimensional elastic plate, proposed earlier in [20,21]. General equilibrium equations, including 4-dimensional tangent stress tensor - energy-momentum tensor of matter - are derived. Comparative analysis of multidimensional elasticity theory (MET) and GR is given. Variational principle, boundary conditions, energy-momentum tensor, matter and space-time signature are reviewed within the context of MET.
Navigation in Curved Space-Time
Bahder, T B
2001-01-01
A covariant and invariant theory of navigation in curved space-time with respect to electromagnetic beacons is written in terms of J. L. Synge's two-point invariant world function. Explicit equations are given for navigation in space-time in the vicinity of the Earth in Schwarzschild coordinates and in rotating coordinates. The restricted problem of determining an observer's coordinate time when their spatial position is known is also considered.
Beyond peaceful coexistence the emergence of space, time and quantum
2016-01-01
Beyond Peaceful Coexistence: The Emergence of Space, Time and Quantum brings together leading academics in mathematics and physics to address going beyond the 'peaceful coexistence' of space-time descriptions (local and continuous ones) and quantum events (discrete and non-commutative ones). Formidable challenges waiting beyond the Standard Model require a new semantic consistency within the theories in order to build new ways of understanding, working and relating to them. The original A. Shimony meaning of the peaceful coexistence (the collapse postulate and non-locality) appear to be just the tip of the iceberg in relation to more serious fundamental issues across physics as a whole.Chapters in this book present perspectives on emergent, discrete, geometrodynamic and topological approaches, as well as a new interpretative spectrum of quantum theories after Copenhagen, discrete time theories, time-less approaches and 'super-fluid' pictures of space-time.As well as stimulating further research among establis...
STATISTICAL SPACE-TIME ADAPTIVE PROCESSING ALGORITHM
Yang Jie
2010-01-01
For the slowly changed environment-range-dependent non-homogeneity,a new statistical space-time adaptive processing algorithm is proposed,which uses the statistical methods,such as Bayes or likelihood criterion to estimate the approximative covariance matrix in the non-homogeneous condition. According to the statistical characteristics of the space-time snapshot data,via defining the aggregate snapshot data and corresponding events,the conditional probability of the space-time snapshot data which is the effective training data is given,then the weighting coefficients are obtained for the weighting method. The theory analysis indicates that the statistical methods of the Bayes and likelihood criterion for covariance matrix estimation are more reasonable than other methods that estimate the covariance matrix with the use of training data except the detected outliers. The last simulations attest that the proposed algorithms can estimate the covariance in the non-homogeneous condition exactly and have favorable characteristics.
Space-time orientations, electrodynamics, antiparticles
Tulczyjew, W M [Associated with Instituto Nazionale di Fisica Nucleare Sezione di Napoli, Italy Complesso universitario Monte Sant' Angelo Via Cintia, 80126 Naples (Italy)
2007-11-15
Two definitions of orientation in space-time are introduced. One is a standard definition found for examples presented elsewhere. The other is a new definition based on the Minkowski geometry of space-time. Parities of differential forms appearing in electrodynamics are analysed. Parities of differential forms based on the standard concept of orientation are those introduced by de Rham. Parities based on the relativistic concept of orientation are the intrinsic space-time version of parities normally assigned to electromagnetic objects in texts on electrodynamics. Such assignments are made by Jackson [5] and also by Landau and Lifshitz. We present two formulations of the dynamics of charged particles corresponding to the two assignments of parities to electromagnetic objects. One is due to Stueckelberg and Feynman. The other is an attempt to formulate a classical theory corresponding to Dirac's quantum interpretation of antiparticles following the publications listed.
Galactic space-times in modified theories of gravity
Dey, Dipanjan; Sarkar, Tapobrata
2014-01-01
We study Bertrand space-times (BSTs), which have been proposed as viable models of space-times seeded by galactic dark matter, in modified theories of gravity. We first critically examine the issue of galactic rotation curves in General Relativity, and establish the usefulness of BSTs to fit experimental data in this context. We then study BSTs in metric $f(R)$ gravity and in Brans-Dicke theories. For the former, the nature of the Newtonian potential is established, and we also compute the effective equation of state and show that it can provide good fits to some recent experimental results. For the latter, we calculate the Brans-Dicke scalar analytically in some limits and numerically in general, and find interesting constraints on the parameters of the theory. Our results provide evidence for the physical nature of Bertrand space-times in modified theories of gravity.
Alpha surfaces for complex space-times with torsion
Esposito, G
1993-01-01
This paper studies necessary conditions for the existence of alpha-surfaces in complex space-time manifolds with nonvanishing torsion. For these manifolds, Lie brackets of vector fields and spinor Ricci identities contain explicitly the effects of torsion. This leads to an integrability condition for alpha-surfaces which does not involve just the self-dual Weyl spinor, as in complex general relativity, but also the torsion spinor, in a nonlinear way, and its covariant derivative. Interestingly, a particular solution of the integrability condition is given by conformally right-flat and right-torsion-free space-times.
Energy Imparted by Gravitational Waves in Inhomogeneous Space-times
Aydogdu, O; Aydogdu, Oktay; Salti, Mustafa
2006-01-01
In this paper, considering Einstein, Bergmann-Thomson and Landau-Lifshitz's energy-momentum definitions in both general relativity and teleparallel gravity, we compute the total energy distribution (due to matter and fields including gravitation) of the universe based on generalized inhomogeneous space-times. We obtain that Einstein and Bergmann-Thomson definitions of the energy-momentum complexes give the same results, while Landau-Lifshitz's energy-momentum definition does not provide same results for these type of metric. However, it is shown that the results obtained are reduced to the energy-momentum density of the Robertson-Walker space-times already available in the literature.
Quantum field theory and the antipodal identification of space time
Domenech, G.; Levinas, M.L. (IAFE-CONICET, C.C. 67, Suc. 28, 1428, Buenos Aires (AR)); Sanchez, N. (UA 336 CNRS-DEMIRM, Observatoire de Paris, Section de Meudon, 92195 Meudon Principal Cedex (FR))
1988-01-01
The authors investigate the elliptic interpretation of space-time (identification of antipodal points or vents) in anti-deSitter and in Rindler manifolds and its consequences for QFT. They compare and give a complete description of antipodal identification in space-times with and without event horizons. Antipodal identification relates the field theories on deSitter and on anti-deSitter spaces. In the elliptic Rindler manifold, imaginary time is periodic with period {beta}/2 but the Green functions (for both identifications with and without Conical singularity) have period {beta}. Additional new properties for the Green functions are obtained and the new terms added to the stress tensor computed.
Space-Time Approximation with Sparse Grids
Griebel, M; Oeltz, D; Vassilevski, P S
2005-04-14
In this article we introduce approximation spaces for parabolic problems which are based on the tensor product construction of a multiscale basis in space and a multiscale basis in time. Proper truncation then leads to so-called space-time sparse grid spaces. For a uniform discretization of the spatial space of dimension d with O(N{sup d}) degrees of freedom, these spaces involve for d > 1 also only O(N{sup d}) degrees of freedom for the discretization of the whole space-time problem. But they provide the same approximation rate as classical space-time Finite Element spaces which need O(N{sup d+1}) degrees of freedoms. This makes these approximation spaces well suited for conventional parabolic and for time-dependent optimization problems. We analyze the approximation properties and the dimension of these sparse grid space-time spaces for general stable multiscale bases. We then restrict ourselves to an interpolatory multiscale basis, i.e. a hierarchical basis. Here, to be able to handle also complicated spatial domains {Omega}, we construct the hierarchical basis from a given spatial Finite Element basis as follows: First we determine coarse grid points recursively over the levels by the coarsening step of the algebraic multigrid method. Then, we derive interpolatory prolongation operators between the respective coarse and fine grid points by a least squares approach. This way we obtain an algebraic hierarchical basis for the spatial domain which we then use in our space-time sparse grid approach. We give numerical results on the convergence rate of the interpolation error of these spaces for various space-time problems with two spatial dimensions. Also implementational issues, data structures and questions of adaptivity are addressed to some extent.
String theory in curved space-time
Viswanathan, K S
1997-01-01
Intrinsic and extrinsic geometric properties of string world sheets in curved space-time background are explored. In our formulation, the only dynamical degrees of freedom of the string are its immersion coordinates. Classical equation of motion and the space-time energy-momentum tensor of the string are obtained. The equations of motion for the extrinsic curvature action are second order for the scalar mean curvature of the world sheet. 1-loop divergent terms are calculated using the background field method. Asymptotic freedom of the extrinsic curvature coupling is established.
Space-time duality and superduality
Burgess, C P; Kamela, M; Knutt-Wehlau, M E; Page, P; Quevedo, Fernando; Zebarjad, M
1999-01-01
We introduce a new class of duality symmetries amongst quantum field theories. The new class is based upon global space-time symmetries, such as Poincare invariance and supersymmetry, in the same way as the existing duality transformations are based on global internal symmetries. We illustrate these new duality transformations by dualizing several scalar and spin-half field theories in 1 + 1 space-time dimensions, involving non-supersymmetric as well as (1, 1) and (2, 2) supersymmetric models. For (2, 2) models the new duality transformations can interchange chiral and twisted chiral multiplets.
Astrophysics of Bertrand Space-times
Dey, Dipanjan; Sarkar, Tapobrata
2013-01-01
We construct a model for galactic dark matter that arises as a solution of Einstein gravity, and is a Bertrand space-time matched with an external Schwarzschild metric. This model can explain galactic rotation curves. Further, we study gravitational lensing in these space-times, and in particular we consider Einstein rings, using the strong lensing formalism of Virbhadra and Ellis. Our results are in good agreement with observational data, and indicate that under certain conditions, gravitational lensing effects from galactic dark matter may be similar to that from Schwarzschild backgrounds.
Dirac theory in space-time without torsion
Hannibal, L
1994-01-01
It is proven that the usual quadratic general-covariant Lagrangian for the Dirac field leads to a symmetric, divergence-free energy-momentum tensor in the standard Riemannian framework of space-time without torsion, provided the tetrad field components are the only quantities related to gravitation that are varied independently.
Parabosonic string and space-time non-commutativity
Seridi, M. A.; Belaloui, N. [Laboratoire de Physique Mathematique et Subatomique, Universite Mentouri Constantine (Algeria)
2012-06-27
We investigate the para-quantum extension of the bosonic strings in a non-commutative space-time. We calculate the trilinear relations between the mass-center variables and the modes and we derive the Virasoro algebra where a new anomaly term due to the non-commutativity is obtained.
Proper Time in Weyl space-time
Avalos, R; Romero, C
2016-01-01
We discuss the question of whether or not a general Weyl structure is a suitable mathematical model of space-time. This is an issue that has been in debate since Weyl formulated his unified field theory for the first time. We do not present the discussion from the point of view of a particular unification theory, but instead from a more general standpoint, in which the viability of such a structure as a model of space-time is investigated. Our starting point is the well known axiomatic approach to space-time given by Elhers, Pirani and Schild (EPS). In this framework, we carry out an exhaustive analysis of what is required for a consistent definition for proper time and show that such a definition leads to the prediction of the so-called "second clock effect". We take the view that if, based on experience, we were to reject space-time models predicting this effect, this could be incorporated as the last axiom in the EPS approach. Finally, we provide a proof that, in this case, we are led to a Weyl integrable ...
Wave Equations in Bianchi Space-Times
S. Jamal
2012-01-01
Full Text Available We investigate the wave equation in Bianchi type III space-time. We construct a Lagrangian of the model, calculate and classify the Noether symmetry generators, and construct corresponding conserved forms. A reduction of the underlying equations is performed to obtain invariant solutions.
Space-Time radar waveforms: circulating codes
Babur, G.; Aubry, P.; Le Chevalier, F.
2013-01-01
This paper describes a concept of the circulating codes covering the whole class of the space-time codes. The circulating codes do not narrow the radiated pattern of the antenna array, thus providing a wide angular coverage, possibly tunable. In turn, the beam-forming on transmit is achievable by me
Optics in the Schwarzschild space-time
Cadez, A; Cadez, Andrej; Kostic, Uros
2004-01-01
Light coming from the strong gravity region in the vicinity of a black hole is marked by large Doppler shifts, redshifts and aberration effects. In order to understand these effects it is useful to solve the light propagation problem between any two given points in the curved space of a black hole. Here we describe the complete solution for the Schwarzschild space-time.
SPACE-TIME ESTIMATE TO HEAT EQUATION
2007-01-01
In this article, we prove the Strichartz type estimate for the solutions of linear heat equation with initial data in Hardy space H1(Rd). As an application, we obtain the full space-time estimate to the solutions of heat equation with initial data in LP(Rd) for 1＜p＜∞.
Eigenvalues of Killing Tensors and Separable Webs on Riemannian and Pseudo-Riemannian Manifolds
Giovanni Rastelli
2007-02-01
Full Text Available Given a $n$-dimensional Riemannian manifold of arbitrary signature, we illustrate an algebraic method for constructing the coordinate webs separating the geodesic Hamilton-Jacobi equation by means of the eigenvalues of $m leq n$ Killing two-tensors. Moreover, from the analysis of the eigenvalues, information about the possible symmetries of the web foliations arises. Three cases are examined: the orthogonal separation, the general separation, including non-orthogonal and isotropic coordinates, and the conformal separation, where Killing tensors are replaced by conformal Killing tensors. The method is illustrated by several examples and an application to the L-systems is provided.
Non-coherent space-time code based on full diversity space-time block coding
无
2008-01-01
A non-unitary non-coherent space-time code which is capable of achieving full algebraic diversity is proposed based on full diversity space-time block coding. The error performance is optimized by transforming the non-unitary space-time code into unitary space-time code. By exploiting the desired structure of the proposed code, a grouped generalized likelihood ratio test decoding algorithm is presented to overcome the high complexity of the optimal algorithm. Simulation results show that the proposed code possesses high spectrum efficiency in contrast to the unitary space-time code despite slight loss in the SNR, and besides, the proposed grouped decoding algorithm provides good tradeoff between performance and complexity.
Classical Space-Times from the S Matrix
Neill, Duff
2013-01-01
We show that classical space-times can be derived directly from the S-matrix for a theory of massive particles coupled to a massless spin two particle. As an explicit example we derive the Schwarzchild space-time as a series in $G_N$. At no point of the derivation is any use made of the Einstein-Hilbert action or the Einstein equations. The intermediate steps involve only on-shell S-matrix elements which are generated via BCFW recursion relations and unitarity sewing techniques. The notion of a space-time metric is only introduced at the end of the calculation where it is extracted by matching the potential determined by the S-matrix to the geodesic motion of a test particle. Other static space-times such as Kerr follow in a similar manner. Furthermore, given that the procedure is action independent and depends only upon the choice of the representation of the little group, solutions to Yang-Mills (YM) theory can be generated in the same fashion. Moreover, the squaring relation between the YM and gravity thre...
Synthetic Differential Geometry A Way to Intuitionistic Models of General Relativity in Toposes
Grinkevich, Y B
1996-01-01
W.Lawvere suggested a approach to differential geometry and to others mathematical disciplines closed to physics, which allows to give definitions of derivatives, tangent vectors and tangent bundles without passages to the limits. This approach is based on a idea of consideration of all settings not in sets but in some cartesian closed category E, particular in some elementary topos. The synthetic differential geometry (SDG) is the theory developed by A.Kock in a context of Lawvere's ideas. In a base of the theory is an assumption of that a geometric line is not a filed of real numbers, but a some nondegenerate commutative ring R of a line type in E. In this work we shall show that SDG allows to develop a Riemannian geometry and write the Einstein's equations of a field on pseudo-Riemannian formal manifold. This give a way for constructing a intuitionistic models of general relativity in suitable toposes.
Differential Space-Time Coded Modulation
CHENZhonglin; ZHUGuangxi
2004-01-01
Relying on amicable orthogonal design, we develop for multiple-antenna systems a General differential space-time block code (GDSTBC), which imposes no restrictions on underlying signal constellation compared with the existing differential space-time designs. This generalization potentially allows the spectral efficiency to be increased by carrying information not only on phases but also on amplitudes. We then derive a Noncoherent decoder (NCD) for fiat Rayleigh fading channels. We show that NCD may recover data symbols with full antenna diversity and linear complexity at high signal-to-noise ratio. Particularly, while three kinds of conventional signal constellations are used in GDSTBC, we derive the simplified versions of NCDs which can effectively reduce the cost of implementation.
Space-Time Crystals of Trapped Ions
2012-10-15
Space-Time Crystals of Trapped Ions Tongcang Li,1 Zhe-Xuan Gong ,2,3 Zhang- Qi Yin,3,4 H. T. Quan,5 Xiaobo Yin,1 Peng Zhang,1 L.-M. Duan,2,3 and Xiang...Z.-X. Gong , G.-D. Lin, and L.-M. Duan, Phys. Rev. Lett. 105, 265703 (2010). [12] K. Kim, M.-S. Chang, S. Korenblit, R. Islam, E. E. Edwards, J. K
Brane Space-Time and Cosmology
Naboulsi, R
2003-01-01
I reconsider the cosmology of a 3-brane universe imbedded in a five-dimensional anti-de Sitter space AdS5 with a cosmological constant and show that the resulting Friedmann equations for this system are identical to those standard obtained in 4D FRW space-time in the presence of an additional density, playing two roles: the tension of the brane and the gravitino density We discuss some important concequences on hot big bang cosmology.
Mass Formulae for Broken Supersymmetry in Curved Space-Time
Ferrara, Sergio
2016-01-01
We derive the mass formulae for ${\\cal N}=1$, $D=4$ matter-coupled Supergravity for broken (and unbroken) Supersymmetry in curved space-time. These formulae are applicable to de Sitter configurations as is the case for inflation. For unbroken Supersymmetry in anti-de Sitter (AdS) one gets the mass relations modified by the AdS curvature. We compute the mass relations both for the potential and its derivative non-vanishing.
Dual constellations space-time modulation
ZOU Li; ZHAO Yuping; WANG Bing; LIANG Qinglin; XIANG Haige
2005-01-01
Next generation communication systems will be expected to operate under environment with high-speed motion and increasing number of antennas where it will be difficult or even impractical to estimate the real-time channel coefficients. For this reason,the DSTM (differential space time modulation) and USTM (unitary space time modulation) approaches that do not require the channel estimation became hot topics in recent years.In this paper, we propose a general approach to designing high spectral-efficiency signaling schemes. A novel modulation, dual constellations space-time modulation (DCSTM), is derived by extending DSTM and USTM theoretically. DCSTM preserves the good features of USTM such as low error rate and the capability of being demodulated without channel estimation. At the same time, it enhances the spectral efficiency and reduces the complexity of the modulation/demodulation. It can be adapted to different data rates and thus has a wider applicable area. Simulation results verify the theoretical analysis and the design of the new modulation method.
Geometry of almost-product Lorentzian manifolds and relativistic observer
Borowiec, Andrzej
2013-01-01
The notion of relativistic observer is confronted with Naveira's classification of (pseudo-)Riemannian almost-product structures on space-time manifolds. Some physical properties and their geometrical counterparts are shortly discussed.
Quantum singularities in static and conformally static space-times
Konkowski, D A; 10.1142/S0217751X11054334
2011-01-01
The definition of quantum singularity is extended from static space-times to conformally static space-times. After the usual definitions of classical and quantum singularities are reviewed, examples of quantum singularities in static space-times are given. These include asymptotically power-law space-times, space-times with diverging higher-order differential invariants, and a space-time with a 2-sphere singularity. The theory behind quantum singularities in conformally static space-times is followed by an example, a Friedmann-Robertson-Walker space-time with cosmic string. The paper concludes by discussing areas of future research.
Lifshitz Space-Times for Schroedinger Holography
Hartong, Jelle; Obers, Niels A
2014-01-01
We show that asymptotically locally Lifshitz space-times are holographically dual to field theories that exhibit Schroedinger invariance. This involves a complete identification of the sources, which describe torsional Newton-Cartan geometry on the boundary and transform under the Schroedinger algebra. We furthermore identify the dual vevs from which we define and construct the boundary energy-momentum tensor and mass current and show that these obey Ward identities that are organized by the Schroedinger algebra. We also point out that even though the energy flux has scaling dimension larger than z+2, it can be expressed in terms of computable vev/source pairs.
Smarandache Curves in Minkowski Space-time
Turgut, Melih; Yilmaz, Suha
2008-01-01
A regular curve in Minkowski space-time, whose position vector is composed by Frenet frame vectors on another regular curve, is called a Smarandache Curve. In this paper, we define a special case of such curves and call it Smarandache TB2 Curves in the space E41. Moreover, we compute formulas of its Frenet apparatus according to base curve via the method expressed in [3]. By this way, we obtain an another orthonormal frame of E41.
Noncommutative Space-time from Quantized Twistors
Lukierski, Jerzy
2013-01-01
We consider the relativistic phase space coordinates (x_{\\mu},p_{\\mu}) as composite, described by functions of the primary pair of twistor coordinates. It appears that if twistor coordinates are canonicaly quantized the composite space-time coordinates are becoming noncommutative. We obtain deformed Heisenberg algebra which in order to be closed should be enlarged by the Pauli-Lubanski four-vector components. We further comment on star-product quantization of derived algebraic structures which permit to introduce spin-extended deformed Heisenberg algebra.
Corrected Hawking Temperature in Snyder's Quantized Space-time
Ma, Meng-Sen; Liu, Fang; Zhao, Ren
2015-06-01
In the quantized space-time of Snyder, generalized uncertainty relation and commutativity are both included. In this paper we analyze the possible form for the corrected Hawking temperature and derive it from the both effects. It is shown that the corrected Hawking temperature has a form similar to the one of noncommutative geometry inspired Schwarzschild black hole, however with an requirement for the noncommutative parameter 𝜃 and the minimal length a.
Causality in noncommutative two-sheeted space-times
Franco, Nicolas; Eckstein, Michał
2015-10-01
We investigate the causal structure of two-sheeted space-times using the tools of Lorentzian spectral triples. We show that the noncommutative geometry of these spaces allows for causal relations between the two sheets. The computation is given in detail when the sheet is a 2- or 4-dimensional globally hyperbolic spin manifold. The conclusions are then generalised to a point-dependent distance between the two sheets resulting from the fluctuations of the Dirac operator.
Causality in noncommutative two-sheeted space-times
Franco, Nicolas
2015-01-01
We investigate the causal structure of two-sheeted space-times using the tools of Lorentzian spectral triples. We show that the noncommutative geometry of these spaces allows for causal relations between the two sheets. The computation is given in details when the sheet is a 2- or 4-dimensional globally hyperbolic spin manifold. The conclusions are then generalised to a point-dependent distance between the two sheets resulting from the fluctuations of the Dirac operator.
Monopoles in Space-Time Noncommutative Born-Infeld theory
Aschieri, Paolo
2001-01-01
We transform static solutions of space-noncommutative Dirac-Born-Infeld theory (DBI) into static solutions of space-time noncommutative DBI. Via Seiberg-Witten map we match this symmetry transformation with a corresponding symmetry of commutative DBI. This allows to: 1) study new BPS type magnetic monopoles, with constant electric and magnetic background and describe them both in the commutative and in the noncommutative setting; 2) relate by S-duality space-noncommutative magnetic monopoles ...
Causality in noncommutative space-time
Neves, M.J.; Abreu, E.M.C. [Universidade Federal Rural do Rio de Janeiro (UFRRJ), Seropedica, RJ (Brazil)
2011-07-01
Full text: Space-time noncommutativity has been investigated in the last years as a real possibility to describe physics at fundamental scale. This subject is associated with many tough issues in physics, i.e., strings, gravity, noncommutative field theories and others. The first formulation for a noncommutative spacetime was proposed by Snyder in 1947, where the object of noncommutativity is considered as a constant matrix that breaks the Lorentz symmetry. His objective was to get rid of the infinities that intoxicate quantum field theory. Unfortunately it was demonstrated not a success. Here we consider an alternative recent formulation known as Doplicher-Fredenhagen-Roberts-Amorim (DFRA) algebra in which the object of noncommutativity is treated as an ordinary coordinate by constructing an extended space-time with 4 + 6 dimensions (x + {phi}) - spacetime. In this way, the Lorentz symmetry is preserved in DFRA algebra. A quantum field theory is constructed in accordance with DFRA Poincare algebra, as well as a Lagrangian density formulation. By means of the Klein-Gordon equation in this (x + {phi}) - spacetime. We analyze the aspects of causality by studying the advanced and retarded Green functions. (author)
Relativistic tidal effects in non standard Kerr space-time
Maselli, Andrea; Laguna, Pablo
2016-01-01
Astrophysical phenomena involving massive black holes (BHs) in close binaries are expected to leave detectable signatures in the electromagnetic and gravitational-wave spectrum. Such imprints may provide precious information to probe the space-time around rotating BHs, and to reveal new insights on the nature of gravity in the strong-field regime. To support this observational window it is crucial to develop suitable tests to verify the predictions of General Relativity (GR). In this framework, the metric recently proposed by Johannsen and Psaltis parametrises strong field deviations from a Kerr space-time in a theory-independent way. In the following, we make use of this approach to describe the tidal field produced by spinning BHs. We compute the gravito-magnetic and gravito-electric tidal tensors for particles moving on equatorial circular geodesics, comparing our results with those obtained in the standard GR scenario. Our calculations show significant differences even for distances far form the last stab...
Composite quarks and leptons in higher space-time dimensions
Chaichian, Masud; Kobakhidze, A B
2002-01-01
A new approach towards the composite structure of quarks and leptons in the context of the higher dimensional unified theories is proposed. Owing to the certain strong dynamics, much like an ordinary QCD, every possible vectorlike set of composites appears in higher dimensional bulk space-time, however, through a proper Sherk-Schwarz compactification only chiral multiplets of composite quarks and leptons survive as the massless states in four dimensions. In this scenario restrictions related with the 't Hooft's anomaly matching condition are turned out to be avoided and, as a result, the composite models look rather simple and economic. We demonstrate our approach by an explicit construction of model of preons and their composites unified in the supersymmetric SU(5) GUT in five space-time dimensions. The model predicts exactly three families of the composite quarks and leptons being the triplets of the chiral horizontal symmetry SU(3)_h which automatically appears in the composite spectrum when going to ordin...
Pre-Big Bang, space-time structure, asymptotic Universe
Gonzalez-Mestres Luis
2014-04-01
Full Text Available Planck and other recent data in Cosmology and Particle Physics can open the way to controversial analyses concerning the early Universe and its possible ultimate origin. Alternatives to standard cosmology include pre-Big Bang approaches, new space-time geometries and new ultimate constituents of matter. Basic issues related to a possible new cosmology along these lines clearly deserve further exploration. The Planck collaboration reports an age of the Universe t close to 13.8 Gyr and a present ratio H between relative speeds and distances at cosmic scale around 67.3 km/s/Mpc. The product of these two measured quantities is then slightly below 1 (about 0.95, while it can be exactly 1 in the absence of matter and cosmological constant in patterns based on the spinorial space-time we have considered in previous papers. In this description of space-time we first suggested in 1996-97, the cosmic time t is given by the modulus of a SU(2 spinor and the Lundmark-Lemaître-Hubble (LLH expansion law turns out to be of purely geometric origin previous to any introduction of standard matter and relativity. Such a fundamental geometry, inspired by the role of half-integer spin in Particle Physics, may reflect an equilibrium between the dynamics of the ultimate constituents of matter and the deep structure of space and time. Taking into account the observed cosmic acceleration, the present situation suggests that the value of 1 can be a natural asymptotic limit for the product H t in the long-term evolution of our Universe up to possible small corrections. In the presence of a spinorial space-time geometry, no ad hoc combination of dark matter and dark energy would in any case be needed to get an acceptable value of H and an evolution of the Universe compatible with observation. The use of a spinorial space-time naturally leads to unconventional properties for the space curvature term in Friedmann-like equations. It therefore suggests a major modification of
Dirac equation on coordinate dependent noncommutative space-time
Kupriyanov, V G
2014-01-01
We consider the consistent deformation of the relativistic quantum mechanics introducing the noncommutativity of the space-time and preserving the Lorentz symmetry. The relativistic wave equation describing the spinning particle on coordinate dependent noncommutative space-time (noncommutative Dirac equation) is proposed. The fundamental properties of this equation, like the Lorentz covariance and the continuity equation for the probability density are verified. To this end using the properties of the star product we derive the corresponding probability current density and prove its conservation. The energy-momentum tensor for the free noncommutative spinor field is calculated. We solve the free noncommutative Dirac equation and show that the standard energy-momentum dispersion relation remains valid in the noncommutative case.
k-Inflation in noncommutative space-time
Feng, Chao-Jun; Li, Xin-Zhou; Liu, Dao-Jun
2015-02-01
The power spectra of the scalar and tensor perturbations in the noncommutative k-inflation model are calculated in this paper. In this model, all the modes created when the stringy space-time uncertainty relation is satisfied, and they are generated inside the sound/Hubble horizon during inflation for the scalar/tensor perturbations. It turns out that a linear term describing the noncommutative space-time effect contributes to the power spectra of the scalar and tensor perturbations. Confronting the general noncommutative k-inflation model with latest results from Planck and BICEP2, and taking and as free parameters, we find that it is well consistent with observations. However, for the two specific models, i.e. the tachyon and DBI inflation models, it is found that the DBI model is not favored, while the tachyon model lies inside the contour, when the e-folding number is assumed to be around.
Quantization on Space-Time Hyperboloids
Biernat, Elmar P
2011-01-01
We quantize a relativistic massive complex spin-0 field and a relativistic massive spin-1/2 field on a space-time hyperboloid. We call this procedure point-form canonical quantization. Lorentz invariance of the hyperboloid implies that the 4 generators for translations become dynamic and interaction dependent, whereas the 6 generators for Lorentz transformations remain kinematic and interaction free. We expand the fields in terms of usual plane waves and prove the equivalence to equal-time quantization by representing the Poincare generators in a momentum basis. We formulate a generalized scattering theory for interacting fields by considering evolution of the system generated by the interaction dependent four-momentum operator. Finally we expand our generalized scattering operator in powers of the interaction and show its equivalence to the Dyson expansion of usual time-ordered perturbation theory.
Space-time curvature and cosmology
Nurgaliev, I. S.; Ponomarev, V. N.
1982-10-01
The possibility is considered of obtaining a steady-state cosmological solution in the framework of the Einstein-Cartan theory. It is found that the Einstein-Cartan equations without the cosmological constant admit a solution in the form of the static de Sitter metric for a specific value of the spin-spin gravitational interaction constant, whose introduction is required by gauge theory. It is shown that the steady-state solution might serve as a model for the pre-Friedmann stage of the expansion of the universe, when the spin-curvature interaction was comparable to the interaction between space-time curvature and energy-momentum. A value of about 10 to the -20th is obtained for the spin-spin interaction constant in the case where the de Sitter stage occurs at quantum densities (10 to the 94th g/cu cm).
MMSE Optimal Algebraic Space-Time Codes
Rajan, G Susinder
2007-01-01
Design of Space-Time Block Codes (STBCs) for Maximum Likelihood (ML) reception has been predominantly the main focus of researchers. However, the ML decoding complexity of STBCs becomes prohibitive large as the number of transmit and receive antennas increase. Hence it is natural to resort to a suboptimal reception technique like linear Minimum Mean Squared Error (MMSE) receiver. Barbarossa et al and Liu et al have independently derived necessary and sufficient conditions for a full rate linear STBC to be MMSE optimal, i.e achieve least Symbol Error Rate (SER). Motivated by this problem, certain existing high rate STBC constructions from crossed product algebras are identified to be MMSE optimal. Also, it is shown that a certain class of codes from cyclic division algebras which are special cases of crossed product algebras are MMSE optimal. Hence, these STBCs achieve least SER when MMSE reception is employed and are fully diverse when ML reception is employed.
Experimental Constraints of the Exotic Shearing of Space-Time
Richardson, Jonathan William [Univ. of Chicago, IL (United States)
2016-08-01
The Holometer program is a search for rst experimental evidence that space-time has quantum structure. The detector consists of a pair of co-located 40-m power-recycled interferometers whose outputs are read out synchronously at 50 MHz, achieving sensitivity to spatiallycorrelated uctuations in dierential position on time scales shorter than the light-crossing time of the instruments. Unlike gravitational wave interferometers, which time-resolve transient geometrical disturbances in the spatial background, the Holometer is searching for a universal, stationary quantization noise of the background itself. This dissertation presents the nal results of the Holometer Phase I search, an experiment congured for sensitivity to exotic coherent shearing uctuations of space-time. Measurements of high-frequency cross-spectra of the interferometer signals obtain sensitivity to spatially-correlated eects far exceeding any previous measurement, in a broad frequency band extending to 7.6 MHz, twice the inverse light-crossing time of the apparatus. This measurement is the statistical aggregation of 2.1 petabytes of 2-byte dierential position measurements obtained over a month-long exposure time. At 3 signicance, it places an upper limit on the coherence scale of spatial shear two orders of magnitude below the Planck length. The result demonstrates the viability of this novel spatially-correlated interferometric detection technique to reach unprecedented sensitivity to coherent deviations of space-time from classicality, opening the door for direct experimental tests of theories of relational quantum gravity.
Smart Travel Based on Space-Time Behavior Study
Chai; Yanwei; Shen; Yue; Ta; Na; Qian; Fang
2015-01-01
In view of the significant demands and development trends of urbanization during the 12 th Five-Year Plan period, "smart city" has attracted wide attention as an advanced city development concept in China. Under the circumstance of rapid urbanization, traffic congestion and accessibility defi ciency become major challenges to many Chinese cities, as transportation and travel are closely related to the effi ciency of a city’s operation and the quality of people’s life. As essential part of smart city planning and management, smart travel offers an effective behavior planning countermeasure to reduce the amount of urban traffi c and optimize the space-time distribution of travels and provides an effective technology to enrich the theories and methodologies of urban and transportation planning. Orienting at the practical demand of citizens and focusing on their travel behavior, this paper carries out a discussion on the smart travel framework based on space-time behavior study and analyzes smart travel planning and its policy route from multiple perspectives, including a prediction on travel demand, transportation planning, public policy-making, and urban planning. What’s more, the paper suggests travel services for citizens based on space-time behavior analysis, such as providing personalized information, smart decision-making support, and individual behavior planning.
Experimental Constraints of the Exotic Shearing of Space-Time
Richardson, Jonathan William [Chicago U.
2016-01-01
The Holometer program is a search for rst experimental evidence that space-time has quantum structure. The detector consists of a pair of co-located 40-m power-recycled interferometers whose outputs are read out synchronously at 50 MHz, achieving sensitivity to spatiallycorrelated uctuations in dierential position on time scales shorter than the light-crossing time of the instruments. Unlike gravitational wave interferometers, which time-resolve transient geometrical disturbances in the spatial background, the Holometer is searching for a universal, stationary quantization noise of the background itself. This dissertation presents the nal results of the Holometer Phase I search, an experiment congured for sensitivity to exotic coherent shearing uctuations of space-time. Measurements of high-frequency cross-spectra of the interferometer signals obtain sensitivity to spatially-correlated eects far exceeding any previous measurement, in a broad frequency band extending to 7.6 MHz, twice the inverse light-crossing time of the apparatus. This measurement is the statistical aggregation of 2.1 petabytes of 2-byte dierential position measurements obtained over a month-long exposure time. At 3 signicance, it places an upper limit on the coherence scale of spatial shear two orders of magnitude below the Planck length. The result demonstrates the viability of this novel spatially-correlated interferometric detection technique to reach unprecedented sensitivity to coherent deviations of space-time from classicality, opening the door for direct experimental tests of theories of relational quantum gravity.
Relativistic Positioning System in Perturbed Space-time
Kostić, Uroš; Gomboc, Andreja
2015-01-01
We present a variant of a Global Navigation Satellite System called a Relativistic Positioning System (RPS), which is based on emission coordinates. We modelled the RPS dynamics in a space-time around Earth, described by a perturbed Schwarzschild metric, where we included the perturbations due to Earth multipoles (up to the 6th), the Moon, the Sun, Venus, Jupiter, solid tide, ocean tide, and Kerr rotation effect. The exchange of signals between the satellites and a user was calculated using a ray-tracing method in the Schwarzschild space-time. We find that positioning in a perturbed space-time is feasible and is highly accurate already with standard numerical procedures: the positioning algorithms used to transform between the emission and the Schwarzschild coordinates of the user are very accurate and time efficient -- on a laptop it takes 0.04 s to determine the user's spatial and time coordinates with a relative accuracy of $10^{-28}-10^{-26}$ and $10^{-32}-10^{-30}$, respectively.
Energy in the Kantowski–Sachs space-time using teleparallel geometry
Anuradha Das Purkayastha
2013-04-01
The purpose of this paper is to examine the energy content of the inflationary Universe described by Kantowski–Sachs space-time in quasilocal approach of teleparallel gravity and in the Hamiltonian structure of the teleparallel equivalent of general relativity. The teleparallel versions of field equations are also derived in such a space-time.
Spin 1 fields in Riemann-Cartan space-times "via" Duffin-Kemmer-Petiau theory
Casana, R; Lunardi, J T; Teixeira, R G
2002-01-01
We consider massive spin 1 fields, in Riemann-Cartan space-times, described by Duffin-Kemmer-Petiau theory. We show that this approach induces a coupling between the spin 1 field and the space-time torsion which breaks the usual equivalence with the Proca theory, but that such equivalence is preserved in the context of the Teleparallel Equivalent of General Relativity.
Different Approaches for the Einstein Energy Associated with the de Sitter C-Space-time
Salti, M
2005-01-01
The paper is purposed to elaborate the problem of gravitational energy localization in de Sitter(dS) C-space-time (the C space-time in a background with a cosmological constant $\\Lambda$). In this connection, using the energy-momentum definition of Einstein, we find the same energy in both general relativity and tele-parallel gravity.
Rigid covariance as a natural extension of Painlev\\'e--Gullstrand space-times: gravitational waves
Jaén, Xavier
2016-01-01
The group of rigid motions is considered to guide the search for a natural system of space-time coordinates in General Relativity. This search leads us to a natural extension of the space-times that support Painlev\\'{e}--Gullstrand synchronization. As an interesting example, here we describe a system of rigid coordinates for the cross mode of gravitational linear plane waves.
Mass formulae for broken supersymmetry in curved space-time
Ferrara, Sergio [Theoretical Physics Department, CERN, Geneva (Switzerland); INFN - Laboratori Nazionali di Frascati, Frascati (Italy); Department of Physics and Astronomy, U.C.L.A, Los Angeles, CA (United States); Proeyen, Antoine van [KU Leuven, Institute for Theoretical Physics, Leuven (Belgium)
2016-11-15
We derive the mass formulae for N = 1, D = 4 matter-coupled Supergravity for broken (and unbroken) Supersymmetry in curved space-time. These formulae are applicable to De Sitter configurations as is the case for inflation. For unbroken Supersymmetry in anti-de Sitter (AdS) one gets the mass relations modified by the AdS curvature. We compute the mass relations both for the potential and its derivative non-vanishing. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Belachsen, Idit; Marra, Francesco; Peleg, Nadav; Morin, Efrat
2017-04-01
Space-time patterns of rainfall are important climatic characteristics that influence runoff generation and flash flood magnitude. Their derivation requires high-resolution measurements to adequately represent the rainfall distribution, and is best provided by remote sensing tools. This need is further emphasized in dry climate regions, where rainfall is scarce and, often, local and highly variable. Our research is focused on understanding the nature of rainfall events in the dry Dead Sea region (Eastern Mediterranean) by identifying and characterizing the spatial structure and the dynamics of convective storm cores (known as rain cells). To do so, we take advantage of 25 years of corrected and gauge-adjusted weather radar data. A statistical analysis of convective rain-cells spatial and temporal characteristics was performed with respect to synoptic pattern, geographical location, and flash flood generation. Rain cells were extracted from radar data using a cell segmentation method and a tracking algorithm and were divided into rain events. A total of 10,500 rain cells, 2650 cell tracks and 424 rain events were elicited. Rain cell properties, such as mean areal and maximal rain intensity, area, life span, direction and speed, were derived. Rain events were clustered, according to several ERA-Interim atmospheric parameters, and associated with three main synoptic patterns: Cyprus Low, Low to the East of the study region and Active Red Sea Trough. The first two originate from the Mediterranean Sea, while the third is an extension of the African monsoon. On average, the convective rain cells in the region are 90 km2 in size, moving from West to East in 13 ms-1 and living 18 minutes. Several significant differences between rain cells of the various synoptic types were observed. In particular, Active Red Sea Trough rain cells are characterized by higher rain intensities and lower speeds, suggesting a higher flooding potential for small catchments. The north
Geometric properties of a 2-D space-time arising in 4-D black hole physics
Casals, Marc
2015-01-01
The Schwarzschild exterior space-time is conformally related to a direct product space-time, $\\mathcal{M}_2 \\times S_2$, where $\\mathcal{M}_2$ is a two-dimensional space-time. This direct product structure arises naturally when considering the wave equation on the Schwarzschild background. Motivated by this, we establish some geometrical results relating to $\\mathcal{M}_2$ that are useful for black hole physics. We prove that $\\mathcal{M}_2$ has the rare property of being a causal domain. Consequently, Synge's world function and the Hadamard form for the Green function on this space-time are well-defined globally. We calculate the world function and the van Vleck determinant on $\\mathcal{M}_2$ numerically and point out how these results will be used to establish global properties of Green functions on the Schwarzschild black hole space-time.
DYNAMICS IN NEWTONIAN-RIEMANNIAN SPACE-TIME(Ⅳ)
张荣业
2001-01-01
Lagrangian mechanics in Newtonian-Riemannian space-time and relationship between Lagrangian mechanics and Newtonian mechanics, and between Lagrangian mechanics and Hamiltonian mechanics in N-R space-time are discussed.
Charged fluid distribution in higher dimensional spheroidal space-time
G P Singh; S Kotambkar
2005-07-01
A general solution of Einstein field equations corresponding to a charged fluid distribution on the background of higher dimensional spheroidal space-time is obtained. The solution generates several known solutions for superdense star having spheroidal space-time geometry.
On the metric structure of space-time
Rau, Jochen
2010-01-01
I present an analysis of the physical assumptions needed to obtain the metric structure of space-time. For this purpose I combine the axiomatic approach pioneered by Robb with ideas drawn from works on Weyl's "Raumproblem". The concept of a Lorentzian manifold is replaced by the weaker concept of an "event manifold", defined in terms of volume element, causal structure and affine connection(s). Exploiting properties of its structure group, I show that distinguishing Lorentzian manifolds from other classes of event manifolds requires the key idea of general relativity: namely that the manifold's physical structure, rather than being fixed, is itself a variable.
Space-Time, Phenomenology, and the Picture Theory of Language
Grelland, Hans Herlof
To estimate Minkowski's introduction of space-time in relativity, the case is made for the view that abstract language and mathematics carries meaning not only by its connections with observation but as pictures of facts. This view is contrasted to the more traditional intuitionism of Hume, Mach, and Husserl. Einstein's attempt at a conceptual reconstruction of space and time as well as Husserl's analysis of the loss of meaning in science through increasing abstraction is analysed. Wittgenstein's picture theory of language is used to explain how meaning is conveyed by abstract expressions, with the Minkowski space as a case.
Energy Momentum Localization in Marder Space-Time
Aygun, S; Tarhan, I; Aygun, Melis; Aygun, Sezgin; Tarhan, Ismail
2006-01-01
Considering the Einstein, Moller, Bergmann-Thomson, Landau-Lifshitz (LL), Papapetrou, Qadir-Sharif and Weinberg's definitions in general relativity, we find the momentum four-vector of the closed universe based on Marder space-time. The momentum four-vector (due to matter plus field) is found to be zero. These results supports the viewpoints of Banerjee-Sen, Xulu and Aydogdu-Salti. Another point is that our study agree with previous works of Cooperstock-Israelit, Rosen, Johri et al.
Dirac equation on coordinate dependent noncommutative space-time
Kupriyanov, V. G.
2014-05-01
In this paper we discuss classical aspects of spinor field theory on the coordinate dependent noncommutative space-time. The noncommutative Dirac equation describing spinning particle in an external vector field and the corresponding action principle are proposed. The specific choice of a star product allows us to derive a conserved noncommutative probability current and to obtain the energy-momentum tensor for free noncommutative spinor field. Finally, we consider a free noncommutative Dirac fermion and show that if the Poisson structure is Lorentz-covariant, the standard energy-momentum dispersion relation remains valid.
Introducing the Dimensional Continuous Space-Time Theory
Martini, Luiz Cesar
2013-04-01
This article is an introduction to a new theory. The name of the theory is justified by the dimensional description of the continuous space-time of the matter, energy and empty space, that gathers all the real things that exists in the universe. The theory presents itself as the consolidation of the classical, quantum and relativity theories. A basic equation that describes the formation of the Universe, relating time, space, matter, energy and movement, is deduced. The four fundamentals physics constants, light speed in empty space, gravitational constant, Boltzmann's constant and Planck's constant and also the fundamentals particles mass, the electrical charges, the energies, the empty space and time are also obtained from this basic equation. This theory provides a new vision of the Big-Bang and how the galaxies, stars, black holes and planets were formed. Based on it, is possible to have a perfect comprehension of the duality between wave-particle, which is an intrinsic characteristic of the matter and energy. It will be possible to comprehend the formation of orbitals and get the equationing of atomics orbits. It presents a singular comprehension of the mass relativity, length and time. It is demonstrated that the continuous space-time is tridimensional, inelastic and temporally instantaneous, eliminating the possibility of spatial fold, slot space, worm hole, time travels and parallel universes. It is shown that many concepts, like dark matter and strong forces, that hypothetically keep the cohesion of the atomics nucleons, are without sense.
Critique of proposed limit to space-time measurement, based on Wigner's clocks and mirrors
Diósi, L; Diosi, L; Lukacs, B
1995-01-01
Based on a relation between inertial time intervals and the Riemannian curvature, we show that space--time uncertainty derived by Ng and van Dam implies absurd uncertainties of the Riemannian curvature.
Measuring Space-Time Geometry over the Ages
Stebbins, Albert; /Fermilab
2012-05-01
Theorists are often told to express things in the 'observational plane'. One can do this for space-time geometry, considering 'visual' observations of matter in our universe by a single observer over time, with no assumptions about isometries, initial conditions, nor any particular relation between matter and geometry, such as Einstein's equations. Using observables as coordinates naturally leads to a parametrization of space-time geometry in terms of other observables, which in turn prescribes an observational program to measure the geometry. Under the assumption of vorticity-free matter flow we describe this observational program, which includes measurements of gravitational lensing, proper motion, and redshift drift. Only 15% of the curvature information can be extracted without long time baseline observations, and this increases to 35% with observations that will take decades. The rest would likely require centuries of observations. The formalism developed is exact, non-perturbative, and more general than the usual cosmological analysis.
k-Inflation in noncommutative space-time
Feng, Chao-Jun; Li, Xin-Zhou; Liu, Dao-Jun [Shanghai Normal University, Shanghai United Center for Astrophysics (SUCA), Shanghai (China)
2015-02-01
The power spectra of the scalar and tensor perturbations in the noncommutative k-inflation model are calculated in this paper. In this model, all the modes created when the stringy space-time uncertainty relation is satisfied, and they are generated inside the sound/Hubble horizon during inflation for the scalar/tensor perturbations. It turns out that a linear term describing the noncommutative space-time effect contributes to the power spectra of the scalar and tensor perturbations. Confronting the general noncommutative k-inflation model with latest results from Planck and BICEP2, and taking c{sub S} and and λ as free parameters, we find that it is well consistent with observations. However, for the two specific models, i.e. the tachyon and DBI inflation models, it is found that the DBI model is not favored, while the tachyon model lies inside the 1σ contour, when the e-folding number is assumed to be around 50 ∝ 60. (orig.)
K-Inflation in Noncommutative Space-Time
Feng, Chao-Jun; Liu, Dao-Jun
2014-01-01
The power spectra of the scalar and tensor perturbations in the noncommutative k-inflation model are calculated in this paper. In this model, all the modes created when the stringy space-time uncertainty relation is satisfied are generated inside the sound/Hubble horizon during inflation for the scalar/tensor perturbations. It turns out that a linear term describing the noncommutative space-time effect contributes to the power spectra of the scalar and tensor perturbations. Confronting the general noncommutative k-inflation model with latest results from \\textit{Planck} and BICEP2, and taking $c_S$ and $\\lambda$ as free parameters, we find that it is well consistent with observations. However, for the two specific models, i.e. the tachyon and DBI inflation models, it is found that the DBI model is not favored, while the tachyon model lies inside the $1\\sigma$ contour, if the e-folds number is assumed to be around $50\\sim60$.
Holographic Space-time Models of Anti-deSitter Space-times
Banks, Tom
2016-01-01
We study the constraints on HST models of AdS space-time. The causal diamonds of HST along time-like geodesics of AdS space-time, fit nicely into the FRW patch of AdS space. The coordinate singularity of the FRW patch is identified with the proper time at which the Hilbert space of the causal diamond becomes infinite dimensional. For diamonds much smaller than the AdS radius, RAdS, the time dependent Hamiltonians of HST are the same as those used to describe similar diamonds in Minkowski space. In particular, they are invariant under the fuzzy analog of volume preserving diffeomorphisms of the holographic screen, which leads to fast scrambling of perturbations on the horizon of a black hole of size smaller than RAdS. We argue that, in order to take a limit of this system which converges to a CFT, one must choose Hamiltonians, in a range of proper times of order RAdS, which break this invariance, and become local in a particular choice of basis for the variables. We show that, beginning with flat, sub-RAdS, pa...
Terazawa, Hidezumi
2013-01-01
Exotic forms of matter such as carbon nanofoams, hexalambdas and strange stars, pentaquarks, color-balls, etc. and their relations to current problems in cosmo-particle physics such as dark matter and energy are discussed in some details.
Teleparallel formalism of galilean gravity
Ulhoa, S C; Santana, A E
2011-01-01
A pseudo-Riemannian manifold is introduced, with light-cone coordinates in (4+1) dimensional space-time, to describe a Galilei covariant gravity. The notion of 5-bein and torsion are developed and a galilean version of teleparallelism is constructed in this manifold. The formalism is applied to two spherically symmetric configurations. The first one is an ansatz which is inferred by following the Schwarzschild solution in general relativity. The second one is a solution of galilean covariant equations. In addition, this Galilei teleparallel approach provides a prescription to couple the 5-bein field to the galilean covariant Dirac field.
Space time manifolds and contact structures
K. L. Duggal
1990-01-01
Full Text Available A new class of contact manifolds (carring a global non-vanishing timelike vector field is introduced to establish a relation between spacetime manifolds and contact structures. We show that odd dimensional strongly causal (in particular, globally hyperbolic spacetimes can carry a regular contact structure. As examples, we present a causal spacetime with a non regular contact structure and a physical model [Gödel Universe] of Homogeneous contact manifold. Finally, we construct a model of 4-dimensional spacetime of general relativity as a contact CR-submanifold.
Representations of space, time, and number in neonates.
de Hevia, Maria Dolores; Izard, Véronique; Coubart, Aurélie; Spelke, Elizabeth S; Streri, Arlette
2014-04-01
A rich concept of magnitude--in its numerical, spatial, and temporal forms--is a central foundation of mathematics, science, and technology, but the origins and developmental relations among the abstract concepts of number, space, and time are debated. Are the representations of these dimensions and their links tuned by extensive experience, or are they readily available from birth? Here, we show that, at the beginning of postnatal life, 0- to 3-d-old neonates reacted to a simultaneous increase (or decrease) in spatial extent and in duration or numerical quantity, but they did not react when the magnitudes varied in opposite directions. The findings provide evidence that representations of space, time, and number are systematically interrelated at the start of postnatal life, before acquisition of language and cultural metaphors, and before extensive experience with the natural correlations between these dimensions.
Influence length and space-time correlation between earthquakes
Tosi, P; Loreto, V; Pietronero, L; Tosi, Patrizia; Rubeis, Valerio De; Loreto, Vittorio; Pietronero, Luciano
2004-01-01
Short and long range interactions between earthquakes are attracting increasing interest. Scale invariant properties of seismicity in time, space and energy argue for the presence of complex triggering mechanisms where, like a cascade process, each event produces aftershocks. A definitive method to assess any connection between two earthquakes separated in time and distance does not exist. Here we propose a novel method of data analysis that, based on the space-time combined generalization of the correlation integral leads to a self-consistent visualization and analysis of both spatial and temporal correlations. When analyzing global seismicity we discovered a universal relation linking the spatial Influence Length of a given earthquake to the time elapsed from the event itself. Following an event, time correlations (i.e. causality effects) exist in a region that shrinks over time, suggesting a long-range dissipating stress transfer. A different process is acting in the short-range where events are randomly s...
Travelling waves in the expanding spatially homogeneous space-times
Alekseev, George
2014-01-01
Some classes of the so called "travelling wave" solutions of Einstein and Einstein - Maxwell equations in General Relativity and of dynamical equations for massless bosonic fields in string gravity in four and higher dimensions are presented. Similarly to the well known pp-waves, these travelling wave solutions may depend on arbitrary functions of a null coordinate which determine the arbitrary profiles and polarizations of the waves. However, in contrast with pp-waves, these waves do not admit the null Killing vector fields and can exist in some curved (expanding and spatially homogeneous) background space-times, where these waves propagate in certain directions without any scattering. Mathematically, some of these classes of solutions arise as the fixed points of Kramer-Neugebauer transformations for hyperbolic integrable reductions of the mentioned above field equations, or, in the other cases, -- after imposing of the ansatz that these waves do not change the part of spatial metric transversal to the dire...
Geometrical Models of the Locally Anisotropic Space-Time
Balan, V; Kokarev, S S; Pavlov, D G; Siparov, S V; Voicu, N
2011-01-01
Along with the construction of non-Lorentz-invariant effective field theories, recent studies which are based on geometric models of Finsler space-time become more and more popular. In this respect, the Finslerian approach to the problem of Lorentz symmetry violation is characterized by the fact that the violation of Lorentz symmetry is not accompanied by a violation of relativistic symmetry. That means, in particular, that preservation of relativistic symmetry can be considered as a rigorous criterion of the viability for any non-Lorentz-invariant effective field theory. Although this paper has a review character, it contains (with few exceptions) only those results on Finsler extensions of relativity theory, that were obtained by the authors.
[Sharing space/time among hospitalized patients].
Bellato, Roseney; de Carvalho, Emília Campos
2002-01-01
By means of a comprehensive approach and based on the theoretical framework stemming from the studies of Michel Maffesoli, we attempted to understand the sharing dimension existing among ill people during hospitalization. Through interviews and observation, we were able to apprehend that, in spite of all the standardization of hospitalization, people weave a relational web and engender a "destination community" within the hospital.
Space-Time--Time Five-dimensional Kaluza--Weyl Space
Ellis, H G
2001-01-01
Space-time--time couples Kaluza's five-dimensional geometry with Weyl's conformal space-time geometry to produce an extension that goes beyond what either of those theories can achieve by itself. Kaluza's ``cylinder condition'' is replaced by an ``exponential expansion constraint'' that causes translations along the secondary time dimension to induce both the electromagnetic gauge transformations found in the Kaluza and the Weyl theories and the metrical gauge transformations unique to the Weyl theory, related as Weyl had postulated. A space-time--time geodesic describes a test particle whose rest mass, space-time momentum, and electric charge q, all defined kinematically, evolve in accord with definite dynamical laws. Its motion is governed by four apparent forces: the Einstein gravitational force, the Lorentz electromagnetic force, a force proportional to the electromagnetic potential, and a force proportional to a scalar field's gradient d(ln phi). The test particles exhibit quantum behavior: (1) they appe...
Two special classes of space-times admitting a non-null valence two Killing spinor
Bergh, Norbert Van den
2009-01-01
Non-conformally flat space-times admitting a non-null Killing spinor of valence two are investigated in the Geroch-Held-Penrose formalism. Contrary to popular belief these space-times are not all explicitly known. It is shown that the standard construction hinges on the tacit assumption that certain integrability conditions hold, implying two algebraic relations, KS1 and KS2, for the spin coefficients and the components of the Ricci spinor. An exhaustive list of (conformal classes of) space-times, in which either KS1 or KS2 are violated, is presented. The resulting space-times are each other's Sachs transforms, in general admit no Killing vectors and are characterized by a single arbitrary function.
Space-time domain decomposition method for scalar conservation laws
Doucoure, S
2012-01-01
The Space-Time Integrated Least-Squares (STILS) method is considered to analyze a space-time domain decomposition algorithm for scalar conservation laws. Continuous and discrete convergence estimates are given. Next using a time-marching finite element formulation, the STILS solution and its domain decomposition form are numerically compared.
Photoelectric Effect for Twist-deformed Space-time
Daszkiewicz, M.
In this article, we investigate the impact of twisted space-time on the photoelectric effect, i.e., we derive the $\\theta$-deformed threshold frequency. In such a way we indicate that the space-time noncommutativity strongly enhances the photoelectric process.
Space-time modeling of electricity spot prices
Abate, Girum Dagnachew; Haldrup, Niels
In this paper we derive a space-time model for electricity spot prices. A general spatial Durbin model that incorporates the temporal as well as spatial lags of spot prices is presented. Joint modeling of space-time effects is necessarily important when prices and loads are determined in a network...
CONSTRUCTIONS OF THREE-TRANSMIT-ANTENNA SPACE-TIME CODES
Hongxi TONG; Fei YU
2007-01-01
In this paper, we give design methods for three-transmit-antenna space-time codes which have reasonable parameters. A few examples are given to show that some unitary space-time codes constructed with our methods are better than the previously best-known ones.
Asymptotic symmetries of de Sitter space-time
Chrusciel, P.T. (Polska Akademia Nauk, Warsaw. Inst. Fizyki)
1981-01-01
The general form of the metric of an axially-symmetrical asymptotically de Sitter space-time fulfilling a radiation condition was found. Using the Bondi-Metzner method, the group of asymptotic symmetries of de Sitter space-time was found. The results obtained in this work agree only partially with Penrose's theory.
Electrodynamics in Non-commutative Curved Space Time
Jafari, Abolfazl
2009-01-01
We study the issue of the electrodynamics theory in noncommutative curved space time (NCCST) with a new star-product. In this paper, the motion equation of electrodynamics and canonical energy-momentum tensor in noncommutative curved space time will be found. The most important point is the assumption of the noncommutative parameter ($\\theta$) be $x^{\\m}$-independent.
Space-time discontinuous Galerkin finite element methods
Vegt, van der J.J.W.; Deconinck, H.; Ricchiuto, M.
2006-01-01
In these notes an introduction is given to space-time discontinuous Galerkin (DG) finite element methods for hyperbolic and parabolic conservation laws on time dependent domains. the space-time DG discretization is explained in detail, including the definition of the numerical fluxes and stabilizati
Space-time discontinuous Galerkin method for compressible flow
Klaij, C.M.
2006-01-01
The space-time discontinuous Galerkin method allows the simulation of compressible flow in complex aerodynamical applications requiring moving, deforming and locally refined meshes. This thesis contains the space-time discretization of the physical model, a fully explicit solver for the resulting
Photoelectric effect for twist-deformed space-time
Daszkiewicz, Marcin
2016-01-01
In this article, we investigate the impact of twisted space-time on the photoelectric effect, i.e., we derive the $\\theta$-deformed threshold frequency. In such a way we indicate that the space-time noncommutativity strongly enhances the photoelectric process.
Hsu, Jong-Ping
2013-01-01
Yang-Mills gravity is a new theory, consistent with experiments, that brings gravity back to the arena of gauge field theory and quantum mechanics in flat space-time. It provides solutions to long-standing difficulties in physics, such as the incompatibility between Einstein's principle of general coordinate invariance and modern schemes for a quantum mechanical description of nature, and Noether's 'Theorem II' which showed that the principle of general coordinate invariance in general relativity leads to the failure of the law of conservation of energy. Yang-Mills gravity in flat space-time a
Space-Time Resolved Capillary Wave Turbulence
Berhanu, Michael
2012-01-01
We report experiments on the full space and time resolved statistics of capillary wave turbulence at the air-water interface. The three-dimensional shape of the free interface is measured as a function of time by using the optical method of Diffusing Light Photography associated with a fast camera. Linear and nonlinear dispersion relations are extracted from the spatio-temporal power spectrum of wave amplitude. When wave turbulence regime is reached, we observe power-law spectra both in frequency and in wave number, whose exponents are found in agreement with the predictions of capillary wave turbulence theory. Finally, the temporal dynamics of the spatial energy spectrum highlights the occurrence of stochastic bursts transferring wave energy through the spatial scales.
Spherically Symmetric Space Time with Regular de Sitter Center
Dymnikova, Irina
We formulate the requirements which lead to the existence of a class of globally regular solutions of the minimally coupled GR equations asymptotically de Sitter at the center.REFID="S021827180300358XFN001"> The source term for this class, invariant under boosts in the radial direction, is classified as spherically symmetric vacuum with variable density and pressure Tμ ν vac associated with an r-dependent cosmological term Λ μ ν = 8π GTμ ν vac, whose asymptotic at the origin, dictated by the weak energy condition, is the Einstein cosmological term Λgμν, while asymptotic at infinity is de Sitter vacuum with λ < Λ or Minkowski vacuum. For this class of metrics the mass m defined by the standard ADM formula is related to both the de Sitter vacuum trapped at the origin and the breaking of space time symmetry. In the case of the flat asymptotic, space time symmetry changes smoothly from the de Sitter group at the center to the Lorentz group at infinity through radial boosts in between. Geometry is asymptotically de Sitter as r → 0 and asymptotically Schwarzschild at large r. In the range of masses m ≥ mcrit, the de Sitter Schwarzschild geometry describes a vacuum nonsingular black hole (ΛBH), and for m < mcrit it describes G-lump — a vacuum selfgravitating particle-like structure without horizons. In the case of de Sitter asymptotic at infinity, geometry is asymptotically de Sitter as r → 0 and asymptotically Schwarzschild de Sitter at large r. Λμν geometry describes, dependently on parameters m and q = √ {Λ /λ } and choice of coordinates, a vacuum nonsingular cosmological black hole, self-gravitating particle-like structure at the de Sitter background λgμν, and regular cosmological models with cosmological constant evolving smoothly from Λ to λ.
Theory of Quantum Gravity Beyond Einstein and Space-time Dynamics with Quantum Inflation
Wu, Yue-Liang
2015-01-01
In this talk, I present a theory of quantum gravity beyond Einstein. The theory is established based on spinnic and scaling gauge symmetries by treating the gravitational force on the same footing as the electroweak and strong forces. A bi-frame space-time is initiated to describe the laws of nature. One frame space-time is a globally flat coordinate Minkowski space-time that acts as an inertial reference frame for the motions of fields, the other is a locally flat non-coordinate Gravifield space-time that functions as an interaction representation frame for the degrees of freedom of fields. The Gravifield is sided on both the globally flat coordinate space-time and locally flat non-coordinate space-time and characterizes the gravitational force. Instead of the principle of general coordinate invariance in Einstein theory of general relativity, some underlying principles with the postulates of coordinate independence and gauge invariance are motivated to establish the theory of quantum gravity. When transmuti...
Real-time Space-time Integration in GIScience and Geography.
Richardson, Douglas B
2013-01-01
Space-time integration has long been the topic of study and speculation in geography. However, in recent years an entirely new form of space-time integration has become possible in GIS and GIScience: real-time space-time integration and interaction. While real-time spatiotemporal data is now being generated almost ubiquitously, and its applications in research and commerce are widespread and rapidly accelerating, the ability to continuously create and interact with fused space-time data in geography and GIScience is a recent phenomenon, made possible by the invention and development of real-time interactive (RTI) GPS/GIS technology and functionality in the late 1980s and early 1990s. This innovation has since functioned as a core change agent in geography, cartography, GIScience and many related fields, profoundly realigning traditional relationships and structures, expanding research horizons, and transforming the ways geographic data is now collected, mapped, modeled, and used, both in geography and in science and society more broadly. Real-time space-time interactive functionality remains today the underlying process generating the current explosion of fused spatiotemporal data, new geographic research initiatives, and myriad geospatial applications in governments, businesses, and society. This essay addresses briefly the development of these real-time space-time functions and capabilities; their impact on geography, cartography, and GIScience; and some implications for how discovery and change can occur in geography and GIScience, and how we might foster continued innovation in these fields.
Entropy of space-time outcome in a movement speed-accuracy task.
Hsieh, Tsung-Yu; Pacheco, Matheus Maia; Newell, Karl M
2015-12-01
The experiment reported was set-up to investigate the space-time entropy of movement outcome as a function of a range of spatial (10, 20 and 30 cm) and temporal (250-2500 ms) criteria in a discrete aiming task. The variability and information entropy of the movement spatial and temporal errors considered separately increased and decreased on the respective dimension as a function of an increment of movement velocity. However, the joint space-time entropy was lowest when the relative contribution of spatial and temporal task criteria was comparable (i.e., mid-range of space-time constraints), and it increased with a greater trade-off between spatial or temporal task demands, revealing a U-shaped function across space-time task criteria. The traditional speed-accuracy functions of spatial error and temporal error considered independently mapped to this joint space-time U-shaped entropy function. The trade-off in movement tasks with joint space-time criteria is between spatial error and timing error, rather than movement speed and accuracy.
Space-Time Structures from IIB Matrix Model
Aoki, H; Kawai, H; Kitazawa, Y; Tada, T
1998-01-01
We derive a long distance effective action for space-time coordinates from a IIB matrix model. It provides us an effective tool to study the structures of space-time. We prove the finiteness of the theory for finite $N$ to all orders of the perturbation theory. Space-time is shown to be inseparable and its dimensionality is dynamically determined. The IIB matrix model contains a mechanism to ensure the vanishing cosmological constant which does not rely on the manifest supersymmetry. We discuss possible mechanisms to obtain realistic dimensionality and gauge groups from the IIB matrix model.
A construction of fully diverse unitary space-time codes
YU Fei; TONG HongXi
2009-01-01
Fully diverse unitary space-time codes are useful in multiantenna communications,especially in multiantenna differential modulation.Recently,two constructions of parametric fully diverse unitary space-time codes for three antennas system have been introduced.We propose a new construction method based on the constructions.In the present paper,fully diverse codes for systems of odd prime number antennas are obtained from this construction.Space-time codes from present construction are found to have better error performance than many best known ones.
A construction of fully diverse unitary space-time codes
无
2009-01-01
Fully diverse unitary space-time codes are useful in multiantenna communications, especially in multiantenna differential modulation. Recently, two constructions of parametric fully diverse unitary space-time codes for three antennas system have been introduced. We propose a new construction method based on the constructions. In the present paper, fully diverse codes for systems of odd prime number antennas are obtained from this construction. Space-time codes from present construction are found to have better error performance than many best known ones.
ROTATING RINDLER SPACE TIME WITH CONSTANT ANGULAR VELOCITY
WANG YONG-CHENG
2000-01-01
A new space time metric is derived from Kerr metric if its mass and location approach to infinite in an appropriate way. The new space-time is an infinitesimal neighborhood nearby one of the two horizon poles of an infinite Kerr black hole. In other words, it is the second order infinitesimal neighborhood nearby one of the two horizon poles of a Kerr black hole. It is fiat and has event horizon and infinite red shift surface. We prove that it is a rotating Rindler space time with constant angular velocity.
Novel space-time multiuser detection algorithm of WCDMA system
Zhang Xiaofei; Xu Dazhuan; Yang Bei
2005-01-01
The structure and performance of space-time multiuser detection receiver at base stations of WCDMA system is analyzed, in which smart antenna is employed. WCDMA uplink signal model is established in this paper. Space-time multiuser receiver presented in this paper combines 2D-RAKE with parallel interference cancellation (PIC), and the improved parallel interference cancellation methods are given. A novel space-time multiuser detection scheme,2DRAKE-GPPIC is proposed. This scheme employs smart antenna to suppress unexpected DOA (Direction Of Arrival) signal, uses RAKE receiver to combine different delays of expected signal, and utilizes grouped partial parallel interference cancellation (GPPIC) algorithm to suppress further the interference signal in the main lobe of array antennas. The simulation results reveal that the scheme of space-time multiuser detection presented in this paper has better performance for WCDMA system.
Quantization of the space-time with topological defect
高长军; 沈有根
2003-01-01
We present the classical solution of Lagrange equations for the black hole with a global monopole or with a cosmic string. Then we obtain the wavefunction of the space-time by solving the Wheeler-De Witt equation. De Broglie-Bohm interpretation applied to the wavefunction gives the quantum solution of the space-time. In the end, the quantum effect on Hawking radiation is studied.
Space-Time Noncommutative Field Theories And Unitarity
Gomis, Jaume; Mehen, Thomas
2000-01-01
We study the perturbative unitarity of noncommutative scalar field theories. Field theories with space-time noncommutativity do not have a unitary S-matrix. Field theories with only space noncommutativity are perturbatively unitary. This can be understood from string theory, since space noncommutative field theories describe a low energy limit of string theory in a background magnetic field. On the other hand, there is no regime in which space-time noncommutative field theory is an appropriat...
Space-time Contraction and the Dynamics of Urban Systems
Denise Pumain
1998-07-01
Full Text Available An attempt is made to identify the dynamics of urban systems during the historical process of their evolution. An illustration is made with the case of European cities between 1200 and 1990, using harmonised historical data bases. Simple maps show first a general expansion in cities number and size over time, reflecting the ability of the system to continuously adapt its structure over time. A second trend is an increased hierarchisation in city size, which may be related to the continuous improvement in the speed and capacity of transportation means. Because of this space-time contraction, large cities short-circuit small towns, and inequalities in city size are widening. A third trend leading to a spatial reorganisation, emerges from maps of the urban population potentials. Among all possible mathematical equations and parameters values which could describe the intensity and the spatial range of interactions between cities, we choose those which give rather stable results and which are compatible with the analysis of urban historians, as De Vries, Braudel, Bairoch, Hohenberg and Lees, for the centuries preceding industrial revolution, by using evaluations of distances in terms of time and cost. Urban systems dynamics is better approached with reference to this relative space than on usual topographic maps.
THE SEISMICITY MIGRATION STUDY BASED ON SPACE-TIME DIAGRAMS
E. A. Levina
2015-09-01
Full Text Available Seismicity migration is studied by a new method based on space-time diagrams and a combination of cluster and regression analyses. Data from the global and Baikal regional earthquake catalogues are analysed with the application of the specially designed geographic information system (GIS in order to establish parameters and mechanisms of seismicity migration in space and time. We study the migration of seismic events in the following geostructural systems: the Baikal rift zone (BRZ, the area between BRZ and the Indo-Eurasian interplate collision zone, the area between BRZ and the West-Pacific seismic foci Benoiff zone, and two segments of the Middle Atlantic ridge.As evidenced by the obtained results, studying regimes of seismic migration provides for analyses of space-time distribution of seismic energy in the fault-block structure of the lithosphere and facilitates more detailed studies of the origin of deformation waves and mechanisms of the seismotectonic regime of the Earth. Forward (from the equator and backward (towards the equator migration of seismic events are established in all the regions under study. It is assumed that this phenomenon may result from regular changes of the polar compression of the Earth due to variations of its rotation regime. Besides, it is revealed that energy clusters of migration are regularly generated, and the regularity may be related to the 11-year cycle of the solar activity which impacts the seismic regime. We discuss the need to study the interference of wave deformations in the lithosphere which are initiated by several external energy sources. It is proposed to consider the regimes of planetary seismicity migration as a reflection of redistribution of endogenic (primarily heat energy of the Earth during the destruction of its lithospheric shell under the impacts of cosmogenic factors via triggering mechansms. With reference to our positive experiences of applying the proposed concept to BRZ, we
Quantum Space-times: Beyond the Continuum of Minkowski and Einstein
Ashtekar, Abhay
2008-01-01
In general relativity space-time ends at singularities. The big bang is considered as the Beginning and the big crunch, the End. However these conclusions are arrived at by using general relativity in regimes which lie well beyond its physical domain of validity. Examples where detailed analysis is possible show that these singularities are naturally resolved by quantum geometry effects. Quantum space-times can be vastly larger than what Einstein had us believe. These non-trivial space-time extensions enable us to answer of some long standing questions and resolve of some puzzles in fundamental physics. Thus, a century after Minkowski's revolutionary ideas on the nature of space and time, yet another paradigm shift appears to await us in the wings.
Discrete random walk models for space-time fractional diffusion
Gorenflo, Rudolf; Mainardi, Francesco; Moretti, Daniele; Pagnini, Gianni; Paradisi, Paolo
2002-11-01
A physical-mathematical approach to anomalous diffusion may be based on generalized diffusion equations (containing derivatives of fractional order in space or/and time) and related random walk models. By space-time fractional diffusion equation we mean an evolution equation obtained from the standard linear diffusion equation by replacing the second-order space derivative with a Riesz-Feller derivative of order {alpha} is part of (0,2] and skewness {theta} (module{theta}{<=}{l_brace}{alpha},2-{alpha}{r_brace}), and the first-order time derivative with a Caputo derivative of order {beta} is part of (0,1]. Such evolution equation implies for the flux a fractional Fick's law which accounts for spatial and temporal non-locality. The fundamental solution (for the Cauchy problem) of the fractional diffusion equation can be interpreted as a probability density evolving in time of a peculiar self-similar stochastic process that we view as a generalized diffusion process. By adopting appropriate finite-difference schemes of solution, we generate models of random walk discrete in space and time suitable for simulating random variables whose spatial probability density evolves in time according to this fractional diffusion equation.
Need for space-time analyses of research reactor transients
Jatuff, F.E. [INVAP S.E., de Bariloche (Argentina)
1997-12-01
The success of the point-kinetics approximation to represent the time behavior of research reactors relies on the fact that research reactor cores are small enough to be neutronically tightly coupled; the core is small when measured in diffusion lengths. This fact implies that a certain change in a part of the core is immediately observed by the whole system. The propagation of changes is so fast that the core exhibits a shape function that is practically unchanged during the transient; the amplitude function, the only unknown of the problem, represents the full knowledge of the core response. One is immediately warned to look for the truth of this assumption. How small should a research reactor core be to be sure that point kinetics is a valid assumption? This question is becoming increasingly important because the tendency is to increase the size of research reactor cores to make them capable of various simultaneous uses (multipurpose characteristics), with powers in the range of tens of thermal megawatts. One of the lines of investigation at the Department of Reactor Physics is related to scenarios of Materials Test Reactor (MTR)-type research reactor transients for which space-time kinetics would bring a more profound insight than point kinetics.
Voluble: a space-time diagram of the solar system
Aguilera, Julieta C.; SubbaRao, Mark U.
2008-02-01
Voluble is a dynamic space-time diagram of the solar system. Voluble is designed to help users understand the relationship between space and time in the motion of the planets around the sun. Voluble is set in virtual reality to relate these movements to our experience of immediate space. Beyond just the visual, understanding dynamic systems is naturally associated to the articulation of our bodies as we perform a number of complex calculations, albeit unconsciously, to deal with simple tasks. Such capabilities encompass spatial perception and memory. Voluble investigates the balance between the visually abstract and the spatially figurative in immersive development to help illuminate phenomena that are beyond the reach of human scale and time. While most diagrams, even computer-based interactive ones, are flat, three-dimensional real-time virtual reality representations are closer to our experience of space. The representation can be seen as if it was "really there," engaging a larger number of cues pertaining to our everyday spatial experience.
Space-Time Coding and Signal Processing for MIMO Communications
Inaki Berenguer; Xiaodong Wang
2003-01-01
Rapid growth in mobile computing and other wireless multimedia services is inspiring many research and development activities on high-speed wireless communication systems.Main challenges in this area include the development of efficient coding and modulation signal processing techniques for improving the quality and spectral efficiency of wireless systems. The recently emerged space-time coding and signal processing techniques for wireless communication systems employing multiple transmit and receive antennas offer a powerful paradigm for meeting these challenges. This paper provides an overview on the recent development in space-time coding and signal processing techniques for multiple-input multiple-output (MIMO) communication systems. We first review the information theoretic results on the capacities of wireless systems employing multiple transmit and receive antennas. We then describe two representative categories of space-time systems, namely, the BLAST system and the space-time block coding system, both of which have been proposed for next-generation high-speed wireless system. Signal processing techniques for channel estimation and decoding in space-time systems are also discussed. Finally, some other coding and signal processing techniques for wireless systems employing multiple transmit and receive antennas that are currently under intensive research are also briefly touched upon.
Space-Time Correlations and Dynamic Coupling in Turbulent Flows
He, Guowei; Jin, Guodong; Yang, Yue
2017-01-01
Space-time correlation is a staple method for investigating the dynamic coupling of spatial and temporal scales of motion in turbulent flows. In this article, we review the space-time correlation models in both the Eulerian and Lagrangian frames of reference, which include the random sweeping and local straining models for isotropic and homogeneous turbulence, Taylor's frozen-flow model and the elliptic approximation model for turbulent shear flows, and the linear-wave propagation model and swept-wave model for compressible turbulence. We then focus on how space-time correlations are used to develop time-accurate turbulence models for the large-eddy simulation of turbulence-generated noise and particle-laden turbulence. We briefly discuss their applications to two-point closures for Kolmogorov's universal scaling of energy spectra and to the reconstruction of space-time energy spectra from a subset of spatial and temporal signals in experimental measurements. Finally, we summarize the current understanding of space-time correlations and conclude with future issues for the field.
Vacuum Domain Walls in D-dimensions Local and Global Space-Time Structure
Cvetic, M; Cvetic, Mirjam; Wang, Jing
2000-01-01
We study local and global gravitational effects of (D-2)-brane configurations (domain-walls) in the vacuum of D-dimensional space-time. We focus on infinitely thin vacuum domain walls with arbitrary cosmological constants on either side of the wall. In the comoving frame of the wall we derive a general metric Ansatz, consistent with the homogeneity and isotropy of the space-time intrinsic to the wall, and employ Israel's matching conditions at the wall. The space-time, intrinsic to the wall, is that of (D-1)-dimensional Freedman-Lemaitre-Robertson-Walker universe (with k=-1,0,1) which has a (local) description as either anti-deSitter, Minkowski or deSitter space-time. For each of these geometries, we provide a systematic classification of the local and global space-time structure transverse to the walls, for those with both positive and negative tension; they fall into different classes according to the values of their energy density relative to that of the extreme (superysmmetric) configurations. We find tha...
Space-time correlations of fluctuating velocities in turbulent shear flows.
Zhao, Xin; He, Guo-Wei
2009-04-01
Space-time correlations or Eulerian two-point two-time correlations of fluctuating velocities are analytically and numerically investigated in turbulent shear flows. An elliptic model for the space-time correlations in the inertial range is developed from the similarity assumptions on the isocorrelation contours: they share a uniform preference direction and a constant aspect ratio. The similarity assumptions are justified using the Kolmogorov similarity hypotheses and verified using the direct numerical simulation (DNS) of turbulent channel flows. The model relates the space-time correlations to the space correlations via the convection and sweeping characteristic velocities. The analytical expressions for the convection and sweeping velocities are derived from the Navier-Stokes equations for homogeneous turbulent shear flows, where the convection velocity is represented by the mean velocity and the sweeping velocity is the sum of the random sweeping velocity and the shear-induced velocity. This suggests that unlike Taylor's model where the convection velocity is dominating and Kraichnan and Tennekes' model where the random sweeping velocity is dominating, the decorrelation time scales of the space-time correlations in turbulent shear flows are determined by the convection velocity, the random sweeping velocity, and the shear-induced velocity. This model predicts a universal form of the space-time correlations with the two characteristic velocities. The DNS of turbulent channel flows supports the prediction: the correlation functions exhibit a fair good collapse, when plotted against the normalized space and time separations defined by the elliptic model.
Rate-embedded differential space-time-frequency coding scheme
无
2007-01-01
In multiple-input-multiple-output orthogonal-frequency-division-multiplexing (MIMO-OFDM) system, a rate-embedded differential space-time-frequency (DSTF) coding scheme was proposed. Both the conventional space-time codes and coding techniques in frequency domain were employed to build high rate and low rate space-time-frequency message matrices. Then both types of message matrices were differentially transmitted alternately in the frequency domain. Consequently, the total transmission rate could be improved greatly. At receiver, a simple decision feedback differential detector (SDF-DD) was adopted to further enhance the total error performance with approximate DD complexity. Simulation results verified that the proposed scheme can implement high rate and high reliability differential transmission. Compared with the conventional DSTF coding schemes, the proposed scheme achieves higher spectral efficiency and much better error performance.
Emergence of Space-Time from Topologically Homogeneous Causal Networks
D'Ariano, Giacomo Mauro
2011-01-01
In this paper we study the emergence of Minkowski space-time from a causal network. Differently from previous approaches, we require the network to be topologically homogeneous, so that the metric is derived from pure event-counting. Emergence from events has an operational motivation in requiring that every physical quantity---including space-time---be defined through precise measurement procedures. Topological homogeneity is a requirement for having space-time metric emergent from the pure topology of causal connections, whereas physically corresponds to the universality of the physical law. We analyze in detail the case of 1+1 dimension. Coordinate systems are established via an Einsteinian protocol, and lead to a digital version of the Lorentz transformations. In a computational analogy, the foliation construction can also be regarded as the synchronization with a global clock of the calls to independent subroutines (corresponding to the causally independent events) in a parallel distributed computation, ...
A potential foundation for emergent space-time
Knuth, Kevin H.; Bahreyni, Newshaw
2014-11-01
We present a novel derivation of both the Minkowski metric and Lorentz transformations from the consistent quantification of a causally ordered set of events with respect to an embedded observer. Unlike past derivations, which have relied on assumptions such as the existence of a 4-dimensional manifold, symmetries of space-time, or the constant speed of light, we demonstrate that these now familiar mathematics can be derived as the unique means to consistently quantify a network of events. This suggests that space-time need not be physical, but instead the mathematics of space and time emerges as the unique way in which an observer can consistently quantify events and their relationships to one another. The result is a potential foundation for emergent space-time.
Mach's Principle selects 4 space-time dimensions
Altshuler, Boris L
2012-01-01
Bi-tensor kernel in integral form of Einstein equations realizing Mach's idea of non-existence of empty space-times is taken as an inverse of differential operator ("Mach operator") defined conventionally as a second variation of Einstein's gravity Action over contravariant components of metric tensor. The choice of transverse gauge condition used in this definition does not influence results of the paper since only transverse and traceless tensor modes written on different background space-times are studied. Presence of ghosts among modes of Mach operator invalidates the integral formulation of Einstein equations. And the demand of absence of these ghosts proves to be a selection rule for dimensionality of the background space-time. In particular Mach operator written on De Sitter background or on the background of so called "Einstein Universe" does not possess tensor ghosts only in 4-dimensions. The similar demand gives non-trivial formula for dimensionalities of subspaces of the Freund-Rubin background.
Curvature singularities and abstract boundary singularity theorems for space-time
Ashley, M J S L; Ashley, Michael J. S. L.; Scott, Susan M.
2003-01-01
The abstract boundary construction of Scott and Szekeres is a general and flexible way to define singularities in General Relativity. The abstract boundary construction also proves of great utility when applied to questions about more general boundary features of space-time. Within this construction an essential singularity is a non-regular boundary point which is accessible by a curve of interest (e.g. a geodesic) within finite (affine) parameter distance and is not removable. Ashley and Scott proved the first theorem linking abstract boundary essential singularities with the notion of causal geodesic incompleteness for strongly causal, maximally extended space-times. The relationship between this result and the classical singularity theorems of Penrose and Hawking has enabled us to obtain abstract boundary singularity theorems. This paper describes essential singularity results for maximally extended space-times and presents our recent efforts to establish a relationship between the strong curvature singula...
Space-time fractional diffusion equation using a derivative with nonsingular and regular kernel
Gómez-Aguilar, J. F.
2017-01-01
In this paper, using the fractional operators with Mittag-Leffler kernel in Caputo and Riemann-Liouville sense the space-time fractional diffusion equation is modified, the fractional equation will be examined separately; with fractional spatial derivative and fractional temporal derivative. For the study cases, the order considered is 0 < β , γ ≤ 1 respectively. In this alternative representation we introduce the appropriate fractional dimensional parameters which characterize consistently the existence of the fractional space-time derivatives into the fractional diffusion equation, these parameters related to equation results in a fractal space-time geometry provide a new family of solutions for the diffusive processes. The proposed mathematical representation can be useful to understand electrochemical phenomena, propagation of energy in dissipative systems, viscoelastic materials, material heterogeneities and media with different scales.
General covariance and the objectivity of space-time point-events
Lusanna, L
2005-01-01
"The last remnant of physical objectivity of space-time" is disclosed, beyond the Leibniz equivalence, in the case of a continuous family of spatially non-compact models of general relativity. The {\\it physical individuation} of point-events is furnished by the intrinsic degrees of freedom of the gravitational field, (viz, the {\\it Dirac observables}) that represent - as it were - the {\\it ontic} part of the metric field. The physical role of the {\\it epistemic} part (viz. the {\\it gauge} variables) is likewise clarified. At the end, a peculiar four-dimensional {\\it holistic and structuralist} view of space-time emerges which includes elements common to the tradition of both {\\it substantivalism} and {\\it relationism}. The observables of our models undergo real {\\it temporal change} and thereby provide a counter-example to the thesis of the {\\it frozen-time} picture of evolution. Invited Contribution to the ESF 2004 Oxford Conference on Space-Time
Stringy Space-Time Foam and High-Energy Cosmic Photons
Mavromatos, Nick E
2011-01-01
In this review, I discuss briefly stringent tests of Lorentz-violating quantum space-time foam models inspired from String/Brane theories, provided by studies of high energy Photons from intense celestial sources, such as Active Galactic Nuclei or Gamma Ray Bursts. The theoretical models predict modifications to the radiation dispersion relations, which are quadratically suppressed by the string mass scale, and time delays in the arrival times of photons (assumed to be emitted more or less simultaneously from the source), which are proportional to the photon energy, so that the more energetic photons arrive later. Although the astrophysics at the source of these energetic photons is still not understood, and such non simultaneous arrivals, that have been observed recently, might well be due to non simultaneous emission as a result of conventional physics effects, nevertheless, rather surprisingly, the observed time delays can also fit excellently the stringy space-time foam scenarios, provided the space-time ...
Note on Power-Law Inflation in Noncommutative Space-Time
Feng, Chao-Jun; Liu, Dao-Jun
2014-01-01
In this paper, we propose a new method to calculate the mode functions in the noncommutative power-law inflation model. In this model, all the modes created when the stringy space-time uncertainty relation is satisfied are generated inside the Hubble horizon during inflation. It turns out that a linear term describing the noncommutative space-time effect contributes to the power spectra of the scalar and tensor perturbations. Confronting this model with latest results from \\textit{Planck} and BICEP2, we constrain the parameters in this model and we find it is well consistent with observations.
Impact of curvature divergences on physical observers in a wormhole space-time with horizons
Olmo, Gonzalo J; Sanchez-Puente, A
2016-01-01
The impact of curvature divergences on physical observers in a black hole space-time which, nonetheless, is geodesically complete is investigated. This space-time is an exact solution of certain extensions of General Relativity coupled to Maxwell's electrodynamics and, roughly speaking, consists on two Reissner-Nordstr\\"{o}m (or Schwarzschild or Minkowski) geometries connected by a spherical wormhole near the center. We find that, despite the existence of infinite tidal forces, causal contact is never lost among the elements making up the observer. This suggests that curvature divergences may not be as pathological as traditionally thought.
Space-Time Diffeomorphisms in Noncommutative Gauge Theories
L. Román Juarez
2008-07-01
Full Text Available In previous work [Rosenbaum M. et al., J. Phys. A: Math. Theor. 40 (2007, 10367–10382] we have shown how for canonical parametrized field theories, where space-time is placed on the same footing as the other fields in the theory, the representation of space-time diffeomorphisms provides a very convenient scheme for analyzing the induced twisted deformation of these diffeomorphisms, as a result of the space-time noncommutativity. However, for gauge field theories (and of course also for canonical geometrodynamics where the Poisson brackets of the constraints explicitely depend on the embedding variables, this Poisson algebra cannot be connected directly with a representation of the complete Lie algebra of space-time diffeomorphisms, because not all the field variables turn out to have a dynamical character [Isham C.J., Kuchar K.V., Ann. Physics 164 (1985, 288–315, 316–333]. Nonetheless, such an homomorphic mapping can be recuperated by first modifying the original action and then adding additional constraints in the formalism in order to retrieve the original theory, as shown by Kuchar and Stone for the case of the parametrized Maxwell field in [Kuchar K.V., Stone S.L., Classical Quantum Gravity 4 (1987, 319–328]. Making use of a combination of all of these ideas, we are therefore able to apply our canonical reparametrization approach in order to derive the deformed Lie algebra of the noncommutative space-time diffeomorphisms as well as to consider how gauge transformations act on the twisted algebras of gauge and particle fields. Thus, hopefully, adding clarification on some outstanding issues in the literature concerning the symmetries for gauge theories in noncommutative space-times.
Unsupervised action classification using space-time link analysis
Liu, Haowei; Feris, Rogerio; Krüger, Volker
2010-01-01
In this paper we address the problem of unsupervised discovery of action classes in video data. Different from all existing methods thus far proposed for this task, we present a space-time link analysis approach which matches the performance of traditional unsupervised action categorization methods...... in a standard dataset. Our method is inspired by the recent success of link analysis techniques in the image domain. By applying these techniques in the space-time domain, we are able to naturally take into account the spatio-temporal relationships between the video features, while leveraging the power of graph...
Joint Estimation and Decoding of Space-Time Trellis Codes
Zhang Jianqiu
2002-01-01
Full Text Available We explore the possibility of using an emerging tool in statistical signal processing, sequential importance sampling (SIS, for joint estimation and decoding of space-time trellis codes (STTC. First, we provide background on SIS, and then we discuss its application to space-time trellis code (STTC systems. It is shown through simulations that SIS is suitable for joint estimation and decoding of STTC with time-varying flat-fading channels when phase ambiguity is avoided. We used a design criterion for STTCs and temporally correlated channels that combats phase ambiguity without pilot signaling. We have shown by simulations that the design is valid.
ON MARKOV CHAINS IN SPACE-TIME RANDOM ENVIRONMENTS
Hu Dihe; Hu Xiaoyu
2009-01-01
In Section 1, the authors establish the models of two kinds of Markov chains in space-time random environments (MCSTRE and MCSTRE(+)) with Abstract state space. In Section 2, the authors construct a MCSTRE and a MCSTRE(+) by an initial distribution Ф and a random Markov kernel (RMK) p(γ). In Section 3, the authors establish several equivalence theorems on MCSTRE and MCSTRE(+). Finally, the authors give two very important examples of MCMSTRE, the random walk in spce-time random environment and the Markov branching chain in space-time random environment.
Covariant hamiltonian spin dynamics in curved space-time
d'Ambrosi, G; van Holten, J W
2015-01-01
The dynamics of spinning particles in curved space-time is discussed, emphasizing the hamiltonian formulation. Different choices of hamiltonians allow for the description of different gravitating systems. We give full results for the simplest case with minimal hamiltonian, constructing constants of motion including spin. The analysis is illustrated by the example of motion in Schwarzschild space-time. We also discuss a non-minimal extension of the hamiltonian giving rise to a gravitational equivalent of the Stern-Gerlach force. We show that this extension respects a large class of known constants of motion for the minimal case.
Theory and Phenomenology of Space-Time Defects
Sabine Hossenfelder
2014-01-01
Full Text Available Whether or not space-time is fundamentally discrete is of central importance for the development of the theory of quantum gravity. If the fundamental description of spacetime is discrete, typically represented in terms of a graph or network, then the apparent smoothness of geometry on large scales should be imperfect—it should have defects. Here, we review a model for space-time defects and summarize the constraints on the prevalence of these defects that can be derived from observation.
Convexity and the "Pythagorean" metric of space(-time)
Kalogeropoulos, Nikos
2016-01-01
We address the question about the reasons why the "Wick-rotated", positive-definite, space-time metric obeys the Pythagorean theorem. An answer is proposed based on the convexity and smoothness properties of the functional spaces providing the kinematic framework for the statistical or quantum treatments of gravity. We rely on particular moduli of convexity and smoothness which are extremized by Hilbert spaces. In the spirit of the variational principles employed in classical and quantum Physics, such Hilbert spaces dominate in a functional integral approach. The "Pythagorean" metric of space(-time) is then induced by such Hilbert spaces.
Modeling of Space-Time Focusing of Localized Nondiffracting Pulses
Zamboni-Rached, Michel
2015-01-01
In this paper we develop a method capable of modeling the space-time focusing of nondiffracting pulses. The new pulses can possess arbitrary peak velocities and, in addition to being resistant to diffraction, can have their peak intensities and focusing positions chosen a priori. More specifically, we can choose multiple locations (spatial ranges) of space/time focalization; also, the pulse intensities can be chosen in advance. The pulsed wave solutions presented here can have very interesting applications in many different fields, such as free-space optical communications, remote sensing, medical apparatus, etc.
Space-time curvature signatures in Bose-Einstein condensates
Matos, Tonatiuh; Gomez, Eduardo
2015-05-01
We derive a generalized Gross-Pitaevski (GP) equation for a Bose Einstein Condensate (BEC) immersed in a weak gravitational field starting from the covariant Complex Klein-Gordon field in a curved space-time. We compare it with the traditional GP equation where the gravitational field is added by hand as an external potential. We show that there is a small difference of order gz/c2 between them that could be measured in the future using Bose-Einstein Condensates. This represents the next order correction to the Newtonian gravity in a curved space-time.
Space-Time Curvature Signatures in Bose-Einstein Condensates
Matos, Tonatiuh
2015-01-01
We derive a generalized Gross-Pitaevski (GP) equation immersed on a electromagnetic and a weak gravitational field starting from the covariant Complex Klein-Gordon field in a curved space-time. We compare it with the GP equation where the gravitational field is added by hand as an external potential. We show that there is a small difference of order $g z/c^2$ between them that could be measured in the future using Bose-Einstein Condensates (BEC). This represents the next order correction to the Newtonian gravity in a curved space-time.
A Model of Emergent Universe in Inhomogeneous Space-Time
Bhattacharya, Subhra
2016-01-01
A scenario of an emergent universe is constructed in the background of an inhomogeneous space-time model which is asymptotically (at spatial infinity) FRW space-time. The cosmic substratum consists of non-interacting two components, namely {\\bf a)} homogeneous and isotropic fluid but dissipative in nature and {\\bf b)} an inhomogeneous and anisotropic barotropic fluid. In non-equilibrium thermodynamic prescription (second order deviations), particle creation mechanism is considered the cause for the dissipative phenomena. It is found that for constant value of the particle creation rate parameter there exists a scenario of emergent universe.
Spherically symmetric solution in a space-time with torsion
Farfan, Filemon; Loaiza-Brito, Oscar; Moreno, Claudia; Yakhno, Alexander
2011-01-01
By using the analysis group method, we obtain a new exact evolving and spherically symmetric solution of the Einstein-Cartan equations of motion, corresponding to a space-time threaded with a three-form Kalb-Ramond field strength. The solution describes in its more generic form, a space-time which scalar curvature vanishes for large distances and for large time. In static conditions, it reduces to a classical wormhole solution already reported in literature. In the process we have found evidence towards the construction of more new solutions.
Holographic analysis of dispersive pupils in space--time optics
Calatroni, J.; Vienot, J.C.
1981-06-01
Extension of space--time optics to objects whose transparency is a function of the temporal frequency v = c/lambda is examined. Considering the effects of such stationary pupils on white light waves, they are called temporal pupils. It is shown that simultaneous encoding both in the space and time frequency domains is required to record pupil parameters. The space-time impulse response and transfer functions are calculated for a dispersive nonabsorbent material. An experimental method providing holographic recording of the dispersion curve of any transparent material is presented.
A Lie-Algebra model for a noncommutative space time geometry
Doerfel, B D
2002-01-01
We propose a Lie-algebra model for noncommutative coordinate and momentum space . Based on a rigid commutation relation for the commutators of space time operators the model is quite constrained if one tries to keep Lorentz invariance as much as possible. We discuss the question of invariants esp. the definition of a mass.
High-Order Space-Time Methods for Conservation Laws
Huynh, H. T.
2013-01-01
Current high-order methods such as discontinuous Galerkin and/or flux reconstruction can provide effective discretization for the spatial derivatives. Together with a time discretization, such methods result in either too small a time step size in the case of an explicit scheme or a very large system in the case of an implicit one. To tackle these problems, two new high-order space-time schemes for conservation laws are introduced: the first is explicit and the second, implicit. The explicit method here, also called the moment scheme, achieves a Courant-Friedrichs-Lewy (CFL) condition of 1 for the case of one-spatial dimension regardless of the degree of the polynomial approximation. (For standard explicit methods, if the spatial approximation is of degree p, then the time step sizes are typically proportional to 1/p(exp 2)). Fourier analyses for the one and two-dimensional cases are carried out. The property of super accuracy (or super convergence) is discussed. The implicit method is a simplified but optimal version of the discontinuous Galerkin scheme applied to time. It reduces to a collocation implicit Runge-Kutta (RK) method for ordinary differential equations (ODE) called Radau IIA. The explicit and implicit schemes are closely related since they employ the same intermediate time levels, and the former can serve as a key building block in an iterative procedure for the latter. A limiting technique for the piecewise linear scheme is also discussed. The technique can suppress oscillations near a discontinuity while preserving accuracy near extrema. Preliminary numerical results are shown
Holism and life manifestations: molecular and space-time biology.
Krecek, J
2010-01-01
Appeals of philosophers to look for new concepts in sciences are being met with a weak response. Limited attention is paid to the relation between synthetic and analytic approach in solving problems of biology. An attempt is presented to open a discussion on a possible role of holism. The term "life manifestations" is used in accordance with phenomenology. Multicellular creatures maintain milieu intérieur to keep an aqueous milieu intracellulair in order to transform the energy of nutrients into the form utilizable for driving cellular life manifestations. Milieu intérieur enables to integrate this kind of manifestations into life manifestations of the whole multicellular creatures. The integration depends on a uniqueness and uniformity of the genome of cells, on their mutual recognition and adherence. The processes of ontogenetic development represent the natural mode of integration of cellular life manifestations. Functional systems of multicellular creatures are being established by organization of integrable cells using a wide range of developmental processes. Starting from the zygote division the new being displays all properties of a whole creature, although its life manifestations vary. Therefore, the whole organism is not only more than its parts, as supposed by holism, but also more than developmental stages of its life manifestations. Implicitly, the units of whole multicellular creature are rather molecular and developmental events than the cells per se. Holism, taking in mind the existence of molecular and space-time biology, could become a guide in looking for a new mode of the combination of analytical and synthetic reasoning in biology.
Space-time clusters of breast cancer using residential histories
Nordsborg, Rikke Baastrup; Meliker, Jaymie R; Ersbøll, Annette Kjær
2014-01-01
selected from the Civil Registration System. Residential addresses of cases and controls from 1971 to 2003 were collected from the Civil Registration System and geo-coded. Q-statistics were used to identify space-time clusters of breast cancer. All analyses were carried out with both control groups...
N=4 supersymmetry on a space-time lattice
Catterall, Simon; Schaich, David; Damgaard, Poul H.
2014-01-01
Maximally supersymmetric Yang–Mills theory in four dimensions can be formulated on a space-time lattice while exactly preserving a single supersymmetry. Here we explore in detail this lattice theory, paying particular attention to its strongly coupled regime. Targeting a theory with gauge group SU...
Quantum space-times in the year 2002
A P Balachandran
2002-08-01
We review certain emergent notions on the nature of space-time from noncommutative geometry and their radical implications. These ideas of space-time are suggested from developments in fuzzy physics, string theory, and deformation quantization. The review focuses on the ideas coming from fuzzy physics. We ﬁnd models of quantum space-time like fuzzy 4 on which states cannot be localized, but which ﬂuctuate into other manifolds like CP3. New uncertainty principles concerning such lack of localizability on quantum space-times are formulated. Such investigations show the possibility of formulating and answering questions like the probability of ﬁnding a point of a quantum manifold in a state localized on another one. Additional striking possibilities indicated by these developments is the (generic) failure of CPT theorem and the conventional spin-statistics connection. They even suggest that Planck’s `constant’ may not be a constant, but an operator which does not commute with all observables. All these novel possibilities arise within the rules of conventional quantum physics, and with no serious input from gravity physics.
Geostatistical analysis of GPS trajectory data: Space-time densities
Hengl, T.; van Loon, E.E.; Shamoun-Baranes, J.; Bouten, W.; Zhang, J.; Goodchild, M.F.
2008-01-01
Creation of density maps and estimation of home range is problematic for observations of animal movement at irregular intervals. We propose a technique to estimate space-time densities by separately modeling animal movement paths and velocities, both as continuous fields. First the length of traject
Neutrino oscillations in a curved space-time with rotation
Sousa, Adellane A.; Pereira, Rosangela B. [Universidade Federal de Mato Grosso (UFMT), Barra do Garcas, MT (Brazil)
2011-07-01
Full text: Several experiments, like Homestake Experiment in the late 1960, which used a chlorine-based detector, observed a deficit in the flux of solar neutrinos. This is the solar neutrino problem. A possible explanation to this problem are the neutrino oscillations, a quantum mechanical phenomenon predicted by Bruno Pontecorvo whereby a neutrino created with a specific lepton flavor (electron, muon or tau) can later be measured to have a different flavor. The probability of measuring a particular flavor for a neutrino varies periodically as it propagates. One possible approach to this problem is to use a background at space-time of Minkowski in the propagation of the neutrinos between the source and the Earth. However, the curved space-time is a more realistic background to neutrino oscillations. We studied the problem of neutrino oscillations in a Riemann space-time in the Lense-Thirring metric rotational using Dirac equation with the prescription of minimum coupling (Levi-Civita connection). The Lense-Thirring effect on the neutrino was confirmed via Dirac Hamiltonian. In particular, we calculated the phase dynamics of the neutrinos and determined the the transition probability in the two-flavor case. We also present a new approach for introducing the torsion space-time into the Dirac equation using the general spin connection (in the context of Riemann-Cartan geometry) and investigated the role of the torsion in the phase of the neutrino via a free parameter b. (author)
Causality violation in asymptotically flat space-times
Tipler, F.J.
1976-10-04
It is shown that a region containing closed timelike lines cannot evolve from regular initial data in a singularity-free asymptotically flat space-time. Furthermore, the causality assumption made in the black-hole uniqueness proofs is justified: It is demonstrated that no physically realistc nonsingular black hole can have a causality-violating exterior. (AIP)
Electromagnetic space-time crystals. II. Fractal computational approach
Borzdov, G. N.
2014-01-01
A fractal approach to numerical analysis of electromagnetic space-time crystals, created by three standing plane harmonic waves with mutually orthogonal phase planes and the same frequency, is presented. Finite models of electromagnetic crystals are introduced, which make possible to obtain various approximate solutions of the Dirac equation. A criterion for evaluating accuracy of these approximate solutions is suggested.
Nucleon structure functions in noncommutative space-time
Rafiei, Ali; Mirjalili, Abolfazl
2016-01-01
In the context of noncommutative space-time, we investigate the nucleon structure functions which plays an important role to identify the internal structure of nucleons. We use the corrected vertices and employ new vertices that appear in two approaches of noncommutativity and calculate the proton structure functions in terms of noncommutative tensor \\theta_{\\mu\
Zen and the Art of Space-Time Manufacturing
Bertolami Orfeu
2013-01-01
We present a general discussion about the so-called emergent properties and discuss whether space-time and gravity can be regarded as emergent features of underlying more fundamental structures. Finally, we discuss some ideas about the multiverse, and speculate on how our universe might arise from the multiverse.
Zen and the Art of Space-Time Manufacturing
Bertolami Orfeu
2013-09-01
Full Text Available We present a general discussion about the so-called emergent properties and discuss whether space-time and gravity can be regarded as emergent features of underlying more fundamental structures. Finally, we discuss some ideas about the multiverse, and speculate on how our universe might arise from the multiverse.
Interference Phase of Mass Neutrinos in Kerr Space-Time
HUANG Xiu-Ju; WANG Yong-Jiu
2003-01-01
Along the geodesic we calculate the interference phase of the mass neutrinos in some special cases. Because of the rotation of the mass resource which induces the gravitational field, the angular momentum per unit mass, a, has a contribution to the phase, which is different from the case in Schwarzschild space-time.
Space-Time Diffeomorphisms in Noncommutative Gauge Theories
Rosenbaum, Marcos; Juarez, L Roman
2008-01-01
In previous work [Rosenbaum M. et al., J. Phys. A: Math. Theor. 40 (2007), 10367-10382, hep-th/0611160] we have shown how for canonical parametrized field theories, where space-time is placed on the same footing as the other fields in the theory, the representation of space-time diffeomorphisms provides a very convenient scheme for analyzing the induced twisted deformation of these diffeomorphisms, as a result of the space-time noncommutativity. However, for gauge field theories (and of course also for canonical geometrodynamics) where the Poisson brackets of the constraints explicitely depend on the embedding variables, this Poisson algebra cannot be connected directly with a representation of the complete Lie algebra of space-time diffeomorphisms, because not all the field variables turn out to have a dynamical character [Isham C.J., Kuchar K.V., Ann. Physics 164 (1985), 288-315, 316-333]. Nonetheless, such an homomorphic mapping can be recuperated by first modifying the original action and then adding addi...
Simple Space-Time Symmetries: Generalizing Conformal Field Theory
Mack, G; Mack, Gerhard; Riese, Mathias de
2004-01-01
We study simple space-time symmetry groups G which act on a space-time manifold M=G/H which admits a G-invariant global causal structure. We classify pairs (G,M) which share the following additional properties of conformal field theory: 1) The stability subgroup H of a point in M is the identity component of a parabolic subgroup of G, implying factorization H=MAN, where M generalizes Lorentz transformations, A dilatations, and N special conformal transformations. 2) special conformal transformations in N act trivially on tangent vectors to the space-time manifold M. The allowed simple Lie groups G are the universal coverings of SU(m,m), SO(2,D), Sp(l,R), SO*(4n) and E_7(-25) and H are particular maximal parabolic subgroups. All these groups G admit positive energy representations. It will also be shown that the classical conformal groups SO(2,D) are the only allowed groups which possess a time reflection automorphism; in all other cases space-time has an intrinsic chiral structure.
Cinematic chronotopes: affective encounters in space-time
Hesselberth, P.
2012-01-01
This study makes a case for analyzing the chronotopes of the cinematic as affective encounters in space-time. It argues that, while the site of cinema is on the move, the extent to which technologically mediated sounds and images continue to be experienced as cinematic today is largely dependent on
The Energy of Marder Space-Time in Moller Prescription
Aygun, S; Tarhan, I; Aygun, Sezgin; Baysal, Husnu; Tarhan, Ismail
2006-01-01
We use the Moller energy-momentum complex in teleparallel gravity to calculate Marder space time. The energy distribution is found to be zero everywhere. This result agrees with previous works of the authors and Cooperstock-Israelit, Salti et al., Israelit, Rosen, Johri et al. and Banerjee-Sen.
Space-time singularities and the Kaehler cone
Jaerv, L.; Mayer, C.; Mohaupt, T.; Saueressig, F. [Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universitaet Jena, Max-Wien-Platz 1, 07743 Jena (Germany)
2004-06-01
We review recent results on the interplay between the five-dimensional space-time and the internal manifold in Calabi-Yau compactifications of M-theory. Black string, black hole and domain wall solutions as well as Kasner type cosmologies cannot develop a naked singularity as long as the moduli take values inside the Kaehler cone. (Abstract Copyright [2004], Wiley Periodicals, Inc.)
Super-Poincare' algebras, space-times and supergravities (II)
Santi, Andrea
2011-01-01
The presentation of supergravity theories of our previous paper "Super-Poincare' algebras, space-times and supergravities (I)" is re-formulated in the language of Berezin-Leites-Kostant theory of supermanifolds. It is also shown that the equations of Cremmer, Julia and Scherk's theory of 11D-supergravity are equivalent to manifestly covariant equations on a supermanifold.
Space-time design of the public city
Thomaier, Susanne; Könecke, Benjamin; Zedda, Roberto; Stabilini, Stefano
2013-01-01
Time has become an increasingly important topic in urban studies and urban planning. The spatial-temporal interplay is not only of relevance for the theory of urban development and urban politics, but also for urban planning and governance. The space-time approach focuses on the human being with its various habits and routines in the city. Understanding and taking those habits into account in urban planning and public policies offers a new way to improve the quality of life in our cities. Adapting the supply and accessibility of public spaces and services to the inhabitants’ space-time needs calls for an integrated approach to the physical design of urban space and to the organization of cities. In the last two decades the body of practical and theoretical work on urban space-time topics has grown substantially. The book offers a state of the art overview of the theoretical reasoning, the development of new analytical tools, and practical experience of the space-time design of public cities in major Europea...
f-symbols in Robertson-Walker space-times
Popa, F C; Popa, Florian Catalin; Tintareanu-Mircea, Ovidiu
2004-01-01
In a Robertson-Walker space-time a spinning particle model is investigated and we show that in a stationary case, there exists a class of new structures called f-symbols which can generate reducible Killing tensors and supersymmetry algebras.
Hermitian realizations of κ-Minkowski space-time
Kovačević, Domagoj; Meljanac, Stjepan; Samsarov, Andjelo; Škoda, Zoran
2015-01-01
General realizations, star products and plane waves for κ-Minkowski space-time are considered. Systematic construction of general Hermitian realization is presented, with special emphasis on noncommutative plane waves and Hermitian star product. Few examples are elaborated and possible physical applications are mentioned.
An extended Dirac equation in noncommutative space-time
Mendes, R Vilela
2015-01-01
Stabilizing, by deformation, the algebra of relativistic quantum mechanics a non-commutative space-time geometry is obtained. The exterior algebra of this geometry leads to an extended massless Dirac equation which has both a massless and a large mass solution. The nature of the solutions is discussed, as well as the effects of coupling the two solutions.
Noncommutative geometry, symmetries and quantum structure of space-time
Govindarajan, T R [Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600113 (India); Gupta, Kumar S [Theory Division, Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700064 (India); Harikumar, E [School of Physics, University of Hyderabad, Hyderabad 500046 (India); Meljanac, S, E-mail: trg@imsc.res.in, E-mail: kumars.gupta@saha.ac.in, E-mail: harisp@uohyd.ernet.in, E-mail: meljanac@irb.hr [Rudjer Botkovic Institute, Bijenicka c.54, HR-10002 Zagreb (Croatia)
2011-07-08
We discuss how space-time noncommutativity affects the symmetry groups and particle statistics. Assuming that statistics is superselected under a symmetry transformation, we argue that the corresponding flip operator must be twisted. It is argued that the twisted statistics naturally leads to a deformed oscillator algebra for scalar fields in such a background.
Public space, time and space of change: Lisbon and Barcelona
Claudia Sisti
2009-04-01
Using this method of analysis space / time allows us to demonstrate how different contexts and times of intervention, correspond to different types of public space and how the concept of public space is to metamorphose paradigms that can be set in a short time. What next?
Electromagnetic space-time crystals. II. Fractal computational approach
2014-01-01
A fractal approach to numerical analysis of electromagnetic space-time crystals, created by three standing plane harmonic waves with mutually orthogonal phase planes and the same frequency, is presented. Finite models of electromagnetic crystals are introduced, which make possible to obtain various approximate solutions of the Dirac equation. A criterion for evaluating accuracy of these approximate solutions is suggested.
Entanglement in a multiverse with no common space-time
Robles-Pérez, S. J.
2012-01-01
Inter-universal entanglement may even exist in a multiverse in which there is no common space-time among the universes. In particular, the entanglement between the expanding and contracting branches of the universe might have observable consequences in the dynamical and thermodynamical properties of one single branch, making therefore testable the whole multiverse proposal, at least in principle.
Interference phase of mass neutrino in CM space-time
Chen Xia; Wang Yong-Jiu
2009-01-01
In the gravitational field of central mass with electric and magnetic charges and magnetic moment(CM space-time),this paper calculates the interference phase of mass neutrino along geodesic in the radial direction,and discusses the contribution of the electric and magnetic charges and magnetic moment of the central mass to the phase.
Joint space-time geostatistical model for air quality surveillance
Russo, A.; Soares, A.; Pereira, M. J.
2009-04-01
Air pollution and peoples' generalized concern about air quality are, nowadays, considered to be a global problem. Although the introduction of rigid air pollution regulations has reduced pollution from industry and power stations, the growing number of cars on the road poses a new pollution problem. Considering the characteristics of the atmospheric circulation and also the residence times of certain pollutants in the atmosphere, a generalized and growing interest on air quality issues led to research intensification and publication of several articles with quite different levels of scientific depth. As most natural phenomena, air quality can be seen as a space-time process, where space-time relationships have usually quite different characteristics and levels of uncertainty. As a result, the simultaneous integration of space and time is not an easy task to perform. This problem is overcome by a variety of methodologies. The use of stochastic models and neural networks to characterize space-time dispersion of air quality is becoming a common practice. The main objective of this work is to produce an air quality model which allows forecasting critical concentration episodes of a certain pollutant by means of a hybrid approach, based on the combined use of neural network models and stochastic simulations. A stochastic simulation of the spatial component with a space-time trend model is proposed to characterize critical situations, taking into account data from the past and a space-time trend from the recent past. To identify near future critical episodes, predicted values from neural networks are used at each monitoring station. In this paper, we describe the design of a hybrid forecasting tool for ambient NO2 concentrations in Lisbon, Portugal.
Leus, G.; Petré, F.; Moonen, M.
2004-01-01
In the downlink of DS-CDMA, frequency-selectivity destroys the orthogonality of the user signals and introduces multiuser interference (MUI). Space-time chip equalization is an efficient tool to restore the orthogonality of the user signals and suppress the MUI. Furthermore, multiple-input
Leus, G.; Petré, F.; Moonen, M.
2004-01-01
In the downlink of DS-CDMA, frequency-selectivity destroys the orthogonality of the user signals and introduces multiuser interference (MUI). Space-time chip equalization is an efficient tool to restore the orthogonality of the user signals and suppress the MUI. Furthermore, multiple-input multiple-
Trajectory data analyses for pedestrian space-time activity study.
Qi, Feng; Du, Fei
2013-01-01
It is well recognized that human movement in the spatial and temporal dimensions has direct influence on disease transmission(1-3). An infectious disease typically spreads via contact between infected and susceptible individuals in their overlapped activity spaces. Therefore, daily mobility-activity information can be used as an indicator to measure exposures to risk factors of infection. However, a major difficulty and thus the reason for paucity of studies of infectious disease transmission at the micro scale arise from the lack of detailed individual mobility data. Previously in transportation and tourism research detailed space-time activity data often relied on the time-space diary technique, which requires subjects to actively record their activities in time and space. This is highly demanding for the participants and collaboration from the participants greatly affects the quality of data(4). Modern technologies such as GPS and mobile communications have made possible the automatic collection of trajectory data. The data collected, however, is not ideal for modeling human space-time activities, limited by the accuracies of existing devices. There is also no readily available tool for efficient processing of the data for human behavior study. We present here a suite of methods and an integrated ArcGIS desktop-based visual interface for the pre-processing and spatiotemporal analyses of trajectory data. We provide examples of how such processing may be used to model human space-time activities, especially with error-rich pedestrian trajectory data, that could be useful in public health studies such as infectious disease transmission modeling. The procedure presented includes pre-processing, trajectory segmentation, activity space characterization, density estimation and visualization, and a few other exploratory analysis methods. Pre-processing is the cleaning of noisy raw trajectory data. We introduce an interactive visual pre-processing interface as well as an
Rateless Space Time Block Code for Massive MIMO Systems
Ali H. Alqahtani
2014-01-01
Full Text Available This paper presents a rateless space time block code (RSTBC for massive MIMO systems. The paper illustrates the basis of rateless space time codes deployments in massive MIMO transmissions over wireless erasure channels. In such channels, data may be lost or is not decodable at the receiver due to a variety of factors such as channel fading, interference, or antenna element failure. We show that RSTBC guarantees the reliability of the system in such cases, even when the data loss rate is 25% or more. In such a highly lossy channel, the conventional fixed-rate codes fail to perform well, particularly when channel state information is not available at the transmitter. Simulation results are provided to demonstrate the BER performance and the spectral efficiency of the proposed scheme.
Direct data domain approach to space-time adaptive processing
Wen Xiaoqin; Han Chongzhao
2006-01-01
In non-homogeneous environment, traditional space-time adaptive processing doesn' t effectively suppress interference and detect target, because the secondary data don' t exactly reflect the statistical characteristic of the range cell under test. A novel methodology utilizing the direct data domain approach to space- time adaptive processing (STAP) in airborne radar non-homogeneous environments is presented. The deterministic least squares adaptive signal processing technique operates on a "snapshot-by-snapshot" basis to determine the adaptive weights for nulling interferences and estimating signal of interest (SOI). Furthermore, this approach eliminates the requirement for estimating the covariance through the data of neighboring range rell,which eliminates calculating the inverse of covariance, and can be implemented to operate in resl-time. Simulation results illustrate the efficiency of interference suppression in non-homogeneous environment.
Quantum gravity effects in Myers-Perry space-times
Litim, Daniel F
2013-01-01
We study quantum gravity effects for Myers-Perry black holes assuming that the leading contributions arise from the renormalization group evolution of Newton's coupling. Provided that gravity weakens following the asymptotic safety conjecture, we find that quantum effects lift a degeneracy of higher-dimensional black holes, and dominate over kinematical ones induced by rotation, particularly for small black hole mass, large angular momentum, and higher space-time dimensionality. Quantum-corrected space-times display inner and outer horizons, and show the existence of a black hole of smallest mass in any dimension. Ultra-spinning solutions no longer persist. Thermodynamic properties including temperature, specific heat, the Komar integrals, and aspects of black hole mechanics are studied as well. Observing a softening of the ring singularity, we also discuss the validity of classical energy conditions.
Scalar Field Cosmologies and the Initial Space-Time Singularity
Foster, S
1998-01-01
The singularity structure of cosmological models whose matter content consists of a scalar field with arbitrary non-negative potential is discussed. The special case of spatially flat FRW space-time is analysed in detail using a dynamical systems approach which may readily be generalised to more complicated space-times. It is shown that for a very large and natural class of models a simple and regular past asymptotic structure exists. More specifically, there exists a family of solutions which is in continuous 1-1 correspondence with the exactly integrable massless scalar field cosmologies, this correspondence being realised by a unique asymptotic approximation. The set of solutions which do not fall into this class has measure zero. The significance of this result to the cosmological initial value problem is briefly discussed.
Cremonian Space-Time(s) as an Emergent Phenomenon
Saniga, M
2004-01-01
It is shown that the notion of fundamental elements can be extended to_any_, i.e. not necessarily homaloidal, web of rational surfaces in a three-dimensional projective space. A Cremonian space-time can then be viewed as an_emergent_ phenomenon when the condition of "homaloidity" of the corresponding web is satisfied. The point is illustrated by a couple of particular types of "almost-homaloidal" webs of quadratic surfaces. In the first case, the quadrics have a line and two distinct points in common and the corresponding pseudo-Cremonian manifold is endowed with just two spatial dimensions. In the second case, the quadrics share six distinct points, no three of them collinear, that lie in quadruples in three different planes, and the corresponding pseudo-Cremonian configuration features three time dimensions. In both the cases, the limiting process of the emergence of generic Cremonian space-times is explicitly demonstrated.
Gaussian quantum metrology and space-time probes
Šafránek, Dominik
2016-01-01
In this thesis we focus on Gaussian quantum metrology in the phase-space formalism and its applications in quantum sensing and the estimation of space-time parameters. We derive new formulae for the optimal estimation of multiple parameters encoded into Gaussian states. We discuss the discontinuous behavior of the figure of merit - the quantum Fisher information. Using derived expressions we devise a practical method of finding optimal probe states for the estimation of Gaussian channels and we illustrate this method on several examples. We show that the temperature of a probe state affects the estimation generically and always appears in the form of four multiplicative factors. We also discuss how well squeezed thermal states perform in the estimation of space-time parameters. Finally we study how the estimation precision changes when two parties exchanging a quantum state with the encoded parameter do not share a reference frame. We show that using a quantum reference frame could counter this effect.
Interference Cancellation Using Space-Time Processing and Precoding Design
Li, Feng
2013-01-01
Interference Cancellation Using Space-Time Processing and Precoding Design introduces original design methods to achieve interference cancellation, low-complexity decoding and full diversity for a series of multi-user systems. In multi-user environments, co-channel interference will diminish the performance of wireless communications systems. In this book, we investigate how to design robust space-time codes and pre-coders to suppress the co-channel interference when multiple antennas are available. This book offers a valuable reference work for graduate students, academic researchers and engineers who are interested in interference cancellation in wireless communications. Rigorous performance analysis and various simulation illustrations are included for each design method. Dr. Feng Li is a scientific researcher at Cornell University.
Convexity and the Euclidean Metric of Space-Time
Nikolaos Kalogeropoulos
2017-02-01
Full Text Available We address the reasons why the “Wick-rotated”, positive-definite, space-time metric obeys the Pythagorean theorem. An answer is proposed based on the convexity and smoothness properties of the functional spaces purporting to provide the kinematic framework of approaches to quantum gravity. We employ moduli of convexity and smoothness which are eventually extremized by Hilbert spaces. We point out the potential physical significance that functional analytical dualities play in this framework. Following the spirit of the variational principles employed in classical and quantum Physics, such Hilbert spaces dominate in a generalized functional integral approach. The metric of space-time is induced by the inner product of such Hilbert spaces.
Construction of New Delay-Tolerant Space-Time Codes
Sarkiss, Mireille; Damen, Mohamed Oussama; Belfiore, Jean-Claude
2010-01-01
Perfect Space-Time Codes (STC) are optimal codes in their original construction for Multiple Input Multiple Output (MIMO) systems. Based on Cyclic Division Algebras (CDA), they are full-rate, full-diversity codes, have Non-Vanishing Determinants (NVD) and hence achieve Diversity-Multiplexing Tradeoff (DMT). In addition, these codes have led to optimal distributed space-time codes when applied in cooperative networks under the assumption of perfect synchronization between relays. However, they loose their diversity when delays are introduced and thus are not delay-tolerant. In this paper, using the cyclic division algebras of perfect codes, we construct new codes that maintain the same properties as perfect codes in the synchronous case. Moreover, these codes preserve their full-diversity in asynchronous transmission.
Production of Dirac particle in twisted Minkowsky space-time
Samary, Dine Ousmane; Kanfon, Antonin
2015-01-01
In this paper we study the Dirac equation interacting with external gravitation field. This curve background, which correspond to the deformation of Minkowsky space-time is described with the tetrad of the form $e_b^\\mu(x)=\\varepsilon(\\delta_b^\\mu+\\omega_{ba}^\\mu x^a)$, where $\\varepsilon=1$ for $\\mu=0$ and $\\varepsilon=i$ for $\\mu=1,2,3.$ Using separation of variables the corresponding Dirac equation is solved. The probability density of the vacuum-vacuum pair creation is given. In particular case of vanishing electromagnetic fields, we point out that, this external gravitation field modify weakly the well know probability of pair production of the Dirac particle given in ordinary space-time.
Trapping Horizons in Sultana-Dyer Space-Time
SUN Cheng-Yi
2011-01-01
The Sultana-Dyer space-time is suggested as a model describing a black hole embedded in an expanding universe.Recently, its global structure is analyzed and the trapping horizons are shown.In the paper, by directly calculating the expansions of the radial null vector fields normal to the space-like two-spheres foliating the trapping horizons, we find that the trapping horizon outside the event horizon in the Sultana-Dyer space-time is a past trapping horizon.Further, we find that the past trapping horizon is an outer, instantaneously degenerate or inner trapping horizon accordingly when the radial coordinate is less than, equal to or greater than some value.
Quantum gravity effects in Myers-Perry space-times
Litim, Daniel F.; Nikolakopoulos, Konstantinos [Department of Physics and Astronomy, University of Sussex,Falmer Campus, Brighton BN1 9QH (United Kingdom)
2014-04-03
We study quantum gravity effects for Myers-Perry black holes assuming that the leading contributions arise from the renormalization group evolution of Newton’s coupling. Provided that gravity weakens following the asymptotic safety conjecture, we find that quantum effects lift a degeneracy of higher-dimensional black holes, and dominate over kinematical ones induced by rotation, particularly for small black hole mass, large angular momentum, and higher space-time dimensionality. Quantum-corrected space-times display inner and outer horizons, and show the existence of a black hole of smallest mass in any dimension. Ultra-spinning solutions no longer persist. Thermodynamic properties including temperature, specific heat, the Komar integrals, and aspects of black hole mechanics are studied as well. Observing a softening of the ring singularity, we also discuss the validity of classical energy conditions.
Radiation reaction in curved space-time: local method
Gal'tsov, D; Staub, S; Gal'tsov, Dmitri; Spirin, Pavel; Staub, Simona
2006-01-01
Although consensus seems to exist about the validity of equations accounting for radiation reaction in curved space-time, their previous derivations were criticized recently as not fully satisfactory: some ambiguities were noticed in the procedure of integration of the field momentum over the tube surrounding the world-line. To avoid these problems we suggest a purely local derivation dealing with the field quantities defined only {\\em on the world-line}. We consider point particle interacting with scalar, vector (electromagnetic) and linearized gravitational fields in the (generally non-vacuum) curved space-time. To properly renormalize the self-action in the gravitational case, we use a manifestly reparameterization-invariant formulation of the theory. Scalar and vector divergences are shown to cancel for a certain ratio of the corresponding charges. We also report on a modest progress in extending the results for the gravitational radiation reaction to the case of non-vacuum background.
The $21^{st}$ century map making of dielectric analog space-times
Fathi, Mohsen
2016-01-01
It is commonly assumed that if the optical metric of a dielectric medium is identical to the metric of a vacuum space-time then light propagation through the dielectric mimics light propagation in the vacuum. However, just as the curved surface of the Earth cannot be mapped into a flat plane without distortion of some surface features, so too is it impossible to project the behavior of light from the vacuum into a dielectric analog residing in Minkowski space-time without introducing distortions. We study the covariance properties of dielectric analog space-times and the kinematics of a congruence of light in the analog, and show how certain features can be faithfully emulated in the analog depending on the choice of projection, but that not all features can be simultaneously emulated without distortion. These findings indicate conceptual weaknesses in the idea of using analog space-times as a basis for transformation optics, and we show that a certain formulation of transformation optics closely related to a...
Class of Einstein-Maxwell-Dilaton-Axion Space-Times
2009-01-01
We use the harmonic maps ansatz to find exact solutions of the Einstein-Maxwell-Dilaton-Axion (EMDA) equations. The solutions are harmonic maps invariant to the symplectic real group in four dimensions $Sp(4,\\Rreal)\\sim O(5)$. We find solutions of the EMDA field equations for the one and two dimensional subspaces of the symplectic group. Specially, for illustration of the method, we find space-times that generalise the Schwarzschild solution with dilaton, axion and electromagnetic fields.
ROTATION CONSTELLATION FOR DIFFERENTIAL UNITARY SPACE-TIME MODULATION
Li Jun; Cao Haiyan; Wei Gang
2006-01-01
A new constellation which is the multiplication of the rotation matrix and the diagonal matrix according to the number of transmitters is proposed to increase the diversity product, the key property to the performance of the differential unitary space-time modulation. Analyses and the simulation results show that the proposed constellation performs better and 2dB or more coding gain can be achieved over the traditional cyclic constellation.
Semianalytic Solution of Space-Time Fractional Diffusion Equation
A. Elsaid
2016-01-01
Full Text Available We study the space-time fractional diffusion equation with spatial Riesz-Feller fractional derivative and Caputo fractional time derivative. The continuation of the solution of this fractional equation to the solution of the corresponding integer order equation is proved. The series solution of this problem is obtained via the optimal homotopy analysis method (OHAM. Numerical simulations are presented to validate the method and to show the effect of changing the fractional derivative parameters on the solution behavior.
Mass neutrino oscillations in Robertson-Walker space-time
Huang Xiu-Ju; Li Ze-Jun; Wang Yong-Jiu
2006-01-01
Along the geodesic we calculate the interference phase of the mass neutrinos propagating in the radial direction in Robertson-Walker space-time. Since our universe is expanding, the phase factor Φ is increasing under the condition of the same proper physical distance l. Different values of curvature parameter k in Robertson-Walker metric represent different cosmological models, correspondingly, we obtain the different interference phases.
Orbits in Homogeneous Oblate Spheroidal Gravitational Space-Time
Chifu E. N.
2009-07-01
Full Text Available The generalized Lagrangian in general relativistic homogeneous oblate spheroidal gravitational fields is constructed and used to study orbits exterior to homogenous oblate spheroids. Expressions for the conservation of energy and angular momentum for this gravitational field are obtained. The planetary equation of motion and the equation of motion of a photon in the vicinity of an oblate spheroid are derived. These equations have additional terms not found in Schwarzschild's space time.
Motion of a spinning particle in curved space-time
Kumar, S Satish
2015-01-01
The motion of spinning test-masses in curved space-time is described with a covariant hamiltonian formalism. A large class of hamiltonians can be used with the model- independent Poisson-Dirac brackets, to obtain equations of motion. Here we apply it to the minimal hamiltonian and also to a non-minimal hamiltonian, describing the gravi- tational Stern-Gerlach force. And a note on ISCO has been added.
Massless DKP fields in Riemann-Cartan space-times
Casana, R; Pimentel, B M; Lunardi, J T; Teixeira, R G
2003-01-01
We study massless Duffin-Kemmer-Petiau (DKP) fields in the context of Einstein-Cartan gravitation theory. In the case of an identically vanishing torsion (Riemannian space-times) we show that there exists local gauge symmetries which reproduce the usual gauge symmetries for the massless scalar and electromagnetic fields. On the other hand, similarly to what happens with the Maxwell theory, a non-vanishing torsion breaks the usual U(1) local gauge symmetry of the electromagnetic field.
On fractal space-time and fractional calculus
Hu Yue
2016-01-01
Full Text Available This paper gives an explanation of fractional calculus in fractal space-time. On observable scales, continuum models can be used, however, when the scale tends to a smaller threshold, a fractional model has to be adopted to describe phenomena in micro/nano structure. A time-fractional Fornberg-Whitham equation is used as an example to elucidate the physical meaning of the fractional order, and its solution process is given by the fractional complex transform.
Nuclear disassembly time scales using space time correlations
Durand, D.; Colin, J.; Lecolley, J.F.; Meslin, C.; Aboufirassi, M.; Bougault, R.; Brou, R. [Caen Univ., 14 (France). Lab. de Physique Corpusculaire; Bilwes, B.; Cosmo, F. [Strasbourg-1 Univ., 67 (France); Galin, J. [Grand Accelerateur National d`Ions Lourds (GANIL), 14 - Caen (France); and others
1996-09-01
The lifetime, {tau}, with respect to multifragmentation of highly excited nuclei is deduced from the analysis of strongly damped Pb+Au collisions at 29 MeV/u. The method is based on the study of space-time correlations induced by `proximity` effects between fragments emitted by the two primary products of the reaction and gives the time between the re-separation of the two primary products and the subsequent multifragment decay of one partner. (author). 2 refs.
Space-time cooperative diversity scheme using full feedback
SUN De-chun; YI Ke-chu; LI Xiao-hui
2009-01-01
This article proposes a new space-time cooperative diversity scheme called full feedback-based cooperative diversity scheme (FFBCD). In contrast to the conventional adaptive space-time cooperative diversity schemes that utilize the feedback from only the destination node, the new scheme utilizes the feedback from both the destination node and the cooperation node. With the feedback from the destination node, the occasional successful reception of the destination node in the information distribution stage can be detected, thus avoiding unnecessary retransmissions in the information delivery stage. The feedback from the cooperation node indicates the receiving state of the cooperation node in the information distribution stage, and the source node and the cooperation node will not perform cooperative retransmission during the information delivery stage unless the cooperation node is received successfully in the information distribution stage. In this way the new scheme can reduce the number of transmission attempt and improve the channel utilization. The expressions of the average number of transmission attempt are given. Numerical approximations and simulation results both show that the new scheme performs better than the non-cooperative scheme and the conventional adaptive space-time cooperative diversity scheme.
Differential modulation based on space-time block codes
李正权; 胡光锐
2004-01-01
A differential modulation scheme using space-time block codes is put forward. Compared with other schemes,our scheme has lower computational complexity and has a simpler decoder. In the case of three or four transmitter antennas, our scheme has a higher rate a higher coding gain and a lower bit error rate for a given rate. Then we made simulations for space-time block codes as well as group codes in the case of two, three, four and five transmit antennas. The simulations prove that using two transmit antennas, one receive antenna and code rate of 4 bits/s/Hz, the differential STBC method outperform the differential group codes method by 4 dB. Useing three, four and five transmit antennas,one receive antenna, and code rate of 3 bits/s/Hz are adopted, the differential STBC method outperform the differential group codes method by 5 dB, 6.5 dB and 7 dB, respectively. In other words, the differential modulation scheme based on space-time block code is better than the corresponding differential modulation scheme
Space-time mechanics: Quantum causal structure and expansive force
Valenzuela, Mauricio
2015-01-01
Combining twistor space and phase space formulation of quantum mechanics we propose a new framework of quantization of geometries which incorporates Wigner functions for geometrical observables. Quantizing the light-cone in 2+1D and 3+1D results in one-sheet "quantum hyperboloids". We propose that the latter rule the causal structure of the space-time, yielding uncertainty of positions and space-time curvature. The quantum hyperboloid predicts accelerated propagation of signals and effective space expansion. These effects are noticeable at scales of the quantization parameter in twistor space and negligible at much larger scales since the hyperboloid is asymptotic to the light-cone. Due to space-time non-commutativity it is necessary to introduce notions of observers which are able to determine distances in specific directions. Thus, in the perspective of a time-observer, time and radius of spatial sections of the quantum hyperboloid become discrete and bounded from below. Hence the time is quantized and punc...
A stochastic space-time model for intermittent precipitation occurrences
Sun, Ying
2016-01-28
Modeling a precipitation field is challenging due to its intermittent and highly scale-dependent nature. Motivated by the features of high-frequency precipitation data from a network of rain gauges, we propose a threshold space-time t random field (tRF) model for 15-minute precipitation occurrences. This model is constructed through a space-time Gaussian random field (GRF) with random scaling varying along time or space and time. It can be viewed as a generalization of the purely spatial tRF, and has a hierarchical representation that allows for Bayesian interpretation. Developing appropriate tools for evaluating precipitation models is a crucial part of the model-building process, and we focus on evaluating whether models can produce the observed conditional dry and rain probabilities given that some set of neighboring sites all have rain or all have no rain. These conditional probabilities show that the proposed space-time model has noticeable improvements in some characteristics of joint rainfall occurrences for the data we have considered.
Space time as a continuum with a point defect
Tartaglia, A
2006-01-01
In cosmology it has become usual to try and explain observational data, such as the temperature distribution of the cosmic microwave background or the accelerated expansion of the universe, introducing new entities as dark matter and dark energy. Here we describe a different approach treating space time as a continuum endowed with properties similar to the ones of ordinary material continua, such as internal viscosity and strain distributions originated by defects in the texture. A Lagrangian modelled on the one valid for simple dissipative phenomena in fluids is build and used for empty space time. The internal "viscosity" is shown to correspond to a four-vector field. Using the known symmetry of the universe, assuming the vector field to be divergence-less and solving the Euler-Lagrange equation we obtain directly inflation and a phase of accelerated expansion of space time. The vector field is shown to be connected with the displacement vector field induced by a point defect in a four-dimensional continuum...
The wave equation on static singular space-times
Mayerhofer, Eberhard
2006-01-01
The first part of my thesis lays the foundations to generalized Lorentz geometry. The basic algebraic structure of finite-dimensional modules over the ring of generalized numbers is investigated. The motivation for this part of my thesis evolved from the main topic, the wave equation on singular space-times. The second and main part of my thesis is devoted to establishing a local existence and uniqueness theorem for the wave equation on singular space-times. The singular Lorentz metric subject to our discussion is modeled within the special algebra on manifolds in the sense of Colombeau. Inspired by an approach to generalized hyperbolicity of conical-space times due to Vickers and Wilson, we succeed in establishing certain energy estimates, which by a further elaborated equivalence of energy integrals and Sobolev norms allow us to prove existence and uniqueness of local generalized solutions of the wave equation with respect to a wide class of generalized metrics. The third part of my thesis treats three diff...
L2 Orthogonal Space Time Code for Continuous Phase Modulation
Hesse, Matthias; Deneire, Luc
2008-01-01
To combine the high power efficiency of Continuous Phase Modulation (CPM) with either high spectral efficiency or enhanced performance in low Signal to Noise conditions, some authors have proposed to introduce CPM in a MIMO frame, by using Space Time Codes (STC). In this paper, we address the code design problem of Space Time Block Codes combined with CPM and introduce a new design criterion based on L2 orthogonality. This L2 orthogonality condition, with the help of simplifying assumption, leads, in the 2x2 case, to a new family of codes. These codes generalize the Wang and Xia code, which was based on pointwise orthogonality. Simulations indicate that the new codes achieve full diversity and a slightly better coding gain. Moreover, one of the codes can be interpreted as two antennas fed by two conventional CPMs using the same data but with different alphabet sets. Inspection of these alphabet sets lead also to a simple explanation of the (small) spectrum broadening of Space Time Coded CPM.
On the performance of diagonal lattice space-time codes
Abediseid, Walid
2013-11-01
There has been tremendous work done on designing space-time codes for the quasi-static multiple-input multiple output (MIMO) channel. All the coding design up-to-date focuses on either high-performance, high rates, low complexity encoding and decoding, or targeting a combination of these criteria [1]-[9]. In this paper, we analyze in details the performance limits of diagonal lattice space-time codes under lattice decoding. We present both lower and upper bounds on the average decoding error probability. We first derive a new closed-form expression for the lower bound using the so-called sphere lower bound. This bound presents the ultimate performance limit a diagonal lattice space-time code can achieve at any signal-to-noise ratio (SNR). The upper bound is then derived using the union-bound which demonstrates how the average error probability can be minimized by maximizing the minimum product distance of the code. Combining both the lower and the upper bounds on the average error probability yields a simple upper bound on the the minimum product distance that any (complex) lattice code can achieve. At high-SNR regime, we discuss the outage performance of such codes and provide the achievable diversity-multiplexing tradeoff under lattice decoding. © 2013 IEEE.
A hypocentral version of the space-time ETAS model
Guo, Yicun; Zhuang, Jiancang; Zhou, Shiyong
2015-10-01
The space-time Epidemic-Type Aftershock Sequence (ETAS) model is extended by incorporating the depth component of earthquake hypocentres. The depths of the direct offspring produced by an earthquake are assumed to be independent of the epicentre locations and to follow a beta distribution, whose shape parameter is determined by the depth of the parent event. This new model is verified by applying it to the Southern California earthquake catalogue. The results show that the new model fits data better than the original epicentre ETAS model and that it provides the potential for modelling and forecasting seismicity with higher resolutions.
Space, Time, Matter, and Form Essays on Aristotle's Physics
Bostock, David
2006-01-01
Space, Time, Matter, and Form collects ten of David Bostock's essays on themes from Aristotle's Physics, four of them published here for the first time. The first five papers look at issues raised in the first two books of the Physics, centred on notions of matter and form, and the idea of substance as what persists through change. They also range over other of Aristotle's scientific works, such as his biology and psychology and the account of change in his De Generatione et Corruptione. The volume's remaining essays examine themes in later books of the Physics, including infinity, place, time
Space-time combined correlation integral and earthquake interactions
L. Pietronero
2004-06-01
Full Text Available Scale invariant properties of seismicity argue for the presence of complex triggering mechanisms. We propose a new method, based on the space-time combined generalization of the correlation integral, that leads to a self-consistent visualization and analysis of both spatial and temporal correlations. The analysis has been applied on global medium-high seismicity. Results show that earthquakes do interact even on long distances and are correlated in time within defined spatial ranges varying over elapsed time. On that base we redefine the aftershock concept.
Particle propagation and effective space-time in gravity's rainbow
Garattini, Remo; Mandanici, Gianluca
2012-01-01
Based on the results obtained in our previous study on gravity’s rainbow, we determine the quantum corrections to the space-time metric for the Schwarzschild and the de Sitter background, respectively. We analyze how quantum fluctuations alter these metrics, inducing modifications on the propagation of test particles. Significantly enough, we find that quantum corrections can become relevant not only for particles approaching the Planck energy but, due to the one-loop contribution, even for low-energy particles as far as Planckian length scales are considered. We briefly compare our results with others obtained in similar studies and with the recent experimental OPERA announcement of superluminal neutrino propagation.
Particle propagation and effective space-time in Gravity's Rainbow
Garattini, Remo
2011-01-01
Basing on the results obtained in a our previous study on Gravity's Rainbow, we determine the quantum corrections to the space-time metric for the Schwarzschild and the de Sitter background, respectively. We analyze how quantum fluctuations alter these metrics inducing modifications on the propagation of test particles. Significantly enough we find that quantum corrections can become relevant not only for particles approaching the Planck energy but, due to the one loop contribution, even for low-energy particles as far as Planckian length scales are considered. We briefly compare our results with others obtained in similar studies and with the recent experimental OPERA announcement of superluminal neutrino propagation.
Gauge invariant perturbations of Petrov type D space-times
Whiting, Bernard; Shah, Abhay
2016-03-01
The Regge-Wheeler and Zerilli equations are satisfied by gauge invariant perturbations of the Schwarzschild black hole geometry. Both the perturbation of the imaginary part of Ψ2 (a component of the Weyl curvature), and its time derivative, are gauge invariant and solve the Regge-Wheeler equation with different sources. The Ψ0 and Ψ4 perturbations of the Weyl curvature are not only gauge, but also tetrad, invariant. We explore the framework in which these results hold, and consider what generalizations may extend to the Kerr geometry, and presumably to Petrov type D space-times in general. NSF Grants PHY 1205906 and 1314529, ERC (EU) FP7 Grant 304978.
Theory and practice of runoff space-time distribution
WANG; Hao; WANG; Chengming; WANG; Jianhua; QIN; Dayong; ZH
2004-01-01
Based on the domestic and foreign concerning researches, this paper submits the runoff space-time distribution theory which shows evident scientific significances and powerful practical functions. On the basis of digital basin unit cell deriving from the digital elevation model (DEM) and assumption of linear confluence, this theory has been applied successfully to the runoff correlation researches in humid regions. In order to prove the adaptability of the theory in arid and semi-drought regions,this paper is used to the runoff correlation analysis in Wuding River basin--a tributary of Yellow River Basin, and has gained preliminary effective verification.
Waveform Design and Scheduling in Space-Time Adaptive Radar
2013-01-01
is the LS estimate of s. After some straightforward matrix algebra , the solution to (25) is simplified further, i.e. ŝi = Hµh H , i = 1, 2, . . . N...L. Timmoneri, “The MVDR vectorial lattice applied to space-time processing for AEW radar with large instantaneous bandwidth,” IEE Proc. Radar, Sonar...1408–1418, Jun. 1969. [9] R. Horn and C. Johnson, Topics in Matrix Analysis. Cambridge University Press, 1994. [10] G. Strang, Linear Algebra and Its Applications. Thomson, Brooks/Cole, 2006.
Concepts of Space, Time, and Consciousness in Ancient India
Kak, S
1999-01-01
This paper describes Indian ideas of the early-Purana/Mahabharata times (centuries BC) on the nature of space, time and consciousness that would be of interest to the physicist. In order to simplify references, we quote mainly from Yoga-Vasistha (YV), which is representative of that period of Indian thought. YV professes to be a book of instruction on the nature of consciousness but it has many fascinating passages on time, space, matter and cognition. This paper presents a random selection that has parallels with recent speculations in physics. It also presents a brief account of the context in which ideas of YV developed.
Modeling of space-time focusing of localized nondiffracting pulses
Zamboni-Rached, Michel; Besieris, Ioannis M.
2016-10-01
In this paper we develop a method capable of modeling the space-time focusing of nondiffracting pulses. These pulses can possess arbitrary peak velocities and, in addition to being resistant to diffraction, can have their peak intensities and focusing positions chosen a priori. More specifically, we can choose multiple locations (spatial ranges) of space and time focalization; also, the pulse intensities can be chosen in advance. The pulsed wave solutions presented here can have very interesting applications in many different fields, such as free-space optical communications, remote sensing, medical apparatus, etc.
Space-time isogeometric analysis of parabolic evolution problems
Langer, Ulrich; Moore, Stephen E.; Neumüller, Martin
2016-07-01
We present and analyze a new stable space-time Isogeometric Analysis (IgA) method for the numerical solution of parabolic evolution equations in fixed and moving spatial computational domains. The discrete bilinear form is elliptic on the IgA space with respect to a discrete energy norm. This property together with a corresponding boundedness property, consistency and approximation results for the IgA spaces yields an a priori discretization error estimate with respect to the discrete norm. The theoretical results are confirmed by several numerical experiments with low- and high-order IgA spaces.
Harmonic Analysis on the Space-Time Gauge Continuum
Bleecker, David D.
1983-06-01
The classical Kaluza-Klein unified field theory has previously been extended to unify and geometrize gravitational and gauge fields, through a study of the geometry of a bundle space P over space-time. Here, we examine the physical relevance of the Laplace operator on the complex-valued functions on P. The spectrum and eigenspaces are shown (via the Peter-Weyl theorem) to determine the possible masses of any type of particle field. In the Euclidean case, we prove that zero-mass particles necessarily come in infinite families. Also, lower bounds on masses of particles of a given type are obtained in terms of the curvature of P.
Space-Time Reference with an Optical Link
Berceau, Paul; Taylor, Michael; Kahn, Joseph M.; Hollberg, Leo
2015-01-01
We describe a method for realizing a high-performance Space-Time Reference (STR) using a stable atomic clock in a precisely defined orbit and synchronizing the orbiting clock to high-accuracy atomic clocks on the ground. The synchronization would be accomplished using a two-way lasercom link between ground and space. The basic concept is to take advantage of the highest-performance cold-atom atomic clocks at national standards laboratories on the ground and to transfer that performance to an ...
THE SPACE-TIME FINITE ELEMENT METHOD FOR PARABOLIC PROBLEMS
李宏; 刘儒勋
2001-01-01
Adaptive space-time finite element method, continuous in space but discontinuous in time for semi-linear parabolic problems is discussed. The approach is based on a combination of finite element and finite difference techniques. The existence and uniqueness of the weak solution are proved without any assumptions on choice of the spacetime meshes. Basic error estimates in L∞ (L2) norm, that is maximum-norm in time, L2norm in space are obtained. The numerical results are given in the last part and the analysis between theoretic and experimental results are obtained.
Asymptotically Flat Space-Times and its Hidden Recesses: An Enigma from GR
Newman, Ezra T
2016-01-01
We begin by emphasizing that we are dealing with standard Einstein or Einstein-Maxwell theory - absolutely no new physics has been inserted. The fresh item is that the well-known asymptotically flat solutions of the Einstein-Maxwell theory are transformed to a new coordinate system with surprising and (seemingly) inexplicable results. We begin with the standard description of (Null) Asymptotically Flat Space-Times described in conventional Bondi-coordinates. After transforming the variables (mainly the asymptotic Weyl tensor components) to a very special set of NU (Newman-Unti) coordinates, we find a series of relations totally mimicking standard Newtonian classical mechanics and Maxwell theory. The surprising and troubling aspect of these relations is that the associated motion and radiation does not take place in physical space-time. Instead these relations takes place in an unusual inherited complex four-dimensional manifold referred to as H-Space that has no immediate relationship with space-time. In fact...
Space-Time Transfinite Interpolation of Volumetric Material Properties.
Sanchez, Mathieu; Fryazinov, Oleg; Adzhiev, Valery; Comninos, Peter; Pasko, Alexander
2015-02-01
The paper presents a novel technique based on extension of a general mathematical method of transfinite interpolation to solve an actual problem in the context of a heterogeneous volume modelling area. It deals with time-dependent changes to the volumetric material properties (material density, colour, and others) as a transformation of the volumetric material distributions in space-time accompanying geometric shape transformations such as metamorphosis. The main idea is to represent the geometry of both objects by scalar fields with distance properties, to establish in a higher-dimensional space a time gap during which the geometric transformation takes place, and to use these scalar fields to apply the new space-time transfinite interpolation to volumetric material attributes within this time gap. The proposed solution is analytical in its nature, does not require heavy numerical computations and can be used in real-time applications. Applications of this technique also include texturing and displacement mapping of time-variant surfaces, and parametric design of volumetric microstructures.
Space-time reference with an optical link
Berceau, P.; Taylor, M.; Kahn, J.; Hollberg, L.
2016-07-01
We describe a concept for realizing a high performance space-time reference using a stable atomic clock in a precisely defined orbit and synchronizing the orbiting clock to high-accuracy atomic clocks on the ground. The synchronization would be accomplished using a two-way lasercom link between ground and space. The basic approach is to take advantage of the highest-performance cold-atom atomic clocks at national standards laboratories on the ground and to transfer that performance to an orbiting clock that has good stability and that serves as a ‘frequency-flywheel’ over time-scales of a few hours. The two-way lasercom link would also provide precise range information and thus precise orbit determination. With a well-defined orbit and a synchronized clock, the satellite could serve as a high-accuracy space-time reference, providing precise time worldwide, a valuable reference frame for geodesy, and independent high-accuracy measurements of GNSS clocks. Under reasonable assumptions, a practical system would be able to deliver picosecond timing worldwide and millimeter orbit determination, and could serve as an enabling subsystem for other proposed space-gravity missions, which are briefly reviewed.
Space-Time Reference with an Optical Link
Berceau, Paul; Kahn, Joseph M; Hollberg, Leo
2015-01-01
We describe a method for realizing a high-performance Space-Time Reference (STR) using a stable atomic clock in a precisely defined orbit and synchronizing the orbiting clock to high-accuracy atomic clocks on the ground. The synchronization would be accomplished using a two-way lasercom link between ground and space. The basic concept is to take advantage of the highest-performance cold-atom atomic clocks at national standards laboratories on the ground and to transfer that performance to an orbiting clock that has good stability and that serves as a "frequency-flywheel" over time-scales of a few hours. The two-way lasercom link would also provide precise range information and thus precise orbit determination (POD). With a well-defined orbit and a synchronized clock, the satellite cold serve as a high-accuracy Space-Time Reference, providing precise time worldwide, a valuable reference frame for geodesy, and independent high-accuracy measurements of GNSS clocks. With reasonable assumptions, a practical system...
Elementary Quantum Mechanics in a Space-time Lattice
Bhatia, Manjit
2010-01-01
Studies of quantum fields and gravity suggest the existence of a minimal length, such as Planck length \\cite{Floratos,Kempf}. It is natural to ask how the existence of a minimal length may modify the results in elementary quantum mechanics (QM) problems familiar to us \\cite{Gasiorowicz}. In this paper we address a simple problem from elementary non-relativistic quantum mechanics, called "particle in a box", where the usual continuum (1+1)-space-time is supplanted by a space-time lattice. Our lattice consists of a grid of $\\lambda_0 \\times \\tau_0 $ rectangles, where $\\lambda_0$, the lattice parameter, is a fundamental length (say Planck length) and, we take $\\tau_0$ to be equal to $\\lambda_0/c$. The corresponding Schrodinger equation becomes a difference equation, the solution of which yields the $q$-eigenfunctions and $q$-eigenvalues of the energy operator as a function of $\\lambda_0 $. The $q$-eigenfunctions form an orthonormal set and both $q$-eigenfunctions and $q$-eigenvalues reduce to continuum solutions...
Cosmic microwave background polarization in Noncommutative space-time
Batebi, S; Mohammadi, R; Tizchang, S
2016-01-01
In the standard model of cosmology (SMC) the B-mode polarization of the CMB can be explained by the gravitational effects in the inflation epoch. However, this is not the only way to explain the B-mode polarization for the CMB. It can be shown that the Compton scattering in presence of a background besides generating a circularly polarized microwave, can leads to a B-mode polarization for the CMB. Here we consider the non-commutative (NC) space time as a background to explore the CMB polarization at the last scattering surface. We obtain the B-mode spectrum of the CMB radiation by scalar perturbation of metric via a correction on the Compton scattering in NC-space-time in terms of the circular polarization power spectrum and the non-commutative energy scale. It can be shown that even for the NC-scale as large as $10TeV$ the NC-effects on the CMB polarization and the r-parameter is significant. We show that the V-mode power spectrum can be obtained in terms of linearly polarized power spectrum in the range Mic...
Canonical quantum gravity on noncommutative space-time
Kober, Martin
2015-06-01
In this paper canonical quantum gravity on noncommutative space-time is considered. The corresponding generalized classical theory is formulated by using the Moyal star product, which enables the representation of the field quantities depending on noncommuting coordinates by generalized quantities depending on usual coordinates. But not only the classical theory has to be generalized in analogy to other field theories. Besides, the necessity arises to replace the commutator between the gravitational field operator and its canonical conjugated quantity by a corresponding generalized expression on noncommutative space-time. Accordingly the transition to the quantum theory has also to be performed in a generalized way and leads to extended representations of the quantum theoretical operators. If the generalized representations of the operators are inserted to the generalized constraints, one obtains the corresponding generalized quantum constraints including the Hamiltonian constraint as dynamical constraint. After considering quantum geometrodynamics under incorporation of a coupling to matter fields, the theory is transferred to the Ashtekar formalism. The holonomy representation of the gravitational field as it is used in loop quantum gravity opens the possibility to calculate the corresponding generalized area operator.
Space-time measures for subluminal and superluminal motions
Calvo-Mozo, Benjam\\'\\in
2014-01-01
In present work we examine the implications on both, space-time measures and causal structure, of a generalization of the local causality postulate by asserting its validity to all motion regimes, the subluminal and superluminal ones. The new principle implies the existence of a denumerable set of metrical null cone speeds, \\{$c_k\\}$, where $c_1$ is the speed of light in vacuum, and $c_k/c \\simeq \\epsilon^{-k+1}$ for $k\\geq2$, where $\\epsilon^2$ is a tiny dimensionless constant which we introduce to prevent the divergence of the $x, t$ measures in Lorentz transformations, such that their generalization keeps $c_k$ invariant and as the top speed for every regime of motion. The non divergent factor $\\gamma_k$ equals $k\\epsilon^{-1}$ at speed $c_k$. We speak then of $k-$timelike and $k-$null intervals and of k-timelike and k-null paths on space-time, and construct a causal structure for each regime. We discuss also the possible transition of a material particle from the subluminal to the first superluminal regim...
Pion charge form factor and constraints from space-time translations
Desplanques, Bertrand
2010-01-01
The role of Poincar\\'e covariant space-time translations is investigated in the case of a relativistic quantum mechanics approach to the pion charge form factor. It is shown that the related constraints are generally inconsistent with the assumption of a single-particle current, which is most often referred to. The only exception is the front-form approach with $q^+=0$. How accounting for the related constraints, as well as restoring the equivalence of different RQM approaches in estimating form factors, is discussed. Some extensions of this work and, in particular, the relationship with a dispersion-relation approach, are presented. Conclusions relative to the underlying dynamics are given.
Gauge-invariant extensions of the Proca model in a noncommutative space-time
Abreu, Everton M C; Fernandes, Rafael L; Mendes, Albert C R
2016-01-01
The gauge invariance analysis of theories described in noncommutative (NC) space-times can lead us to interesting results since noncommutativity is one of the possible paths to investigate quantum effects in classical theories such as general relativity, for example. This theoretical possibility has motivated us to analyze the gauge invariance of the NC version of the Proca model, which is a second-class system, in Dirac's classification, since its classical formulation (commutative space-time) has its gauge invariance broken thanks to the mass term. To obtain such gauge invariant model, we have used the gauge unfixing method to construct a first-class NC version of the Proca model. We have also questioned if the gauge symmetries of NC theories, are affected necessarily or not by the NC parameter. In this way, we have calculated its respective symmetries in a standard way via Poisson brackets.
Iterative multi-user detection and decoding for space-time block coding systems
JIN Yi-dan; ZHANG Feng; WU Wei-ling
2006-01-01
To restrain the interference of co-channel users using space-time block coding (STBC), the proposed Gaussian-forcing soft decision multi-user detection (GFSDMUD) algorithm is applied in flat-fading channels by using the relation among the users' signals, which can enhance the capacity by introducing co-channel users. During iterations, extrinsic information is calculated and exchanged between a soft multi-user detector and a bank of turbo decoders to achieve refined estimates of the users' signals. The simulations show that the proposed iterative receiver techniques provide significant performance improvement around 2 dB over conventional noniterative methods. Furthermore, iterative multi-user space-time processing techniques offer substantial performance gains around 8 dB by adding the number of receiver antennas from 4to 6, and the system performance can be enhanced by using this strategy in multi-user STBC systems, which is very important for enlarging the system capacity.
The global existence of Yang-Mills fields on curved space-times
Ghanem, Sari
2013-01-01
This is an introductory chapter in a series in which we take a systematic study of the Yang-Mills equations on curved space-times. In this first, we provide standard material that consists in writing the proof of the global existence of Yang-Mills fields on arbitrary curved space-times using the Klainerman-Rodnianski parametrix combined with suitable Gr\\"onwall type inequalities. While the Chru\\'sciel-Shatah argument requires a simultaneous control of the $L^{\\infty}_{loc}$ and the $H^{2}_{loc}$ norms of the Yang-Mills curvature, we can get away by controlling only the $H^{1}_{loc}$ norm instead, and write a new gauge independent proof on arbitrary, fixed, sufficiently smooth, globally hyperbolic, curved 4-dimensional Lorentzian manifolds. This manuscript is written in an expository way in order to provide notes to Master's level students willing to learn mathematical General Relativity.
The Framework, Causal and Co-compact Structure of Space-time
Kovár, Martin
2013-01-01
We introduce a canonical, compact topology, which we call weakly causal, naturally generated by the causal site of J. D. Christensen and L. Crane, a pointless algebraic structure motivated by certain problems of quantum gravity. We show that for every four-dimensional globally hyperbolic Lorentzian manifold there exists an associated causal site, whose weakly causal topology is co-compact with respect to the manifold topology and vice versa. Thus, the causal site has the full information about the topology of space-time, represented by the Lorentzian manifold. In addition, we show that there exist also non-Lorentzian causal sites (whose causal relation is not a continuous poset) and so the weakly causal topology and its de Groot dual extends the usual manifold topology of space-time beyond topologies generated by the traditional, smooth model. As a source of inspiration in topologizing the studied causal structures, we use some methods and constructions of general topology and formal concept analysis.
Asymptotics with a positive cosmological constant: II. Linear fields on de Sitter space-time
Ashtekar, Abhay; Kesavan, Aruna
2015-01-01
Linearized gravitational waves in de Sitter space-time are analyzed in detail to obtain guidance for constructing the theory of gravitational radiation in presence of a positive cosmological constant in full, nonlinear general relativity. Specifically: i) In the exact theory, the intrinsic geometry of $\\scri$ is often assumed to be conformally flat in order to reduce the asymptotic symmetry group from $\\Diff$ to the de Sitter group. Our {results show explicitly} that this condition is physically unreasonable; ii) We obtain expressions of energy-momentum and angular momentum fluxes carried by gravitational waves in terms of fields defined at $\\scrip$; iii) We argue that, although energy of linearized gravitational waves can be arbitrarily negative in general, gravitational waves emitted by physically reasonable sources carry positive energy; and, finally iv) We demonstrate that the flux formulas reduce to the familiar ones in Minkowski space-time in spite of the fact that the limit $\\Lambda \\to 0$ is discontin...
Gauge-invariant extensions of the Proca model in a noncommutative space-time
Abreu, Everton M. C.; Neto, Jorge Ananias; Fernandes, Rafael L.; Mendes, Albert C. R.
2016-09-01
The gauge invariance analysis of theories described in noncommutative (NC) space-times can lead us to interesting results since noncommutativity is one of the possible paths to investigate quantum effects in classical theories such as general relativity, for example. This theoretical possibility has motivated us to analyze the gauge invariance of the NC version of the Proca model, which is a second-class system, in Dirac’s classification, since its classical formulation (commutative space-time) has its gauge invariance broken thanks to the mass term. To obtain such gauge invariant model, we have used the gauge unfixing method to construct a first-class NC version of the Proca model. We have also questioned if the gauge symmetries of NC theories are affected necessarily or not by the NC parameter. In this way, we have calculated its respective symmetries in a standard way via Poisson brackets.
Mixer-Duplexer-Antenna Leaky-Wave System Based on Periodic Space-Time Modulation
Taravati, Sajjad
2016-01-01
We present a mixer-duplexer-antenna leaky-wave system based on periodic space-time modulation. This system operates as a full transceiver, where the upconversion and downconversion mixing operations are accomplished via space-time transitions, the duplexing operation is induced by the nonreciprocal nature of the structure, and the radiation operation is provided by the leaky-wave nature of the wave. A rigorous electromagnetic solution is derived for the dispersion relation and field distributions. The system is implemented in the form of a spatio-temporally modulated microstrip leaky-wave structure incorporating an array of sub-wavelengthly spaced varactors modulated by a harmonic wave. In addition to the overall mixer-duplexer-antenna operation, frequency beam scanning at fixed input frequency is demonstrated as one of the interesting features of the system. A prototype is realized and demonstrated by full-wave and experimental results.
Schmitz, Oliver; Soenario, Ivan; Vaartjes, Ilonca; Strak, Maciek; Hoek, Gerard; Brunekreef, Bert; Dijst, Martin; Karssenberg, Derek
2016-04-01
Air pollution is one of the major concerns for human health. Associations between air pollution and health are often calculated using long-term (i.e. years to decades) information on personal exposure for each individual in a cohort. Personal exposure is the air pollution aggregated along the space-time path visited by an individual. As air pollution may vary considerably in space and time, for instance due to motorised traffic, the estimation of the spatio-temporal location of a persons' space-time path is important to identify the personal exposure. However, long term exposure is mostly calculated using the air pollution concentration at the x, y location of someone's home which does not consider that individuals are mobile (commuting, recreation, relocation). This assumption is often made as it is a major challenge to estimate space-time paths for all individuals in large cohorts, mostly because limited information on mobility of individuals is available. We address this issue by evaluating multiple approaches for the calculation of space-time paths, thereby estimating the personal exposure along these space-time paths with hyper resolution air pollution maps at national scale. This allows us to evaluate the effect of the space-time path and resulting personal exposure. Air pollution (e.g. NO2, PM10) was mapped for the entire Netherlands at a resolution of 5×5 m2 using the land use regression models developed in the European Study of Cohorts for Air Pollution Effects (ESCAPE, http://escapeproject.eu/) and the open source software PCRaster (http://www.pcraster.eu). The models use predictor variables like population density, land use, and traffic related data sets, and are able to model spatial variation and within-city variability of annual average concentration values. We approximated space-time paths for all individuals in a cohort using various aggregations, including those representing space-time paths as the outline of a persons' home or associated parcel
Minkowski's Road to Space-Time, and its Consequences and an Alternative
Smith, Felix T.
2014-03-01
The road from Maxwell's equations to early relativity and then to Minkowski's space-time is traced through his Göttingen lecture in 1907 and his paper in 1908 that introduced the 4-dimensional tensor form of electrodynamics. This led to a puzzle: What is the reason for the time dependence in its position space geometry shown in the metric sum ds2 = dx12 + dx22 + dx32 -c2 dt2 ? Having no physical explanation for this, Minkowski made the drastic move of enlarging 3-space into 4-dimensional space-time, advocating it powerfully in his paper ``Space and Time'' (1909). I will discuss the circumstances that led to its rapid acceptance (but not by Poincaré), and its consequences that emerged much later in the partial disconnect between relativity and the other domains of modern physics. Much later still, the Hubble expansion of our cosmos can now be shown to imply that the term -c2 dt2 is a direct concomitant of an expanding, negatively curved 3-space and does not require either a 4-dimensional space-time or multiple time dimensions for multiple particles.
On the stability of scalar-vacuum space-times
Bronnikov, K A; Zhidenko, A
2011-01-01
We study the stability of static, spherically symmetric solutions to the Einstein equations with a scalar field as the source. We describe a general methodology of studying small radial perturbations of scalar-vacuum configurations with arbitrary potentials $V(\\phi)$, and in particular space-times with throats (including wormholes), which are possible if the scalar is phantom. At such a throat, the effective potential for perturbations $V_{eff}$ is known to have a positive pole (a potential wall) that prevents a complete perturbation analysis. We show that, generically, (i) $V_{eff}$ has precisely the form required for regularization by the known S-deformation method, and (ii) a solution with the regularized potential leads to regular scalar field and metric perturbations of the initial configuration. As a particular example, we prove the instability of all static solutions with both normal and phantom scalars and $V(\\phi) \\equiv 0$, under spherically symmetric perturbations. We thus confirm the previous resu...
Effects of quantum space time foam in the neutrino sector
Klapdor-Kleingrothaus, H V; Sarkar, U
2000-01-01
We discuss violations of CPT and quantum mechanics due to interactions of neutrinos with space-time quantum foam. Neutrinoless double beta decay and oscillations of neutrinos from astrophysical sources (supernovae, active galactic nuclei) are analysed. It is found that the propagation distance is the crucial quantity entering any bounds on EHNS parameters. Thus, while the bounds from neutrinoless double beta decay are not significant, the data of the supernova 1987a imply a bound being several orders of magnitude more stringent than the ones known from the literature. Even more stringent limits may be obtained from the investigation of neutrino oscillations from active galactic nuclei sources, which have an impressive potential for the search of quantum foam interactions in the neutrino sector.
Emergent Space-Time via a Geometric Renormalization Method
Rastgoo, Saeed
2016-01-01
We present a purely geometric renormalization scheme for metric spaces (including uncolored graphs), which consists of a coarse graining and a rescaling operation on such spaces. The coarse graining is based on the concept of quasi-isometry, which yields a sequence of discrete coarse grained spaces each having a continuum limit under the rescaling operation. We provide criteria under which such sequences do converge within a superspace of metric spaces, or may constitute the basin of attraction of a common continuum limit, which hopefully, may represent our space-time continuum. We discuss some of the properties of these coarse grained spaces as well as their continuum limits, such as scale invariance and metric similarity, and show that different layers of spacetime can carry different distance functions while being homeomorphic. Important tools in this analysis are the Gromov-Hausdorff distance functional for general metric spaces and the growth degree of graphs or networks. The whole construction is in the...
Computational Complexity of Decoding Orthogonal Space-Time Block Codes
Ayanoglu, Ender; Karipidis, Eleftherios
2009-01-01
The computational complexity of optimum decoding for an orthogonal space-time block code G satisfying the orthogonality property that the Hermitian transpose of G multiplied by G is equal to a constant c times the sum of the squared symbols of the code times an identity matrix, where c is a positive integer is quantified. Four equivalent techniques of optimum decoding which have the same computational complexity are specified. Modifications to the basic formulation in special cases are calculated and illustrated by means of examples. This paper corrects and extends [1],[2], and unifies them with the results from the literature. In addition, a number of results from the literature are extended to the case c > 1.
Entanglement, space-time and the Mayer-Vietoris theorem
Patrascu, Andrei T.
2017-06-01
Entanglement appears to be a fundamental building block of quantum gravity leading to new principles underlying the nature of quantum space-time. One such principle is the ER-EPR duality. While supported by our present intuition, a proof is far from obvious. In this article I present a first step towards such a proof, originating in what is known to algebraic topologists as the Mayer-Vietoris theorem. The main result of this work is the re-interpretation of the various morphisms arising when the Mayer-Vietoris theorem is used to assemble a torus-like topology from more basic subspaces on the torus in terms of quantum information theory resulting in a quantum entangler gate (Hadamard and c-NOT).
Space-time CFTs from the Riemann sphere
Adamo, Tim; Monteiro, Ricardo; Paulos, Miguel F.
2017-08-01
We consider two-dimensional chiral, first-order conformal field theories governing maps from the Riemann sphere to the projective light cone inside Minkowski space — the natural setting for describing conformal field theories in two fewer dimensions. These theories have a SL(2) algebra of local bosonic constraints which can be supplemented by additional fermionic constraints depending on the matter content of the theory. By computing the BRST charge associated with gauge fixing these constraints, we find anomalies which vanish for specific target space dimensions. These critical dimensions coincide precisely with those for which (biadjoint) cubic scalar theory, gauge theory and gravity are classically conformally invariant. Furthermore, the BRST cohomology of each theory contains vertex operators for the full conformal multiplets of single field insertions in each of these space-time CFTs. We give a prescription for the computation of three-point functions, and compare our formalism with the scattering equations approach to on-shell amplitudes.
Emergent space-time and the supersymmetric index
Benjamin, Nathan; Keller, Christoph; Paquette, Natalie M
2015-01-01
It is of interest to find criteria on a 2d CFT which indicate that it gives rise to emergent gravity in a macroscopic 3d AdS space via holography. Symmetric orbifolds in the large $N$ limit have partition functions which are consistent with an emergent space-time string theory with $L_{\\rm string} \\sim L_{\\rm AdS}$. For supersymmetric CFTs, the elliptic genus can serve as a sensitive probe of whether the SCFT admits a large radius gravity description with $L_{\\rm string} \\ll L_{\\rm AdS}$ after one deforms away from the symmetric orbifold point in moduli space. We discuss several classes of constructions whose elliptic genera strongly hint that gravity with $L_{\\rm Planck} \\ll L_{\\rm string} \\ll L_{\\rm AdS}$ can emerge at suitable points in moduli space.
Quantum processes, space-time representation and brain dynamics
Roy, Sisir; Roy, Sisir; Kafatos, Menas
2003-01-01
The recent controversy of applicability of quantum formalism to brain dynamics has been critically analysed. The prerequisites for any type of quantum formalism or quantum field theory is to investigate whether the anatomical structure of brain permits any kind of smooth geometric notion like Hilbert structure or four dimensional Minkowskian structure for quantum field theory. The present understanding of brain function clearly denies any kind of space-time representation in Minkowskian sense. However, three dimensional space and one time can be assigned to the neuromanifold and the concept of probabilistic geometry is shown to be appropriate framework to understand the brain dynamics. The possibility of quantum structure is also discussed in this framework.
Curved Space-Times by Crystallization of Liquid Fiber Bundles
Hélein, Frédéric; Vey, Dimitri
2017-01-01
Motivated by the search for a Hamiltonian formulation of Einstein equations of gravity which depends in a minimal way on choices of coordinates, nor on a choice of gauge, we develop a multisymplectic formulation on the total space of the principal bundle of orthonormal frames on the 4-dimensional space-time. This leads quite naturally to a new theory which takes place on 10-dimensional manifolds. The fields are pairs of ((α ,ω ),π), where (α ,ω ) is a 1-form with coefficients in the Lie algebra of the Poincaré group and π is an 8-form with coefficients in the dual of this Lie algebra. The dynamical equations derive from a simple variational principle and imply that the 10-dimensional manifold looks locally like the total space of a fiber bundle over a 4-dimensional base manifold. Moreover this base manifold inherits a metric and a connection which are solutions of a system of Einstein-Cartan equations.
Emergent space-time and the supersymmetric index
Benjamin, Nathan; Kachru, Shamit [Stanford Institute for Theoretical Physics,Department of Physics, Stanford University, Palo Alto, CA 94305 (United States); Keller, Christoph A. [Department of Mathematics, ETH Zurich,CH-8092 Zurich (Switzerland); Paquette, Natalie M. [Stanford Institute for Theoretical Physics,Department of Physics, Stanford University, Palo Alto, CA 94305 (United States)
2016-05-26
It is of interest to find criteria on a 2d CFT which indicate that it gives rise to emergent gravity in a macroscopic 3d AdS space via holography. Symmetric orbifolds in the large N limit have partition functions which are consistent with an emergent space-time string theory with L{sub string}∼L{sub AdS}. For supersymmetric CFTs, the elliptic genus can serve as a sensitive probe of whether the SCFT admits a large radius gravity description with L{sub string}≪L{sub AdS} after one deforms away from the symmetric orbifold point in moduli space. We discuss several classes of constructions whose elliptic genera strongly hint that gravity with L{sub Planck}≪L{sub string}≪L{sub AdS} can emerge at suitable points in moduli space.
Holographic Space-time Models in $1 + 1$ Dimensions
Banks, T
2015-01-01
We construct Holographic Space-time models that reproduce the dynamics of $1 + 1$ dimensional string theory. The necessity for a dilaton field in the $1 + 1$ effective Lagrangian for classical geometry, the appearance of fermions, and even the form of the universal potential in the canonical $1$ matrix model, follow from general HST considerations. We note that 't Hooft's ansatz for the leading contribution to the black hole S-matrix, accounts for the entire S-matrix in these models in the limit that the string scale coincides with the Planck scale, up to transformations between near horizon and asymptotic coordinates. These $1 + 1$ dimensional models are describable as decoupling limits of the near horizon geometry of higher dimensional extremal black holes or black branes, and this suggests that deformations of the simplest model are equally physical. After proposing a notion of "relevant deformations", we describe deformations, which contain excitations corresponding to linear dilaton black holes, some of ...
Galactic Dark Matter and Bertrand Space-times
Dey, Dipanjan; Sarkar, Tapobrata
2013-01-01
Bertrand space-times (BSTs) are static, spherically symmetric solutions of Einstein's equations, that admit stable, closed orbits. Starting from the fact that to a good approximation, stars in the disc or halo regions of typical galaxies move in such orbits, we propose that, under certain physical assumptions, the dark matter distribution of some low surface brightness (LSB) galaxies can seed a particular class of BSTs. In the Newtonian limit, it is shown that for flat rotation curves, our proposal leads to an analytic prediction of the NFW dark matter profile. We further show that the dark matter distribution that seeds the BST, is described by a two-fluid anisotropic model, and present its analytic solution. A new solution of the Einstein's equations, with an internal BST and an external Schwarzschild metric, is also constructed.
Fermions in odd space-time dimensions: back to basics
Bashir, A; Galicia, Ma. de Jesus Anguiano
2005-01-01
It is a well known feature of odd space-time dimensions $d$ that there exist two inequivalent fundamental representations $A$ and $B$ of the Dirac gamma matrices. Moreover, the parity transformation swaps the fermion fields living in $A$ and $B$. As a consequence, a parity invariant Lagrangian can only be constructed by incorporating both the representations. Based upon these ideas and contrary to long held belief, we show that in addition to a discrete exchange symmetry for the massless case, we can also define chiral symmetry provided the Lagrangian contains fields corresponding to both the inequivalent representations. We also study the transformation properties of the corresponding chiral currents under parity and charge conjugation operations. We work explicitly in 2+1 dimensions and later show how some of these ideas generalize to an arbitrary number of odd dimensions.
Space, time and the limits of human understanding
Ghirardi, Giancarlo
2017-01-01
In this compendium of essays, some of the world’s leading thinkers discuss their conceptions of space and time, as viewed through the lens of their own discipline. With an epilogue on the limits of human understanding, this volume hosts contributions from six or more diverse fields. It presumes only rudimentary background knowledge on the part of the reader. Time and again, through the prism of intellect, humans have tried to diffract reality into various distinct, yet seamless, atomic, yet holistic, independent, yet interrelated disciplines and have attempted to study it contextually. Philosophers debate the paradoxes, or engage in meditations, dialogues and reflections on the content and nature of space and time. Physicists, too, have been trying to mold space and time to fit their notions concerning micro- and macro-worlds. Mathematicians focus on the abstract aspects of space, time and measurement. While cognitive scientists ponder over the perceptual and experiential facets of our consciousness of spac...
Momentum-subtraction renormalization techniques in curved space-time
Foda, O.
1987-10-01
Momentum-subtraction techniques, specifically BPHZ and Zimmermann's Normal Product algorithm, are introduced as useful tools in the study of quantum field theories in the presence of background fields. In a model of a self-interacting massive scalar field, conformally coupled to a general asymptotically-flat curved space-time with a trivial topology, momentum-subtractions are shown to respect invariance under general coordinate transformations. As an illustration, general expressions for the trace anomalies are derived, and checked by explicit evaluation of the purely gravitational contributions in the free field theory limit. Furthermore, the trace of the renormalized energy-momentum tensor is shown to vanish at the Gell-Mann Low eigenvalue as it should.
Space--times with distribution valued curvature tensors
Taub, A.H.
1980-06-01
A space--time in which in an admissible coordinate system the metric tensor is continuous but has a finite jump in its first and second derivatives across a submanifold will have a curvature tensor containing a Dirac delta function. The support of this distribution may be of three, two, or one dimension or may even consist of a single event. Lichnerowicz's formalism for dealing with such tensors is modified so as to obtain a formalism in which the Bianchi identities are satisfied in the sense of distributions. The resulting formalism is then applied to the discussion of the Einstein field equations for problems in which the source of the gravitational field is given by a distribution valued stress-energy tensor. Gravitational shocks are also discussed and their theory is compared with that of high-frequency gravitational waves given by Y. Choquet-Bruhat. By considering a class of line sources as obtainable from cylindrical shells by a limiting process, as was proposed by Israel, one may use the distribution formalism developed for hypersurfaces to treat line sources. The line source model proposed by Israel to represent the Kerr metric in the neighborhood of its singular disk is shown to lead to a gravitational mass and angular momentum inconsistent with those of the latter metric. It is proposed to remove this difficulty by changing the assumptions made by Israel concerning the nature of the space--time inside the cylindrical shell which is the support of the distribution in the curvature tensor. The details of the effect of this change are not given in this paper.
Emergent space-time via a geometric renormalization method
Rastgoo, Saeed; Requardt, Manfred
2016-12-01
We present a purely geometric renormalization scheme for metric spaces (including uncolored graphs), which consists of a coarse graining and a rescaling operation on such spaces. The coarse graining is based on the concept of quasi-isometry, which yields a sequence of discrete coarse grained spaces each having a continuum limit under the rescaling operation. We provide criteria under which such sequences do converge within a superspace of metric spaces, or may constitute the basin of attraction of a common continuum limit, which hopefully may represent our space-time continuum. We discuss some of the properties of these coarse grained spaces as well as their continuum limits, such as scale invariance and metric similarity, and show that different layers of space-time can carry different distance functions while being homeomorphic. Important tools in this analysis are the Gromov-Hausdorff distance functional for general metric spaces and the growth degree of graphs or networks. The whole construction is in the spirit of the Wilsonian renormalization group (RG). Furthermore, we introduce a physically relevant notion of dimension on the spaces of interest in our analysis, which, e.g., for regular lattices reduces to the ordinary lattice dimension. We show that this dimension is stable under the proposed coarse graining procedure as long as the latter is sufficiently local, i.e., quasi-isometric, and discuss the conditions under which this dimension is an integer. We comment on the possibility that the limit space may turn out to be fractal in case the dimension is noninteger. At the end of the paper we briefly mention the possibility that our network carries a translocal far order that leads to the concept of wormhole spaces and a scale dependent dimension if the coarse graining procedure is no longer local.
Space-Time Fractional Diffusion-Advection Equation with Caputo Derivative
José Francisco Gómez Aguilar
2014-01-01
Full Text Available An alternative construction for the space-time fractional diffusion-advection equation for the sedimentation phenomena is presented. The order of the derivative is considered as 0<β, γ≤1 for the space and time domain, respectively. The fractional derivative of Caputo type is considered. In the spatial case we obtain the fractional solution for the underdamped, undamped, and overdamped case. In the temporal case we show that the concentration has amplitude which exhibits an algebraic decay at asymptotically large times and also shows numerical simulations where both derivatives are taken in simultaneous form. In order that the equation preserves the physical units of the system two auxiliary parameters σx and σt are introduced characterizing the existence of fractional space and time components, respectively. A physical relation between these parameters is reported and the solutions in space-time are given in terms of the Mittag-Leffler function depending on the parameters β and γ. The generalization of the fractional diffusion-advection equation in space-time exhibits anomalous behavior.
Measuring space-time fuzziness with high energy γ-ray detectors
Cattaneo Paolo Walter
2017-01-01
Full Text Available There are several suggestions to probe space-time fuzziness (also known as space-time foam due to the quantum mechanics nature of space-time. These effects are predicted to be very small, being related to the Planck length, so that the only hope to experimentally detect them is to look at particles propagating along cosmological distances. Some phenomenological approaches suggest that photons originating from pointlike sources at cosmological distance experience path length fluctuation that could be detected. Also the direction of flight of such photons may be subject to a dispersion such that the image of a point-like source is blurred and detected as a disk. An experimentally accessible signature may be images of point-like sources larger that the size due to the Point Spread Function of the instrument. This additional broadening should increase with distance and photon energy. Some concrete examples that can be studied with the AGILE and FERMI-LAT γ -ray satellite experiments are discussed.
A Short Essay on Quantum Black Holes and Underlying Noncommutative Quantized Space-Time
Tanaka, Sho
2015-01-01
In our preceding paper, "Where does Black- Hole Entropy Lie? - Some Remarks on Area-Entropy Law, Holographic Principle and Noncommutative Space-Time" (Eur. Phys. J. Plus (2014) {\\bf 129}: 11), we emphasized the importance of underlying noncommutative geometry or Lorenz-covariant quantized space-time towards ultimate theory of quantum gravity and Planck scale physics. We focused there our attention on the {\\it statistical} and {\\it substantial} understanding of Bekenstein-Hawking's Area-Entropy Law of black holes on the bases of Kinematical Holographic Relation [KHR] which holds in Yang's quantized space-time. [KHR] really plays an important role in our approach in place of the familiar hypothesis, so called Holographic Principle. In the present paper, we find out a unified form of [KHR] applicable to the whole region ranging from macroscopic to microscopic scales of black holes in spatial dimension $ d=3.$ We notice the existence and behavior of two kinds of temperatures of black holes, $T_{H.R.}$ and $T_S,$ ...
Moller Energy-Momentum Prescription for a Locally Rotationally Symmetric Space-Time
Aydogdu, O
2006-01-01
The energy distribution in the Locally Rotationally Symmetric (LRS) Bianchi type II space-time is obtained by considering the Moller energy-momentum definition in both Einstein's theory of general relativity and teleparallel theory of relativity. The energy distribution which includes both the matter and gravitational field is found to be zero in both of these different gravitation theories. This result agrees with previous works of Cooperstock and Israelit, Rosen, Johri et al., Banerjee and Sen, Vargas, and Aydogdu and Salti. Our result that the total energy of the universe is zero supports the view points of Albrow and Tryon.
Exact holographic mapping and emergent space-time geometry
Qi, Xiao-Liang
2013-01-01
In this paper, we propose an {\\it exact holographic mapping} which is a unitary mapping from the Hilbert space of a lattice system in flat space (boundary) to that of another lattice system in one higher dimension (bulk). By defining the distance in the bulk system from two-point correlation functions, we obtain an emergent bulk space-time geometry that is determined by the boundary state and the mapping. As a specific example, we study the exact holographic mapping for $(1+1)$-dimensional lattice Dirac fermions and explore the emergent bulk geometry corresponding to different boundary states including massless and massive states at zero temperature, and the massless system at finite temperature. We also study two entangled one-dimensional chains and show that the corresponding bulk geometry consists of two asymptotic regions connected by a worm-hole. The quantum quench of the coupled chains is mapped to dynamics of the worm-hole. In the end we discuss the general procedure of applying this approach to intera...
Holographic Description Of Quantum Black Holes And Space- Time
Iizuka, N
2003-01-01
We study the microscopic structure of black holes and curved space-time through the gravity/gauge theory duality. Large N DO-braves have two different dual descriptions: Schwarzschild black hole on warped AdS 2 × S8 geometry, and finite- temperature strongly-coupled gauge quantum mechanics in 0 + 1 dimensions. We work directly in the strongly-coupled quantum mechanics using a mean-field approximation to describe the black hole non-perturbatively. Using a D0- brave as a probe, we obtain the distribution of masses of W-bosons, which represent virtual open strings between the probe and the background black hole. We find a clear separation between light and heavy states as the probe approaches the horizon, and light states are thermally excited at the stringy stretched horizon. This shows that the light states correspond to black hole degrees of freedom and the heavy states correspond to the degrees of freedom of whole AdS space. Effective potential for the probe agrees with supergravity expectations, ...
Nucleon structure functions in noncommutative space-time
Rafiei, A.; Rezaei, Z.; Mirjalili, A. [Yazd University, Physics Department, Yazd (Iran, Islamic Republic of)
2017-05-15
In the context of noncommutative space-time we investigate the nucleon structure functions which play an important role in identifying the internal structure of nucleons. We use the corrected vertices and employ new vertices that appear in two approaches of noncommutativity and calculate the proton structure functions in terms of the noncommutative tensor θ{sub μν}. To check our results we plot the nucleon structure function (NSF), F{sub 2}(x), and compare it with experimental data and the results from the GRV, GJR and CT10 parametrization models. We show that with the new vertex that arises the noncommutativity correction will lead to a better consistency between theoretical results and experimental data for the NSF. This consistency will be better for small values of the Bjorken variable x. To indicate and confirm the validity of our calculations we also act conversely. We obtain a lower bound for the numerical values of Λ{sub NC} scale which correspond to recent reports. (orig.)
Surviving in a Metastable de Sitter Space-Time
Kashyap, Sitender Pratap; Sen, Ashoke; Verma, Mritunjay
2015-01-01
In a metastable de Sitter space any object has a finite life expectancy beyond which it undergoes vacuum decay. However, by spreading into different parts of the universe which will fall out of causal contact of each other in future, a civilization can increase its collective life expectancy, defined as the average time after which the last settlement disappears due to vacuum decay. We study in detail the collective life expectancy of two comoving objects in de Sitter space as a function of the initial separation, the horizon radius and the vacuum decay rate. We find that even with a modest initial separation, the collective life expectancy can reach a value close to the maximum possible value of 1.5 times that of the individual object if the decay rate is less than 1% of the expansion rate. Our analysis can be generalized to any number of objects, general trajectories not necessarily at rest in the comoving coordinates and general FRW space-time. As part of our analysis we find that in the current state of t...
Southern-Tyrrhenian seismicity in space-time-magnitude domain
D. Luzio
2006-06-01
Full Text Available An analysis is conducted on a catalogue containing more than 2000 seismic events occurred in the southern Tyrrhenian Sea between 1988 and October 2002, as an attempt to characterise the main seismogenetic processes active in the area in space, time and magnitude domain by means of the parameters of phenomenological laws. We chose to adopt simple phenomenological models, since the low number of data did not allow to use more complex laws. The two main seismogenetic volumes present in the area were considered for the purpose of this work. The first includes a nearly homogeneous distribution of hypocentres in a NW steeply dipping layer as far as about 400 km depth. This is probably the seismological expression of the Ionian lithospheric slab subducting beneath the Calabrian Arc. The second contains hypocentres concentrated about a sub-horizontal plane lying at an average depth of about 10 km. It is characterised by a background seismicity spread all over the area and by clusters of events that generally show a direction of maximum elongation. The parameters of the models describing seismogenetically homogeneous subsets of the earthquake catalogue in the three analysis domains, along with their confidence intervals, are estimated and analysed to establish whether they can be regarded as representative of a particular subset.
Space-Time Analysis of Crime Patterns in Central London
Cheng, T.; Williams, D.
2012-07-01
Crime continues to cast a shadow over citizen well-being in big cities today, while also imposing huge economic and social costs. Timely understanding of how criminality emerges and how crime patterns evolve is crucial to anticipating crime, dealing with it when it occurs and developing public confidence in the police service. Every day, about 10,000 crime incidents are reported by citizens, recorded and geo-referenced in the London Metropolitan Police Service Computer Aided Dispatch (CAD) database. The unique nature of this dataset allows the patterns to be explored at particularly fine temporal granularity and at multiple spatial resolutions. This study provides a framework for the exploratory spatio-temporal analysis of crime patterns that combines visual inquiry tools (interactive animations, space-time cubes and map matrices) with cluster analysis (spatial-temporal scan statistics and the self-organizing map). This framework is tested on the CAD dataset for the London Borough of Camden in March 2010. Patterns of crime through space and time are discovered and the clustering methods were evaluated on their ability to facilitate the discovery and interpretation of these patterns.
Entangled Harmonic Oscillators and Space-time Entanglement
Baskal, Sibel; Noz, Marilyn E
2016-01-01
The mathematical basis for the Gaussian entanglement is discussed in detail, as well as its implications in the internal space-time structure of relativistic extended particles. It is shown that the Gaussian entanglement shares the same set of mathematical formulas with the harmonic oscillator in the Lorentz-covariant world. It is thus possible to transfer the concept of entanglement to the Lorentz-covariant picture of the bound state which requires both space and time separations between two constituent particles. These space and time variables become entangled as the bound state moves with a relativistic speed. It is shown also that our inability to measure the time-separation variable leads to an entanglement entropy together with a rise in the temperature of the bound state. As was noted by Paul A. M. Dirac in 1963, the system of two oscillators contains the symmetries of O(3,2) de Sitter group containing two O(3,1) Lorentz groups as its subgroups. Dirac noted also that the system contains the symmetry of...
PHAST and RPHAST: phylogenetic analysis with space/time models.
Hubisz, Melissa J; Pollard, Katherine S; Siepel, Adam
2011-01-01
The PHylogenetic Analysis with Space/Time models (PHAST) software package consists of a collection of command-line programs and supporting libraries for comparative genomics. PHAST is best known as the engine behind the Conservation tracks in the University of California, Santa Cruz (UCSC) Genome Browser. However, it also includes several other tools for phylogenetic modeling and functional element identification, as well as utilities for manipulating alignments, trees and genomic annotations. PHAST has been in development since 2002 and has now been downloaded more than 1000 times, but so far it has been released only as provisional ('beta') software. Here, we describe the first official release (v1.0) of PHAST, with improved stability, portability and documentation and several new features. We outline the components of the package and detail recent improvements. In addition, we introduce a new interface to the PHAST libraries from the R statistical computing environment, called RPHAST, and illustrate its use in a series of vignettes. We demonstrate that RPHAST can be particularly useful in applications involving both large-scale phylogenomics and complex statistical analyses. The R interface also makes the PHAST libraries acccessible to non-C programmers, and is useful for rapid prototyping. PHAST v1.0 and RPHAST v1.0 are available for download at http://compgen.bscb.cornell.edu/phast, under the terms of an unrestrictive BSD-style license. RPHAST can also be obtained from the Comprehensive R Archive Network (CRAN; http://cran.r-project.org).
The Black Hole Evolution and Space Time (BEST) Observatory
Krawczynski, Henric; Barthelmy, Scott; Schnittman, Jeremy; Zhang, William; Krolik, Julian; Baring, Matthew G; Treister, Ezequiel; Mushotzky, Richard; Beilicke, Matthias; Buckley, James; Cowsik, Ram; Israel, Martin
2012-01-01
In this white paper, we discuss the concept of a next-generation X-ray mission called BEST (Black hole Evolution and Space Time). The mission concept uses a 3000 square centimeter effective area mirror (at 6 keV) to achieve unprecedented sensitivities for hard X-ray imaging spectrometry (5-70 keV) and for broadband X-ray polarimetry (2-70 keV). BEST can make substantial contributions to our understanding of the inner workings of accreting black holes, our knowledge about the fabric of extremely curved spacetime, and the evolution of supermassive black holes. BEST will allow for time resolved studies of accretion disks. With a more than seven times larger mirror area and a seven times wider bandpass than GEMS, BEST will take X-ray polarimetry to a new level: it will probe the time variability of the X-ray polarization from stellar mass and supermassive black holes, and it will measure the polarization properties in 30 independent energy bins. These capabilities will allow BEST to conduct tests of accretion dis...
Holographic reconstruction of 3D flat space-time
Hartong, Jelle [Physique Théorique et Mathématique and International Solvay Institutes,Université Libre de Bruxelles, C.P. 231, 1050 Brussels (Belgium)
2016-10-19
We study asymptotically flat space-times in 3 dimensions for Einstein gravity near future null infinity and show that the boundary is described by Carrollian geometry. This is used to add sources to the BMS gauge corresponding to a non-trivial boundary metric in the sense of Carrollian geometry. We then solve the Einstein equations in a derivative expansion and derive a general set of equations that take the form of Ward identities. Next, it is shown that there is a well-posed variational problem at future null infinity without the need to add any boundary term. By varying the on-shell action with respect to the metric data of the boundary Carrollian geometry we are able to define a boundary energy-momentum tensor at future null infinity. We show that its diffeomorphism Ward identity is compatible with Einstein’s equations. There is another Ward identity that states that the energy flux vanishes. It is this fact that is responsible for the enhancement of global symmetries to the full BMS{sub 3} algebra when we are dealing with constant boundary sources. Using a notion of generalized conformal boundary Killing vector we can construct all conserved BMS{sub 3} currents from the boundary energy-momentum tensor.
Modified gravity and Space-Time-Matter theory
Darabi, F
2009-01-01
The correspondence between $f(R)$ theories of gravity and model theories explaining induced dark energy in a 5D Ricci-flat universe, known as the Space-Time-Matter theory (STM), is studied. It is shown that such correspondence may be used to interpret the four dimensional expressions, induced from geometry in 5D STM theories, in terms of the extra terms appearing in $f(R)$ theories of gravity. The method is demonstrated by providing an explicit example in which a given $f(R)$ is used to predict the properties of the corresponding 5D Ricci-flat universe. The accelerated expansion and the induced dark energy in a 5D Ricci-flat universe characterized by a big bounce is studied and it is shown that an arbitrary function $\\mu(t)$ in the 5D solutions can be rewritten, in terms of the redshift $z$, as a new arbitrary function $F(z)$ which corresponds to the 4D curvature quintessence models.
Space-time and physical fields inside a black hole
Doroshkevich, A.G.; Novikov, I.D.
1978-01-01
Physical fields and the perturbations of the space-time metric inside a slowly rotating and weakly charged black hole are investigated. It is shown that in the Schwarzschild coordinates r and t for r
Boosted Horizon of a Boosted Space-Time Geometry
Battista, Emmanuele; Scudellaro, Paolo; Tramontano, Francesco
2015-01-01
We apply the ultrarelativistic boosting procedure to map the metric of Schwarzschild-de Sitter spacetime into a metric describing de Sitter spacetime plus a shock-wave singularity located on a null hypersurface, by exploiting the picture of the embedding of an hyperboloid in a five-dimensional Minkowski spacetime. After reverting to the usual four-dimensional formalism, we also solve the geodesic equation and evaluate the Riemann curvature tensor of the boosted Schwarzschild-de Sitter metric by means of numerical calculations, which make it possible to reach the ultrarelativistic regime gradually by letting the boost velocity approach the speed of light. Eventually, the analysis of the Kretschmann invariant (and of the geodesic equation) shows the global structure of space- time, as we demonstrate the presence of a "scalar curvature singularity" within a 3-sphere and find that it is also possible to define what we have called "boosted horizon", a sort of elastic wall where all particles are surprisingly pushe...
No Firewalls in Holographic Space-Time or Matrix Theory
Banks, T
2013-01-01
We use the formalisms of Holographic Space-time (HST) and Matrix Theory[11] to investigate the claim of [1] that old black holes contain a firewall, i.e. an in-falling detector encounters highly excited states at a time much shorter than the light crossing time of the Schwarzschild radius. In both formalisms there is no dramatic change in particle physics inside the horizon until a time of order the Schwarzschild radius. The Matrix Theory formalism has been shown to give rise to an S-matrix, which coincides with effective supergravity for an infinite number of low energy amplitudes. We conclude that the firewall results from an inappropriate use of quantum effective field theory to describe fine details of localized events near a black hole horizon. In both HST and Matrix Theory, the real quantum gravity Hilbert space in a localized region contains many low energy degrees of freedom that are not captured in QU(antum) E(ffective) F(ield) T(heory) and omits many of the high energy DOF in QUEFT.
Conformal quantum mechanics and holography in noncommutative space-time
Gupta, Kumar S.; Harikumar, E.; Zuhair, N. S.
2017-09-01
We analyze the effects of noncommutativity in conformal quantum mechanics (CQM) using the κ-deformed space-time as a prototype. Up to the first order in the deformation parameter, the symmetry structure of the CQM algebra is preserved but the coupling in a canonical model of the CQM gets deformed. We show that the boundary conditions that ensure a unitary time evolution in the noncommutative CQM can break the scale invariance, leading to a quantum mechanical scaling anomaly. We calculate the scaling dimensions of the two and three point functions in the noncommutative CQM which are shown to be deformed. The AdS2 / CFT1 duality for the CQM suggests that the corresponding correlation functions in the holographic duals are modified. In addition, the Breitenlohner-Freedman bound also picks up a noncommutative correction. The strongly attractive regime of a canonical model of the CQM exhibit quantum instability. We show that the noncommutativity softens this singular behaviour and its implications for the corresponding holographic duals are discussed.
Distributed Space Time Coding for Wireless Two-way Relaying
Muralidharan, Vijayvaradharaj T
2012-01-01
We consider the wireless two-way relay channel, in which two-way data transfer takes place between the end nodes with the help of a relay. For the Denoise-And-Forward (DNF) protocol, it was shown by Koike-Akino et. al. that adaptively changing the network coding map used at the relay greatly reduces the impact of Multiple Access interference at the relay. The harmful effect of the deep channel fade conditions can be effectively mitigated by proper choice of these network coding maps at the relay. Alternatively, in this paper we propose a Distributed Space Time Coding (DSTC) scheme, which effectively removes most of the deep fade channel conditions at the transmitting nodes itself without any CSIT and without any need to adaptively change the network coding map used at the relay. It is shown that the deep fades occur when the channel fade coefficient vector falls in a finite number of vector subspaces of $\\mathbb{C}^2$, which are referred to as the singular fade subspaces. DSTC design criterion referred to as ...
Object Detection with Vocabularies of Space-time Descriptors
Y. Hernandez-Heredia
2012-11-01
Full Text Available This paper presents a novel framework for objects detection in security and broadcast videos. Our method assumes thatobject classes are unknown in advance and exploit the temporal-space properties of the videos for the creation of avocabulary that describes these classes. Local space-time features have recently became a popular video representationfor action recognition and object detection. Several methods for feature localization and description have been proposedin the literature and promising recognition results were demonstrated for a number of action classes.In this work we propose the use of different kinds of descriptors for the creation of vocabularies for different detectionobject task. For a better description of the videos we carry out a background model, tryring to clean up and follow theareas where there are objects. The points of interest in the videos to characterize the objects are calculated with atemporary variant of the famous Harris corner detector. With the descriptors obtained from the points of interest, avocabulary is realized usingthe kinds of videos we want to train. Then we obtained the frequency histogramsbetween the videos for training and the vocabulary so, with a binary classifier obtain the trained classes and followingthe same procedure without the vocabulary realized the detection and monitoring of the objects.The new method presented is also compared with a state of the art method, obtaining better results in both accuracyand false object rejection.
LOW RATE SPACE-TIME TRELLIS CODES IN POWER LIMITED WIRELESS COMMUNICATION SYSTEMS
Wu Gang; Chen Ming; Wang Haifeng; Cheng Shixin
2002-01-01
Space-time trellis codes can achieve the best tradeoff among bandwidth effciency,diversity gain, constellation size and trellis complexity. In this paper, some optimum low rate space-time trellis codes are proposed. Performance analysis and simulation show that the low rate space-time trellis codes outperform space-time block codes concatenated with convolutional code at the same bandwidth effciency, and are more suitable for the power limited wireless communication system.
Logarithmic modes of critical gravity in de Sitter space-time
Setare, M R
2012-01-01
In this paper we consider the critical gravity in four dimensional de Sitter space-time. We obtain logarithmic modes in the critical point of the theory. Then we show that these logarithmic modes in de Sitter space-time obey similar properties as the ones in AdS-space-time. Our result in this paper indicate that critical gravity theories in de Sitter space-times could lead to a de Sitter/log CFT correspondence.
Space and time, matter and mind the relationship between reality and space-time
1994-01-01
In principle, the elements of space and time cannot be measured. Therefore, the following question arises: How are reality and space-time related to each other? In this book, it is argued on the basis of many facts that reality is not embedded but projected onto space and time. We can never make statements about the actual reality outside (basic reality), but we can "only" form pictures of it. These are pictures of the same reality on different levels. From this point of view, the "hard" objects (matter) and the products of the mind are similar in character.
On the local form of static plane symmetric space-times in the presence of matter
Gomes, Leandro G
2015-01-01
For any configuration of a static plane-symmetric distribution of matter along space-time, there are coordinates where the metric can be put explicitly as a functional of the energy density and pressures. It satisfies Einstein equations as far as we require the conservation of the energy-momentum tensor, which is the single ODE for self-gravitating hydrostatic equilibrium. As a direct application, a general solution is given when the pressures are linearly related to the energy density, recovering, as special cases, most of known solutions of static plane-symmetric Einstein equations.
A topological-like model for gravity in 4D space-time
Morales, Ivan; Neves, Bruno; Oporto, Zui; Piguet, Olivier [Universidade Federal de Vicosa-UFV, Departamento de Fisica, Vicosa, MG (Brazil)
2016-04-15
In this paper we consider a model for gravity in four-dimensional space-time originally proposed by Chamseddine, which may be derived by dimensional reduction and truncation from a five-dimensional Chern-Simons theory. Its topological origin makes it an interesting candidate for an easier quantization, e.g., in the loop quantization framework. The present paper is dedicated to a classical analysis of the model's properties. Cosmological solutions as well as wave solutions are found and compared with the corresponding solutions of Einstein's general relativity with cosmological constant. (orig.)
Advances and Challenges in Space-time Modelling of Natural Events
Porcu, Emilio; Schlather, Martin
2012-01-01
This book arises as the natural continuation of the International Spring School "Advances and Challenges in Space-Time modelling of Natural Events," which took place in Toledo (Spain) in March 2010. This Spring School above all focused on young researchers (Master students, PhD students and post-doctoral researchers) in academics, extra-university research and the industry who are interested in learning about recent developments, new methods and applications in spatial statistics and related areas, and in exchanging ideas and findings with colleagues.
On Geodesic Flows and Their Deformations in Bertrand Space-times
Kumar, Prashant; Sarkar, Tapobrata
2012-01-01
We study the energy conditions and geodesic equations of Bertrand space-times. We show that these can be thought of as interesting physical space-times in certain regions of the parameter space where the weak and strong energy conditions hold. We further compute the ESR parameters for a class of such space-times and analyze them numerically.
Surviving in a metastable de Sitter space-time
Kashyap, Sitender Pratap; Mondal, Swapnamay [Harish-Chandra Research Institute,Chhatnag Road, Jhusi, Allahabad 211019 (India); Sen, Ashoke [Harish-Chandra Research Institute,Chhatnag Road, Jhusi, Allahabad 211019 (India); School of Physics, Korea Institute for Advanced Study,Seoul 130-722 (Korea, Republic of); Verma, Mritunjay [Harish-Chandra Research Institute,Chhatnag Road, Jhusi, Allahabad 211019 (India); International Centre for Theoretical Sciences,Malleshwaram, Bengaluru 560 012 (India)
2015-09-21
In a metastable de Sitter space any object has a finite life expectancy beyond which it undergoes vacuum decay. However, by spreading into different parts of the universe which will fall out of causal contact of each other in future, a civilization can increase its collective life expectancy, defined as the average time after which the last settlement disappears due to vacuum decay. We study in detail the collective life expectancy of two comoving objects in de Sitter space as a function of the initial separation, the horizon radius and the vacuum decay rate. We find that even with a modest initial separation, the collective life expectancy can reach a value close to the maximum possible value of 1.5 times that of the individual object if the decay rate is less than 1% of the expansion rate. Our analysis can be generalized to any number of objects, general trajectories not necessarily at rest in the comoving coordinates and general FRW space-time. As part of our analysis we find that in the current state of the universe dominated by matter and cosmological constant, the vacuum decay rate is increasing as a function of time due to accelerated expansion of the volume of the past light cone. Present decay rate is about 3.7 times larger than the average decay rate in the past and the final decay rate in the cosmological constant dominated epoch will be about 56 times larger than the average decay rate in the past. This considerably weakens the lower bound on the half-life of our universe based on its current age.
Space-time dynamics estimation from space mission tracking data
Dirkx, D.; Noomen, R.; Visser, P. N. A. M.; Gurvits, L. I.; Vermeersen, L. L. A.
2016-03-01
Aims: Many physical parameters that can be estimated from space mission tracking data influence both the translational dynamics and proper time rates of observers. These different proper time rates cause a variability of the time transfer observable beyond that caused by their translational (and rotational) dynamics. With the near-future implementation of transponder laser ranging, these effects will become increasingly important, and will require a re-evaluation of the common data analysis practice of using a priori time ephemerides, which is the goal of this paper. Methods: We develop a framework for the simultaneous estimation of the initial translational state and the initial proper time of an observer, with the goal of facilitating robust tracking data analysis from next-generation space missions carrying highly accurate clocks and tracking equipment. Using our approach, the influence of physical parameters on both translational and time dynamics are considered at the same level in the analysis, and mutual correlations between the signatures of the two are automatically identified. We perform a covariance analysis using our proposed method with simulated laser data from Earth-based stations to both a Mars and Mercury lander. Results: Using four years of tracking data for the Mars lander simulations, we find a difference between our results using the simultaneous space-time dynamics estimation and the classical analysis technique (with an a priori time ephemeris) of around 0.1% in formal errors and correlation coefficients. For a Mercury lander this rises to around 1% for a one-month mission and 10% for a four-year mission. By means of Monte Carlo simulations, we find that using an a priori time ephemeris of representative accuracy will result in estimation errors that are orders of magnitude above the formal error when processing highly accurate laser time transfer data.
Space, time, error, and power optimization of image compression transforms
Schmalz, Mark S.; Ritter, Gerhard X.; Caimi, Frank M.
2000-11-01
The implementation of an image compression transform on one or more small, embedded processors typically involves stringent constraints on power consumption and form factor. Traditional methods of optimizing compression algorithm performance typically emphasize joint minimization of space and time complexity, often without significant consideration of arithmetic accuracy or power consumption. However, small autonomous imaging platforms typically require joint optimization of space, time, error (or accuracy), and power (STEP) parameters, which the authors call STEP optimization. In response to implementational constraints on space and power consumption, the authors have developed systems and techniques for STEP optimization that are based on recent research in VLSI circuit design, as well as extensive previous work in system optimization. Building on the authors' previous research in embedded processors as well as adaptive or reconfigurable computing, it is possible to produce system-independent STEP optimization that can be customized for a given set of system-specific constraints. This approach is particularly useful when algorithms for image and signal processing (ISP) computer vision (CV), or automated target recognition (ATR), expressed in a machine- independent notation, are mapped to one or more heterogeneous processors (e.g., digital signal processors or DSPs, SIMD mesh processors, or reconfigurable logic). Following a theoretical summary, this paper illustrates various STEP optimization techniques via case studies, for example, real-time compression of underwater imagery on board an autonomous vehicle. Optimization algorithms are taken from the literature, and error profiling/analysis methodologies developed in the authors' previous research are employed. This yields a more rigorous basis for the simulation and evaluation of compression algorithms on a wide variety of hardware models. In this study, image algebra is employed as the notation of choice
Understanding human activity patterns based on space-time-semantics
Huang, Wei; Li, Songnian
2016-11-01
Understanding human activity patterns plays a key role in various applications in an urban environment, such as transportation planning and traffic forecasting, urban planning, public health and safety, and emergency response. Most existing studies in modeling human activity patterns mainly focus on spatiotemporal dimensions, which lacks consideration of underlying semantic context. In fact, what people do and discuss at some places, inferring what is happening at the places, cannot be simple neglected because it is the root of human mobility patterns. We believe that the geo-tagged semantic context, representing what individuals do and discuss at a place and a specific time, drives a formation of specific human activity pattern. In this paper, we aim to model human activity patterns not only based on space and time but also with consideration of associated semantics, and attempt to prove a hypothesis that similar mobility patterns may have different motivations. We develop a spatiotemporal-semantic model to quantitatively express human activity patterns based on topic models, leading to an analysis of space, time and semantics. A case study is conducted using Twitter data in Toronto based on our model. Through computing the similarities between users in terms of spatiotemporal pattern, semantic pattern and spatiotemporal-semantic pattern, we find that only a small number of users (2.72%) have very similar activity patterns, while the majority (87.14%) show different activity patterns (i.e., similar spatiotemporal patterns and different semantic patterns, similar semantic patterns and different spatiotemporal patterns, or different in both). The population of users that has very similar activity patterns is decreased by 56.41% after incorporating semantic information in the corresponding spatiotemporal patterns, which can quantitatively prove the hypothesis.
A conformal boundary for space-times based on light-like geodesics: The 3-dimensional case
Bautista, A.; Ibort, A.; Lafuente, J.; Low, R.
2017-02-01
A new causal boundary, which we will term the l-boundary, inspired by the geometry of the space of light rays and invariant by conformal diffeomorphisms for space-times of any dimension m ≥3 , proposed by one of the authors [R. J. Low, The Space of Null Geodesics (and a New Causal Boundary), Lecture Notes in Physics 692 (Springer, 2006), pp. 35-50] is analyzed in detail for space-times of dimension 3. Under some natural assumptions, it is shown that the completed space-time becomes a smooth manifold with boundary and its relation with Geroch-Kronheimer-Penrose causal boundary is discussed. A number of examples illustrating the properties of this new causal boundary as well as a discussion on the obtained results will be provided.
Aydogdu, O; Salti, M; Aydogdu, Oktay; Korunur, Murat; Salti, Mustafa
2005-01-01
We calculate the total energy (due to matter plus fields) of the universe considering Bergmann-Thomson's energy momentum formulation in both Einstein's theory of general relativity and tele-parallel gravity on two different space-times; namely Reboucas-Tiomno-Korotkii-Obukhov and Godel-type metrics. We also compute some kinematical quantities for these space-times and find that these space-times have shear-free expansion and non-vanishing four-acceleration and vorticity. Different approximations of the Bergmann-Thomson energy-momentum formulation in these different gravitation theories give the same energy density and agree with each other. The results advocate the importance of energy-momentum definitions.
Tracking and visualization of space-time activities for a micro-scale flu transmission study
Qi Feng
2013-02-01
Full Text Available Abstract Background Infectious diseases pose increasing threats to public health with increasing population density and more and more sophisticated social networks. While efforts continue in studying the large scale dissemination of contagious diseases, individual-based activity and behaviour study benefits not only disease transmission modelling but also the control, containment, and prevention decision making at the local scale. The potential for using tracking technologies to capture detailed space-time trajectories and model individual behaviour is increasing rapidly, as technological advances enable the manufacture of small, lightweight, highly sensitive, and affordable receivers and the routine use of location-aware devices has become widespread (e.g., smart cellular phones. The use of low-cost tracking devices in medical research has also been proved effective by more and more studies. This study describes the use of tracking devices to collect data of space-time trajectories and the spatiotemporal processing of such data to facilitate micro-scale flu transmission study. We also reports preliminary findings on activity patterns related to chances of influenza infection in a pilot study. Methods Specifically, this study employed A-GPS tracking devices to collect data on a university campus. Spatiotemporal processing was conducted for data cleaning and segmentation. Processed data was validated with traditional activity diaries. The A-GPS data set was then used for visual explorations including density surface visualization and connection analysis to examine space-time activity patterns in relation to chances of influenza infection. Results When compared to diary data, the segmented tracking data demonstrated to be an effective alternative and showed greater accuracies in time as well as the details of routes taken by participants. A comparison of space-time activity patterns between participants who caught seasonal influenza and those who
Monitoring Murder Crime in Namibia Using Bayesian Space-Time Models
Isak Neema
2012-01-01
Full Text Available This paper focuses on the analysis of murder in Namibia using Bayesian spatial smoothing approach with temporal trends. The analysis was based on the reported cases from 13 regions of Namibia for the period 2002–2006 complemented with regional population sizes. The evaluated random effects include space-time structured heterogeneity measuring the effect of regional clustering, unstructured heterogeneity, time, space and time interaction and population density. The model consists of carefully chosen prior and hyper-prior distributions for parameters and hyper-parameters, with inference conducted using Gibbs sampling algorithm and sensitivity test for model validation. The posterior mean estimate of the parameters from the model using DIC as model selection criteria show that most of the variation in the relative risk of murder is due to regional clustering, while the effect of population density and time was insignificant. The sensitivity analysis indicates that both intrinsic and Laplace CAR prior can be adopted as prior distribution for the space-time heterogeneity. In addition, the relative risk map show risk structure of increasing north-south gradient, pointing to low risk in northern regions of Namibia, while Karas and Khomas region experience long-term increase in murder risk.
Einstein's unfinished symphony listening to the sounds of space-time
Bartusiak, Marcia
2000-01-01
A new generation of observatories, now being completed worldwide, will give astronomers not just a new window on the cosmos but a whole new sense with which to explore and experience the heavens above us. Instead of collecting light waves or radio waves, these novel instruments will allow astronomers to at last place their hands upon the fabric of space-time and feel the very rhythms of the universe. These vibrations in space-time-or gravity waves-are the last prediction of Einstein's general theory of relativity yet to be observed directly. They are his unfinished symphony, waiting nearly a century to be heard. When they finally reveal themselves to astronomers, we will for the first time be able to hear the cymbal crashes from exploding stars, tune in to the periodic drumbeats from swiftly rotating pulsars, listen to the extended chirps from the merger of two black holes, and eavesdrop on the remnant echoes from the mighty jolt of the Big Bang itself. When Einstein introduced general relativity in 1915, it ...
Space-time analysis of snow cover change in the Romanian Carpathians (2001-2016)
Micu, Dana; Cosmin Sandric, Ionut
2017-04-01
seasonal precipitation, especially at lower elevations in all the three divisions of the Romanian Carpathians (generally below 1,700-1,800 m). The space-time patterns of snow cover change are dominated by a significant decreasing trend of snow days and earlier spring snow melt. The key findings of this study provides robust indication of a decreasing snow trends across the Carpathian Mountain region and could provide valuable spatial and temporal snow information for other related research fields as well as for an effective environmental monitoring in the mountain ecosystems of the Carpathian region
The Momentum 4-Vector in Bulk Viscous Bianchi Type-V Space-time
Aydogdu, O; Aydogdu, Oktay; Salti, Mustafa
2006-01-01
Using the Einstein and Bergmann-Thomson prescriptions, the energy and momentum distributions for the Bianchi type-V bulk viscous space-time are evaluated in both general relativity and the teleparallel gravity (the tetrad theory of gravity). It is shown that for the Bianchi type-V bulk viscous solution, the energy and momentum due to matter and fields including gravity are the same in both the methods used. This paper indicates an important point that these energy-momentum definitions agree with each other not only in general relativity but also in teleparallel gravity and sustains the results obtained by some physicist who show that the energy-momentum definitions of Einstein, Landau-Lifshitz, Papapetrou, Weinberg, Penrose and Bergmann-Thomson complexes give the same energy expression in general relativity.
An Improved Group Space-Time Block Code Through Constellation Rotation
ZHANG Hong-wei; ZHANG Hai-bin; SONG Wen-tao; LUO Han-wen; LIU Xing-zhao
2005-01-01
A new improved group space-time block code (G-STBC) based on constellation rotation for four transmit antennas was proposed. In comparison with the traditional G-STBC coding scheme, the proposed space-time code has longer code length and adopts proper rotation-based symbols, which can increase the minimum distance of space-time codes and thereby improve code gain and achieve full diversity performance. The simulation results verify that the proposed group space-time code can achieve better bit error performance than both the traditional group space-time code and other quasi-orthogonal space-time codes. Compared with Ma's full diversity full rate (FDFR) codes, the proposed space-time code also can achieve the same excellent error performance. Furthermore, the design of the new space-time code gives another new and simple method to construct space-time codes with full diversity and high rate in case that it is not easy to design the traditional FDFR space-time codes.
Modulation of homogeneous space-time rainfall cascades to account for orographic influences
M. G. Badas
2006-01-01
Full Text Available The development of efficient space-time rainfall downscaling procedures is highly important for the implementation of a meteo-hydrological forecasting chain operating over small watersheds. Multifractal models based on homogeneous cascade have been successfully applied in literature to reproduce space-time rainfall events retrieved over ocean, where the hypothesis of spatial homogeneity can be reasonably accepted. The feasibility to apply this kind of models to rainfall fields occurring over a mountainous region, where spatial homogeneity may not hold, is herein investigated. This issue is examined through the analysis of rainfall data retrieved by the high temporal resolution rain gage network of the Sardinian Hydrological Survey. The proposed procedure involves the introduction of a modulating function which is superimposed to homogeneous and isotropic synthetic fields to take into account the spatial heterogeneity detected in observed precipitation events. Specifically the modulating function, which reproduces the differences in local mean values of the precipitation intensity probability distribution, has been linearly related to the terrain elevation of the analysed spatial domain. Comparisons performed between observed and synthetic data show how the proposed procedure preserves the observed rainfall fields features and how the introduction of the modulating function improves the reproduction of spatial heterogeneity in rainfall probability distributions.
Assessment of Measurement Distortions in GNSS Antenna Array Space-Time Processing
Thyagaraja Marathe
2016-01-01
Full Text Available Antenna array processing techniques are studied in GNSS as effective tools to mitigate interference in spatial and spatiotemporal domains. However, without specific considerations, the array processing results in biases and distortions in the cross-ambiguity function (CAF of the ranging codes. In space-time processing (STP the CAF misshaping can happen due to the combined effect of space-time processing and the unintentional signal attenuation by filtering. This paper focuses on characterizing these degradations for different controlled signal scenarios and for live data from an antenna array. The antenna array simulation method introduced in this paper enables one to perform accurate analyses in the field of STP. The effects of relative placement of the interference source with respect to the desired signal direction are shown using overall measurement errors and profile of the signal strength. Analyses of contributions from each source of distortion are conducted individually and collectively. Effects of distortions on GNSS pseudorange errors and position errors are compared for blind, semi-distortionless, and distortionless beamforming methods. The results from characterization can be useful for designing low distortion filters that are especially important for high accuracy GNSS applications in challenging environments.
A QCD space-time analysis of quarkonium formation and evolution in hadronic collisions
Kinder-Geiger, Klaus
1998-01-01
The production of heavy quarkonium as QQbar bound-states in hadron-hadron collisions is considered within the framework of a space-time description, combining parton-cascade evolution with a coalescence model for bound-state formation. The `hard' production of the initial QQbar, directly or via gluon fragmentation and including both color-singlet and color-octet contributions, is calculated from the PQCD cross-sections. The subsequent development of the QQbar system is described within a space-time generalization of the DGLAP parton-evolution formalism in position- and momentum-space. The actual formation of the bound-states is accomplished through overlap of the QQbar pair and a spectrum of quarkonium wave-functions. This coalescence can only occur after sufficent gluon radiation reduces the QQbar relative velocity to a value commensurate with the non-relativistic kinematics of these bound systems. The presence of gluon participants in the cascade then is both necessary and leads to the natural inclusion of ...
Energy Density Associated with the Bianchi Type-II Space-Time
Aydogdu, O; Aydogdu, Oktay; Salti, Mustafa
2006-01-01
To calculate the total energy distribution (due to both matter and fields including gravitation) associated with locally rotationally symmetric (LRS) Bianchi type-II space-times. We use the Bergmann-Thomson energy-momentum complex in both general relativity and teleparallel gravity. We find that the energy density in these different gravitation theories is vanishing at all times. This result is the same as that obtained by one of the present authors who solved the problem of finding the energy-momentum in LRS Bianchi type-II by using the energy-momentum complexes of Einstein and Landau and Lifshitz. The results of this paper also are consistent with those given in the previous works of Cooperstock and Israelit, Rosen, Johri et al., Banerjee-Sen, Vargas, and Salti et al. In this paper, we perform the calculations for a non-diagonal expanding space-time to determine whether the Bergmann-Thomson energy momentum prescription is consistent with the other formulations. (We previously considered diagonal and expandi...
A short essay on quantum black holes and underlying noncommutative quantized space-time
Tanaka, Sho
2017-01-01
We emphasize the importance of noncommutative geometry or Lorenz-covariant quantized space-time towards the ultimate theory of quantum gravity and Planck scale physics. We focus our attention on the statistical and substantial understanding of the Bekenstein-Hawking area-entropy law of black holes in terms of the kinematical holographic relation (KHR). KHR manifestly holds in Yang’s quantized space-time as the result of kinematical reduction of spatial degrees of freedom caused by its own nature of noncommutative geometry, and plays an important role in our approach without any recourse to the familiar hypothesis, so-called holographic principle. In the present paper, we find a unified form of KHR applicable to the whole region ranging from macroscopic to microscopic scales in spatial dimension d = 3. We notice a possibility of nontrivial modification of area-entropy law of black holes which becomes most remarkable in the extremely microscopic system close to Planck scale.
On the usefulness of relativistic space-times for the description of the Earth's gravitational field
Soffel, Michael; Frutos, Francisco
2016-12-01
The usefulness of relativistic space-times for the description of the Earth's gravitational field is investigated. A variety of exact vacuum solutions of Einstein's field equations (Schwarzschild, Erez and Rosen, Gutsunayev and Manko, Hernández-Pastora and Martín, Kerr, Quevedo, and Mashhoon) are investigated in that respect. It is argued that because of their multipole structure and influences from external bodies, all these exact solutions are not really useful for the central problem. Then, approximate space-times resulting from an MPM or post-Newtonian approximation are considered. Only in the DSX formalism that is of the first post-Newtonian order, all aspects of the problem can be tackled: a relativistic description (a) of the Earth's gravity field in a well-defined geocentric reference system (GCRS), (b) of the motion of solar system bodies in a barycentric reference system (BCRS), and (c) of inertial and tidal terms in the geocentric metric describing the external gravitational field. A relativistic SLR theory is also discussed with respect to our central problem. Orders of magnitude of many effects related to the Earth's gravitational field and SLR are given. It is argued that a formalism with accuracies better than of the first post-Newtonian order is not yet available.
Exploring space-time structure of human mobility in urban space
Sun, J. B.; Yuan, J.; Wang, Y.; Si, H. B.; Shan, X. M.
2011-03-01
Understanding of human mobility in urban space benefits the planning and provision of municipal facilities and services. Due to the high penetration of cell phones, mobile cellular networks provide information for urban dynamics with a large spatial extent and continuous temporal coverage in comparison with traditional approaches. The original data investigated in this paper were collected by cellular networks in a southern city of China, recording the population distribution by dividing the city into thousands of pixels. The space-time structure of urban dynamics is explored by applying Principal Component Analysis (PCA) to the original data, from temporal and spatial perspectives between which there is a dual relation. Based on the results of the analysis, we have discovered four underlying rules of urban dynamics: low intrinsic dimensionality, three categories of common patterns, dominance of periodic trends, and temporal stability. It implies that the space-time structure can be captured well by remarkably few temporal or spatial predictable periodic patterns, and the structure unearthed by PCA evolves stably over time. All these features play a critical role in the applications of forecasting and anomaly detection.
Critical phenomena of regular black holes in anti-de Sitter space-time
Fan, Zhong-Ying
2016-01-01
In General Relativity coupled to a non-linear electromagnetic field, together with a negative cosmological constant, we obtain the general static spherical symmetric black hole solution with magnetic charges, which is asymptotic to anti-de Sitter (AdS) space-times. In particular, for a degenerate case the solution becomes a Hayward-AdS black hole, which is regular everywhere in the full space-time. The existence of such a regular black hole solution preserves the weak energy condition while the strong energy condition is violated. We then derive the first law and the Smarr formula of the black hole solution. We further discuss its thermodynamic properties and study the critical phenomena in the extended phase space where the cosmological constant is treated as a thermodynamic variable as well as the parameter associated with the non-linear electrodynamics. We obtain many interesting results such as: the Maxwell's equal area law in the $P-V$ (or $S-T$) diagram is violated and consequently the critical point $(...
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2006-01-01
This paper proposes a closed-form joint space-time channel and Direction Of Arrival (DOA) blind estimation algorithm for space-time coded Multi-Carrier Code Division Multiple Access (MC-CDMA) systems equipped with a Uniform Linear Array (ULA) at the base station in frequency-selective fading environments. The algorithm uses an ESPRIT-like method to separate multiple co-channel users with different impinging DOAs. As a result, the DOAs for multiple users are obtained. In particular, a set of signal subspaces,every one of which is spanned by the space-time vector channels of an individual user, are also obtained. From these signal subspaces, the space-time channels of multiple users are estimated using the subspace method.Computer simulations illustrate both the validity and the overall performance of the proposed scheme.
Using clocks to determine the entropy of black holes and other space-time singularities
Ojo, A
2005-01-01
Space-time singularities, viz. Big bang, Big crunch and black holes have been shown to follow from the singularity theorems of General relativity. Whether the entropy at such infinite proper-time objects can be other than zero has also been a longstanding subject of research. Currently the property most commonly chosen to calculate their entropy is a multiple of the surface area of the event horizon and usually gives non-zero entropy values. Though popular, this choice still leaves some substantial questions unanswered hence the motivation for alternative methods for entropy derivation. Here, we use a different property, the proper-time at singularities based on the General relativity predicted behavior of clocks, to derive their entropy. We find, firstly within statistical and thermodynamic principles, secondly when this property is taken into account in the Bekenstein-Hawking formula and thirdly illustrating with a natural analogue, that the entropy of black holes and all other gravitational singularities c...
Computer-games for gravitational wave science outreach: Black Hole Pong and Space Time Quest
Carbone, L.; Bond, C.; Brown, D.; Brückner, F.; Grover, K.; Lodhia, D.; Mingarelli, C. M. F.; Fulda, P.; Smith, R. J. E.; Unwin, R.; Vecchio, A.; Wang, M.; Whalley, L.; Freise, A.
2012-06-01
We have established a program aimed at developing computer applications and web applets to be used for educational purposes as well as gravitational wave outreach activities. These applications and applets teach gravitational wave physics and technology. The computer programs are generated in collaboration with undergraduates and summer students as part of our teaching activities, and are freely distributed on a dedicated website. As part of this program, we have developed two computer-games related to gravitational wave science: 'Black Hole Pong' and 'Space Time Quest'. In this article we present an overview of our computer related outreach activities and discuss the games and their educational aspects, and report on some positive feedback received.
Low Complexity Receiver Structures for Space-Time Coded Multiple-Access Systems
Jayaweera Sudharman K
2002-01-01
Full Text Available Multiuser detection for space-time coded synchronous multiple-access systems in the presence of independent Rayleigh fading is considered. Under the assumption of quasi-static fading, it is shown that optimal (full diversity achieving space-time codes designed for single-user channels, can still provide full diversity in the multiuser channel. The joint optimal maximum likelihood multiuser detector, which can be implemented with a Viterbi-type algorithm, is derived for such space-time coded systems. Low complexity, partitioned detector structures that separate the multiuser detection and space-time decoding into two stages are also developed. Both linear and nonlinear multiuser detection schemes are considered for the first stage of these partitioned space-time multiuser receivers. Simulation results show that these latter methods achieve performance competitive with the single-user bound for space-time coded systems.
Space-Time Modelling of Groundwater Level Using Spartan Covariance Function
Varouchakis, Emmanouil; Hristopulos, Dionissios
2014-05-01
Geostatistical models often need to handle variables that change in space and in time, such as the groundwater level of aquifers. A major advantage of space-time observations is that a higher number of data supports parameter estimation and prediction. In a statistical context, space-time data can be considered as realizations of random fields that are spatially extended and evolve in time. The combination of spatial and temporal measurements in sparsely monitored watersheds can provide very useful information by incorporating spatiotemporal correlations. Spatiotemporal interpolation is usually performed by applying the standard Kriging algorithms extended in a space-time framework. Spatiotemoral covariance functions for groundwater level modelling, however, have not been widely developed. We present a new non-separable theoretical spatiotemporal variogram function which is based on the Spartan covariance family and evaluate its performance in spatiotemporal Kriging (STRK) interpolation. The original spatial expression (Hristopulos and Elogne 2007) that has been successfully used for the spatial interpolation of groundwater level (Varouchakis and Hristopulos 2013) is modified by defining the following space-time normalized distance h = °h2r-+-α h2τ, hr=r- ξr, hτ=τ- ξτ; where r is the spatial lag vector, τ the temporal lag vector, ξr is the correlation length in position space (r) and ξτ in time (τ), h the normalized space-time lag vector, h = |h| is its Euclidean norm of the normalized space-time lag and α the coefficient that determines the relative weight of the time lag. The space-time experimental semivariogram is determined from the biannual (wet and dry period) time series of groundwater level residuals (obtained from the original series after trend removal) between the years 1981 and 2003 at ten sampling stations located in the Mires hydrological basin in the island of Crete (Greece). After the hydrological year 2002-2003 there is a significant
LDPC based time-frequency double differential space-time coding for multi-antenna OFDM systems
TIAN Ji-feng; JIANG Hai-ning; SONG Wen-tao; LUO Han-wen
2006-01-01
Differential space-time coding was proposed recently in the literature for multi-antenna systems, where neither the transmitter nor the receiver knows the fading coefficients. Among existing schemes, double differential space-time (DDST) coding is of special interest because it is applicable to continuous fast time-varying channels. However, it is less effective in frequency-selective fading channels. This paper's authors derived a novel time-frequency double differential space-time (TF-DDST)coding scheme for multi-antenna orthogonal frequency division multiplexing (OFDM) systems ina time-varying frequency-selective fading environment, where double differential space-time coding is introduced into both time domain and frequency domain. Our proposed TF-DDST-OFDM system has a low-complexity non-coherent decoding scheme and is robust for time- and frequency-selective Rayleigh fading. In this paper, we also propose the use of state-of-the-art low-density parity-check (LDPC) code in serial concatenation with our TF-DDST scheme as a channel code. Simulations revealed that the LDPC based TF-DDST OFDM system has low decoding complexity and relatively better performance.
The Fermionic Signature Operator and Quantum States in Rindler Space-Time
Finster, Felix; Röken, Christian
2016-01-01
The fermionic signature operator is constructed in Rindler space-time. It is shown to be an unbounded self-adjoint operator on the Hilbert space of solutions of the massive Dirac equation. In two-dimensional Rindler space-time, we prove that the resulting fermionic projector state coincides with the Fulling-Rindler vacuum. Moreover, the fermionic signature operator gives a covariant construction of general thermal states, in particular of the Unruh state. The fermionic signature operator is shown to be well-defined in asymptotically Rindler space-times. In four-dimensional Rindler space-time, our construction gives rise to new quantum states.
Origin of matter and space-time in the big bang
Mathews, G. J. [University of Notre Dame, Center for Astrophysics/JINA, Notre Dame, IN 46556, USA and Division of Theoretical Astronomy, National Astronomical Observatory of Japan, Mitaka, Tokyo 181-8588 (Japan); Kajino, T. [Division of Theoretical Astronomy, National Astronomical Observatory of Japan, Mitaka, Tokyo 181-8588, Japan and Department of Astronomy, Graduate School of Science, University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-0033 (Japan); Yamazaki, D. [Division of Theoretical Astronomy, National Astronomical Observatory of Japan, Mitaka, Tokyo 181-8588 (Japan); Kusakabe, M. [School of Liberal Arts and Science, Korea Aerospace University, Goyang 412-791, Korea and Department of Physics, Soongsil University, Seoul 156-743 (Korea, Republic of); Cheoun, M.-K. [Department of Physics, Soongsil University, Seoul 156-743 (Korea, Republic of)
2014-05-02
We review the case for and against a bulk cosmic motion resulting from the quantum entanglement of our universe with the multiverse beyond our horizon. Within the current theory for the selection of the initial state of the universe from the landscape multiverse there is a generic prediction that pre-inflation quantum entanglement with other universes should give rise to a cosmic bulk flow with a correlation length of order horizon size and a velocity field relative to the expansion frame of the universe. Indeed, the parameters of this motion are are tightly constrained. A robust prediction can be deduced indicating that there should be an overall motion of of about 800 km/s relative to the background space time as defined by the cosmic microwave background (CMB). This talk will summarize the underlying theoretical motivation for this hypothesis. Of course our motion relative to the background space time (CMB dipole) has been known for decades and is generally attributed to the gravitational pull of the local super cluster. However, this cosmic peculiar velocity field has been recently deduced out to very large distances well beyond that of the local super cluster by using X-ray galaxy clusters as tracers of matter motion. This is achieved via the kinematic component of the Sunyaev-Zeldovich (KSZ) effect produced by Compton scattering of cosmic microwave background photons from the local hot intracluster gas. As such, this method measures peculiar velocity directly in the frame of the cluster. Similar attempts by our group and others have attempted to independently assess this bulk flow via Type la supernova redshifts. In this talk we will review the observation case for and against the existence of this bulk flow based upon the observations and predictions of the theory. If this interpretation is correct it has profound implications in that we may be observing for the first time both the physics that occurred before the big bang and the existence of the multiverse
Origin of matter and space-time in the big bang
Mathews, G. J.; Kajino, T.; Yamazaki, D.; Kusakabe, M.; Cheoun, M.-K.
2014-05-01
We review the case for and against a bulk cosmic motion resulting from the quantum entanglement of our universe with the multiverse beyond our horizon. Within the current theory for the selection of the initial state of the universe from the landscape multiverse there is a generic prediction that pre-inflation quantum entanglement with other universes should give rise to a cosmic bulk flow with a correlation length of order horizon size and a velocity field relative to the expansion frame of the universe. Indeed, the parameters of this motion are are tightly constrained. A robust prediction can be deduced indicating that there should be an overall motion of of about 800 km/s relative to the background space time as defined by the cosmic microwave background (CMB). This talk will summarize the underlying theoretical motivation for this hypothesis. Of course our motion relative to the background space time (CMB dipole) has been known for decades and is generally attributed to the gravitational pull of the local super cluster. However, this cosmic peculiar velocity field has been recently deduced out to very large distances well beyond that of the local super cluster by using X-ray galaxy clusters as tracers of matter motion. This is achieved via the kinematic component of the Sunyaev-Zeldovich (KSZ) effect produced by Compton scattering of cosmic microwave background photons from the local hot intracluster gas. As such, this method measures peculiar velocity directly in the frame of the cluster. Similar attempts by our group and others have attempted to independently assess this bulk flow via Type la supernova redshifts. In this talk we will review the observation case for and against the existence of this bulk flow based upon the observations and predictions of the theory. If this interpretation is correct it has profound implications in that we may be observing for the first time both the physics that occurred before the big bang and the existence of the multiverse
On a Microscopic Representation of Space-Time V
Dahm, Rolf
2016-01-01
In order to extend our approach based on SU$*$(4), we were led to (real) projective and (line) Complex geometry. So here we start from quadratic Complexe which yield naturally the 'light cone' $x_{1}^{2}+x_{2}^{2}+x_{3}^{2}-x_{0}^{2}=0$ when being related to (homogeneous) point coordinates $x_{\\alpha}^{2}$ and infinitesimal dynamics by tetrahedral Complexe (or line elements). This introduces naturally projective transformations by preserving anharmonic ratios. Referring to old work of Pl{\\"u}cker relating quadratic Complexe to optics, we discuss (linear) symplectic symmetry and line coordinates, the main purpose and thread within this paper, however, is the identification and discussion of special relativity as direct invariance properties of line/Complex coordinates as well as their relation to 'quantum field theory' by complexification of point coordinates or Complexe. This can be established by the Lie mapping which relates lines/Complexe to sphere geometry so that SU(2), SU(2)$\\times$U(1), SU(2)$\\times$SU...
On a Microscopic Representation of Space-Time V
Dahm, R.
2017-01-01
In previous parts of this publication series, starting from the Dirac algebra and SU*(4), the ’dual’ compact rank-3 group SU(4) and Lie theory, we have developed some arguments and the reasoning to use (real) projective and (line) Complex geometry directly. Here, we want to extend this approach further in terms of line and Complex geometry and give some analytical examples. As such, we start from quadratic Complexe which we’ve identified in parts III and IV already as yielding naturally the ’light cone’ x_12 + x_22 + x_32 - x_02 = 0 when being related to (homogeneous) point coordinates x_α ^2 and infinitesimal dynamics by tetrahedral Complexe (or line elements). This introduces naturally projective transformations by preserving anharmonic ratios. We summarize some old work of Plücker relating quadratic Complexe to optics and discuss briefly their relation to spherical (and Schrödinger-type) equations as well as an obvious interpretation based on homogeneous coordinates and relations to conics and second order surfaces. Discussing (linear) symplectic symmetry and line coordinates, the main purpose and thread within this paper, however, is the identification and discussion of special relativity as direct invariance properties of line/Complex coordinates as well as their relation to ’quantum field theory’ by complexification of point coordinates or Complexe. This can be established by the Lie mapping1 which relates lines/Complexe to sphere geometry so that SU(2), SU(2)×U(1), SU(2)×SU(2) and the Dirac spinor description emerge without additional assumptions. We give a short outlook in that quadratic Complexe are related to dynamics e.g. power expressions in terms of six-vector products of Complexe, and action principles may be applied. (Quadratic) products like {Fμ ν }{Fμ ν }{{ or }}{Fα {{ }μ ν }}Fμ ν ^α ,1 ≤ α ≤ 3 are natural quadratic Complex expressions which may be extended by line constraints λk · ɛ = 0 with respect to an
Quantization of massive scalar fields over axis symmetric space-time backgrounds
Piedra, O P F; Oca, Alejandro Cabo Montes de; Piedra, Owen Pavel Fernandez
2007-01-01
The renormalized mean value of the quantum Lagrangian and the Energy-Momentum tensor for scalar fields coupled to an arbitrary gravitational field configuration are analytically evaluated in the Schwinger-DeWitt approximation, up to second order in the inverse mass value. The cylindrical symmetry situation is considered. The results furnish the starting point for investigating iterative solutions of the back-reaction problem related with the quantization of cylindrical scalar field configurations. Due to the homogeneity of the equations of motion of the Klein-Gordon field, the general results are also valid for performing the quantization over either vanishing or non-vanishing mean field configurations. As an application, compact analytical expressions are derived here for the quantum mean Lagrangian and Energy-Momentum tensor in the particular background given by the Black-String space-time.
Canonical quantization of gauge fields in static space-times with applications to Rindler spaces
Lenz, F; Yazaki, K
2008-01-01
The canonical quantization in Weyl gauge of gauge fields in static space-times is presented. With an appropriate definition of transverse and longitudinal components of gauge fields, the Gauss law constraint is resolved explicitly for scalar and spinor QED and a complete non-perturbative solution is given for the quantized Maxwell-field coupled to external currents. The formalism is applied in investigations of the electromagnetic field in Rindler spaces. The relation of creation and annihilation operators in Minkowski and Rindler spaces is established and initial value problems associated with bremsstrahlung of a uniformly accelerated charge are studied. The peculiar scaling properties of scalar and gauge theories in Rindler spaces are discussed and various quantities such as the photon condensate or the interaction energy of static charges or scalar sources are computed.
Energy and Momentum of Bell-Szekeres Space-time in Moller Prescription
Aygun, S
2007-01-01
This study is purposed to elaborate the problem of energy and momentum distribution of the Bell-Szekeres space time in General theory of relativity. In this connection, we use the energy-momentum definition of M{\\o}ller and obtained that the energy momentum distributions (due to matter plus field) are vanishing everywhere. This results are exactly same as viewpoint of Aygun et al. and agree with a previous work of Rosen, Salti et al. and Johri et al. who investigated the problem of the energy in Friedmann-Robertson-Walker universe. The result that the total energy-momentum of the universe in these models are zero support the viewpoint of Tryon.
A hybrid method of estimating pulsating flow parameters in the space-time domain
Pałczyński, Tomasz
2017-05-01
This paper presents a method for estimating pulsating flow parameters in partially open pipes, such as pipelines, internal combustion engine inlets, exhaust pipes and piston compressors. The procedure is based on the method of characteristics, and employs a combination of measurements and simulations. An experimental test rig is described, which enables pressure, temperature and mass flow rate to be measured within a defined cross section. The second part of the paper discusses the main assumptions of a simulation algorithm elaborated in the Matlab/Simulink environment. The simulation results are shown as 3D plots in the space-time domain, and compared with proposed models of phenomena relating to wave propagation, boundary conditions, acoustics and fluid mechanics. The simulation results are finally compared with acoustic phenomena, with an emphasis on the identification of resonant frequencies.
Single top quark production in t-channel at the LHC in noncommutative space-time
Yaser Ayazi, Seyed, E-mail: yaserayazi@ipm.ir [School of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of); Esmaeili, Sina [Science and Research Branch, Islamic Azad University (Iran, Islamic Republic of); Mohammadi Najafabadi, Mojtaba [School of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of)
2012-05-30
We study the production cross section of the t-channel single top quark at the LHC in the noncommutative space-time. It is shown that the deviation of the t-channel single top cross section from the Standard Model value because of noncommutativity is significant when |{theta}{sup {yields}}|{>=}0{sup -4} GeV{sup -2}. Using the present experimental precision in measurement of the t-channel cross section, we apply upper limit on the noncommutative parameter. When a single top quark decays, there is a significant amount of angular correlation, in the top quark rest frame between the top spin direction and the direction of the charged lepton momentum from its decay. We study the effect of noncommutativity on the spin correlation and we find that depending on the noncommutative scale, the angular correlation can enhance considerably. Then, we provide limits on the noncommutative scale for various possible relative uncertainties on the spin correlation measurement.
Non-relativistic supergravity in three space-time dimensions
Zojer, Thomas
2016-01-01
This year Einstein's theory of general relativity celebrates its one hundredth birthday. It supersedes the non-relativistic Newtonian theory of gravity in two aspects: i) there is a limiting velocity, nothing can move quicker than the speed of light and ii) the theory is valid in arbitrary coordinat
Non-relativistic supergravity in three space-time dimensions
Zojer, Thomas
2016-01-01
This year Einstein's theory of general relativity celebrates its one hundredth birthday. It supersedes the non-relativistic Newtonian theory of gravity in two aspects: i) there is a limiting velocity, nothing can move quicker than the speed of light and ii) the theory is valid in arbitrary
Linear programming bounds for unitary space time codes
Creignou, Jean
2008-01-01
The linear programming method is applied to the space $\\U_n(\\C)$ of unitary matrices in order to obtain bounds for codes relative to the diversity sum and the diversity product. Theoretical and numerical results improving previously known bounds are derived.
Rational Thinking and Reasonable Thinking in Physics
Isaeva E. A.
2008-04-01
Full Text Available The usual concept of space and time, based on Aristotle's principle of contemplation of the world and of the absoluteness of time, is a product of rational thinking. At the same time, in philosophy, rational thinking differs from reasonable thinking; the aim of logic is to distinguish finite forms from infinite forms. Agreeing that space and time are things of infinity in this work, we shall show that, with regard to these two things, it is necessary to apply reasonable thinking. Spaces with non-Euclidean geometry, for example Riemannian and Finslerian spaces, in particular, the space of the General Theory of the Relativity (four-dimensional pseudo-Riemannian geometry and also the concept of multi-dimensional space-time are products of reasonable thinking. Consequently, modern physical experiment not dealing with daily occurrences (greater speeds than a low speed to the velocity of light, strong fields, singularities, etc. can be covered only by reasonable thinking.
Rational Thinking and Reasonable Thinking in Physics
Isaeva E. A.
2008-04-01
Full Text Available The usual concept of space and time, based on Aristotle’s principle of contemplation of the world and of the absoluteness of time, is a product of rational thinking. At the same time, in philosophy, rational thinking differs from reasonable thinking; the aim of logic is to distinguish finite forms from infinite forms. Agreeing that space and time are things of infinity in this work, we shall show that, with regard to these two things, it is necessary to apply reasonable thinking. Spaces with non-Euclidean geometry, for example Riemannian and Finslerian spaces, in particular, the space of the General Theory of the Relativity (four-dimensional pseudo-Riemannian geometry and also the concept of multi-dimensional space-time are products of reasonable thinking. Consequently, modern physical experiment not dealing with daily occurrences (greater speeds than a low speed to the velocity of light, strong fields, singularities, etc. can be covered only by reasonable thinking.
Superluminal Velocities in the Synchronized Space-Time
Medvedev S. Yu.
2014-07-01
Full Text Available Within the framework of the non-gravitational generalization of the special relativity, a problem of possible superluminal motion of particles and signals is considered. It has been proven that for the particles with non-zero mass the existence of anisotropic light barrier with the shape dependent on the reference frame velocity results from the Tangherlini transformations. The maximal possible excess of neutrino velocity over the absolute velocity of light related to the Earth (using th e clock with instantaneous synchronization has been estimated. The illusoriness of t he acausality problem has been illustrated and conclusion is made on the lack of the upper limit of velocities of signals of informational nature.
Space, time, and quanta an introduction to contemporary physics
Mills, Robert
1994-01-01
This is the ideal supplement for courses emphasizing modern physics. Part I covers special relativity and the meaning of time, Part II discusses quantum physics, Part III looks at elementary particles and force fields. The three self-contained parts can be used separately or in combination. Familiarity with calculus and classical physics, while helpful, is not necessary as the pertinent ideas of these fields are introduced as needed.
Space-Time Processing Applications for Wireless Communications
Hult, Tommy
2008-01-01
Wireless mobile communication networks are rapidly growing at an incredible rate around the world and a number of improved and emerging technologies are seen to be critical to the improved economics and performance of these networks. The technical revolution and continuing growth of mobile radio communication systems has been made possible by extraordinary advances in the related fields of digital computing, high-speed circuit technology, the Internet and, of course, digital signal processing...
On a microscopic representation of space-time IV
Dahm, Rolf
2017-05-01
We summarize some previous work on SU(4) describing hadron representations and transformations as well as its noncompact "counterpart" SU*(4) being the complex embedding of SL(2,H). So after having related the 16-dim Dirac algebra to SU*(4), on the one hand we have access to real, complex, and quaternionic Lie group chains and their respective algebras, on the other hand it is of course possible to relate physical descriptions to the respective representations. With emphasis on the common maximal compact subgroup USp(4), we are led to projective geometry of the real 3-space and various transfer principles which we use to extend the previous work on the rank 3-algebras above. On real spaces, such considerations are governed by the groups SO( n, m) with n + m = 6. The central thread, however, focuses here on line and Complex geometry which finds its well-known counterparts in descriptions of electromagnetism and special relativity as well as—using transfer principles—in Dirac, gauge, and quantum field theory. We discuss a simple picture where Complexe of second grade play the major and dominant rôle to unify (real) projective geometry, complex representation theory and line/Complex representations in order to proceed to dynamics.
Surface tension with Normal Curvature in Curved Space-Time
kumar, Himanshu; Ahmad, Suhail
2012-01-01
With an aim to include the contribution of surface tension in the action of the boundary, we define the tangential pressure in terms of surface tension and Normal curvature in a more naturally geometric way. First, we show that the negative tangential pressure is independent of the four-velocity of a very thin hyper-surface. Second, we relate the 3-pressure of a surface layer to the normal curvature and the surface tension. Third, we relate the surface tension to the energy of the surface layer. Four, we show that the delta like energy flows across the hyper-surface will be zero for such a representation of intrinsic 3-pressure. Five, for the weak field approximation and for static spherically symmetric configuration, we deduce the classical Kelvin's relation. Six, we write a modified action for the boundary having contributions both from surface tension and normal curvature of the surface layer. Also we propose a method to find the physical action assuming a reference background, where the background is not ...
On a Microscopic Representation of Space-Time IV
Dahm, Rolf
2015-01-01
We summarize some previous work on SU(4) describing hadron representations and transformations as well as its noncompact 'counterpart' SU$*$(4) being the complex embedding of Sl(2,$\\mathbb{H}$). So after having related the 16-dim Dirac algebra to SU$*$(4), on the one hand we have access to real, complex and quaternionic Lie group chains and their respective algebras, on the other hand it is of course possible to relate physical descriptions to the respective representations. With emphasis on the common maximal compact subgroup USp(4), we are led to projective geometry of real 3-space and various transfer principles which we use to extend previous work on the rank 3-algebras above. On real spaces, such considerations are governed by the groups SO($n$,$m$) with $n+m=6$. The central thread, however, focuses here on line and Complex geometry which finds its well-known counterparts in descriptions of electromagnetism and special relativity as well as - using transfer principles - in Dirac, gauge and quantum field ...
The infrared sector of quantum fields on cosmological space-times
Janssen, T.M.
2009-01-01
In this thesis the infrared properties of massless scalar fields, with a possible coupling to the Ricci scalar on a cosmological background are studied. Our background space-time is a homogeneous, flat FLRW space-time, with the additional constraint that the deceleration parameter is constant. It
The infrared sector of quantum fields on cosmological space-times
Janssen, T.M.
2009-01-01
In this thesis the infrared properties of massless scalar fields, with a possible coupling to the Ricci scalar on a cosmological background are studied. Our background space-time is a homogeneous, flat FLRW space-time, with the additional constraint that the deceleration parameter is constant. It ha
Using adaptive antenna array in LTE with MIMO for space-time processing
Abdourahamane Ahmed Ali
2015-04-01
Full Text Available The actual methods of improvement the existent wireless transmission systems are proposed. Mathematical apparatus is considered and proved by models, graph of which are shown, using the adaptive array antenna in LTE with MIMO for space-time processing. The results show that improvements, which are joined with space-time processing, positively reflects on LTE cell size or on throughput
Space-time discontinuous Galerkin discretization of rotating shallow water equations on moving grids
Ambati, V.R.; Bokhove, Onno
2006-01-01
A space-time discontinuous Galerkin (DG) discretization is presented for the (rotating) shallow water equations over varying topography. We formulate the space-time DG finite element discretization in an efficient and conservative discretization. The HLLC flux is used as numerical flux through the
Domain Structure of Black Hole Space-Times with a Cosmological Constant
Armas, Jay; Harmark, Troels
2011-01-01
We generalize the domain structure for stationary black hole space-times to include asymptotically de Sitter and Anti-de Sitter space-times. Given a set of commuting Killing vector fields of a space-time the domain structure lives on the submanifold of the orbit space on which at least one of the Killing vector fields has zero norm. In general the domain structure provides topological and geometrical invariants of black hole space-times that in specific cases have proven to be a crucial part of a full characterization leading to uniqueness theorems. In four and five dimensions the domain structure generalizes the rod structure. We examine in detail the domain structure for four, five, six and seven-dimensional black hole space-times including a very general class of spherically symmetric and static black hole space-times as well as the exact solutions for Kerr-(Anti)-de Sitter black holes. While for asymptotically Anti-de Sitter space-times the domain structures resemble that of asymptotically flat space-time...
Space & time discontinuities in Liouville theory and its discrete analogue
Doikou, Anastasia
2016-01-01
We consider the deformed harmonic oscillator as a discrete version of the Liouville theory and study this model in the presence of local integrable defects. From this, the time evolution of the defect degrees of freedom are determined, found in the form of the local equations of motion. We also revisit the continuous Liouville theory, deriving its local integrals of motion and comparing these with previous results from the sine-Gordon point of view.Finally, the generic Backlund type relations are presented, corresponding to the implementation of time-like and space-like impurities in the continuum model.
The Universality of Penrose Limits near Space-Time Singularities
Blau, Matthias; O'Loughlin, M; Papadopoulos, G; Blau, Matthias; Borunda, Monica; Loughlin, Martin O'; Papadopoulos, George
2004-01-01
We prove that Penrose limits of metrics with arbitrary singularities of power-law type show a universal leading u^{-2}-behaviour near the singularity provided that the dominant energy condition is satisfied and not saturated. For generic power-law singularities of this type the oscillator frequencies of the resulting homogeneous singular plane wave turn out to lie in a range which is known to allow for an analytic extension of string modes through the singularity. The discussion is phrased in terms of the recently obtained covariant characterisation of the Penrose limit; the relation with null geodesic deviation is explained in detail.
Threshold exceedance risk assessment in complex space-time systems
Angulo, José M.; Madrid, Ana E.; Romero, José L.
2015-04-01
Environmental and health impact risk assessment studies most often involve analysis and characterization of complex spatio-temporal dynamics. Recent developments in this context are addressed, among other objectives, to proper representation of structural heterogeneities, heavy-tailed processes, long-range dependence, intermittency, scaling behavior, etc. Extremal behaviour related to spatial threshold exceedances can be described in terms of geometrical characteristics and distribution patterns of excursion sets, which are the basis for construction of risk-related quantities, such as in the case of evolutionary study of 'hotspots' and long-term indicators of occurrence of extremal episodes. Derivation of flexible techniques, suitable for both the application under general conditions and the interpretation on singularities, is important for practice. Modern risk theory, a developing discipline motivated by the need to establish solid general mathematical-probabilistic foundations for rigorous definition and characterization of risk measures, has led to the introduction of a variety of classes and families, ranging from some conceptually inspired by specific fields of applications, to some intended to provide generality and flexibility to risk analysts under parametric specifications, etc. Quantile-based risk measures, such as Value-at-Risk (VaR), Average Value-at-Risk (AVaR), and generalization to spectral measures, are of particular interest for assessment under very general conditions. In this work, we study the application of quantile-based risk measures in the spatio-temporal context in relation to certain geometrical characteristics of spatial threshold exceedance sets. In particular, we establish a closed-form relationship between VaR, AVaR, and the expected value of threshold exceedance areas and excess volumes. Conditional simulation allows us, by means of empirical global and local spatial cumulative distributions, the derivation of various statistics of
Space-Time Data fusion for Remote Sensing Applications
Braverman, Amy; Nguyen, H.; Cressie, N.
2011-01-01
NASA has been collecting massive amounts of remote sensing data about Earth's systems for more than a decade. Missions are selected to be complementary in quantities measured, retrieval techniques, and sampling characteristics, so these datasets are highly synergistic. To fully exploit this, a rigorous methodology for combining data with heterogeneous sampling characteristics is required. For scientific purposes, the methodology must also provide quantitative measures of uncertainty that propagate input-data uncertainty appropriately. We view this as a statistical inference problem. The true but notdirectly- observed quantities form a vector-valued field continuous in space and time. Our goal is to infer those true values or some function of them, and provide to uncertainty quantification for those inferences. We use a spatiotemporal statistical model that relates the unobserved quantities of interest at point-level to the spatially aggregated, observed data. We describe and illustrate our method using CO2 data from two NASA data sets.
Enhancements to the GW space-time method
Steinbeck, L.; Rubio, A.; Reining, L.; Torrent, M.; White, I. D.; Godby, R. W.
2000-03-01
We describe the following new features which significantly enhance the power of the recently developed real-space imaginary-time GW scheme (Rieger et al., Comp. Phys. Commun. 117 (1999) 211) for the calculation of self-energies and related quantities of solids: (i) to fit the smoothly decaying time/energy tails of the dynamically screened Coulomb interaction and other quantities to model functions, treating only the remaining time/energy region close to zero numerically and performing the Fourier transformation from time to energy and vice versa by a combination of analytic integration of the tails and Gauss-Legendre quadrature of the remaining part and (ii) to accelerate the convergence of the band sum in the calculation of the Green's function by replacing higher unoccupied eigenstates by free electron states (plane waves). These improvements make the calculation of larger systems (surfaces, clusters, defects etc.) accessible.
Space-Time Quantization, Elementary Particles and Dark Matter
Meessen, A
2011-01-01
Relativity and quantum mechanics are generalized by considering a finite limit for the smallest measurable distance. The value a of this quantum of length is unknown, but it is a universal constant, like c and h. It depends on the total energy content of our universe (hc/2a) and physical laws are modified when it is finite. The eigenvalues of (x, y, z, ct) coordinates are integer or half-integer multiples of a. This yields four new quantum numbers, specifying "particle states" in terms of phase differences at the smallest possible scale. They account for all known elementary particles and predict the existence of neutral ones that could constitute dark matter particles. This theory is thus experimentally testable.
Dynamic Theory: a new view of space, time, and matter
Williams, P.E.
1980-12-01
The theory presented represents a different approach toward unification of the various branches of physics. The foundation of the theory rests upon generalizations of the classical laws of thermodynamics, particularly Caratheodory's abstract statement of the second law. These adopted laws are shown to produce, as special cases, current theories such as Einstein's General and Special Relativity, Maxwell's electromagnetism, classical thermodynamics, and quantum principles. In addition to this unification, the theory provides predictions that may be experimentally investigated. Some of the predictions are a limiting rate of mass conversion, reduced pressures in electromagnetically contained plasmas, increased viscous effects in shocked materials, a finite self-energy for a charged particle, and the possible creation of particles with velocities greater than the speed of light. 8 figures.
Critical phenomena of regular black holes in anti-de Sitter space-time
Fan, Zhong-Ying [Peking University, Center for High Energy Physics, Beijing (China)
2017-04-15
In General Relativity, addressing coupling to a non-linear electromagnetic field, together with a negative cosmological constant, we obtain the general static spherical symmetric black hole solution with magnetic charges, which is asymptotic to anti-de Sitter (AdS) space-times. In particular, for a degenerate case the solution becomes a Hayward-AdS black hole, which is regular everywhere in the full space-time. The existence of such a regular black hole solution preserves the weak energy condition, while the strong energy condition is violated. We then derive the first law and the Smarr formula of the black hole solution. We further discuss its thermodynamic properties and study the critical phenomena in the extended phase space where the cosmological constant is treated as a thermodynamic variable as well as the parameter associated with the non-linear electrodynamics. We obtain many interesting results such as: the Maxwell equal area law in the P-V (or S-T) diagram is violated and consequently the critical point (T{sub *},P{sub *}) of the first order small-large black hole transition does not coincide with the inflection point (T{sub c},P{sub c}) of the isotherms; the Clapeyron equation describing the coexistence curve of the Van der Waals (vdW) fluid is no longer valid; the heat capacity at constant pressure is finite at the critical point; the various exponents near the critical point are also different from those of the vdW fluid. (orig.)
Using stochastic space-time models to map extreme precipitation in southern Portugal
A. C. Costa
2008-07-01
Full Text Available The topographic characteristics and spatial climatic diversity are significant in the South of continental Portugal where the rainfall regime is typically Mediterranean. Direct sequential cosimulation is proposed for mapping an extreme precipitation index in southern Portugal using elevation as auxiliary information. The analysed index (R5D can be considered a flood indicator because it provides a measure of medium-term precipitation total. The methodology accounts for local data variability and incorporates space-time models that allow capturing long-term trends of extreme precipitation, and local changes in the relationship between elevation and extreme precipitation through time. Annual gridded datasets of the flood indicator are produced from 1940 to 1999 on 800 m×800 m grids by using the space-time relationship between elevation and the index. Uncertainty evaluations of the proposed scenarios are also produced for each year. The results indicate that the relationship between elevation and extreme precipitation varies locally and has decreased through time over the study region. In wetter years the flood indicator exhibits the highest values in mountainous regions of the South, while in drier years the spatial pattern of extreme precipitation has much less variability over the study region. The uncertainty of extreme precipitation estimates also varies in time and space, and in earlier decades is strongly dependent on the density of the monitoring stations network. The produced maps will be useful in regional and local studies related to climate change, desertification, land and water resources management, hydrological modelling, and flood mitigation planning.
Trade-offs across space, time, and ecosystem services
Rodriguez, J.P.; Beard, T.D.; Bennett, E.M.; Cumming, Graeme S.; Cork, S.J.; Agard, J.; Dobson, A.P.; Peterson, G.D.
2006-01-01
Ecosystem service (ES) trade-offs arise from management choices made by humans, which can change the type, magnitude, and relative mix of services provided by ecosystems. Trade-offs occur when the provision of one ES is reduced as a consequence of increased use of another ES. In some cases, a trade-off may be an explicit choice; but in others, trade-offs arise without premeditation or even awareness that they are taking place. Trade-offs in ES can be classified along three axes: spatial scale, temporal scale, and reversibility. Spatial scale refers to whether the effects of the trade-off are felt locally or at a distant location. Temporal scale refers to whether the effects take place relatively rapidly or slowly. Reversibility expresses the likelihood that the perturbed ES may return to its original state if the perturbation ceases. Across all four Millennium Ecosystem Assessment scenarios and selected case study examples, trade-off decisions show a preference for provisioning, regulating, or cultural services (in that order). Supporting services are more likely to be "taken for granted." Cultural ES are almost entirely unquantified in scenario modeling; therefore, the calculated model results do not fully capture losses of these services that occur in the scenarios. The quantitative scenario models primarily capture the services that are perceived by society as more important - provisioning and regulating ecosystem services - and thus do not fully capture trade-offs of cultural and supporting services. Successful management policies will be those that incorporate lessons learned from prior decisions into future management actions. Managers should complement their actions with monitoring programs that, in addition to monitoring the short-term provisions of services, also monitor the long-term evolution of slowly changing variables. Policies can then be developed to take into account ES trade-offs at multiple spatial and temporal scales. Successful strategies will
Trade-offs across Space, Time, and Ecosystem Services
Andrew P. Dobson
2006-06-01
Full Text Available Ecosystem service (ES trade-offs arise from management choices made by humans, which can change the type, magnitude, and relative mix of services provided by ecosystems. Trade-offs occur when the provision of one ES is reduced as a consequence of increased use of another ES. In some cases, a trade-off may be an explicit choice; but in others, trade-offs arise without premeditation or even awareness that they are taking place. Trade-offs in ES can be classified along three axes: spatial scale, temporal scale, and reversibility. Spatial scale refers to whether the effects of the trade-off are felt locally or at a distant location. Temporal scale refers to whether the effects take place relatively rapidly or slowly. Reversibility expresses the likelihood that the perturbed ES may return to its original state if the perturbation ceases. Across all four Millennium Ecosystem Assessment scenarios and selected case study examples, trade-off decisions show a preference for provisioning, regulating, or cultural services (in that order. Supporting services are more likely to be “taken for granted.” Cultural ES are almost entirely unquantified in scenario modeling; therefore, the calculated model results do not fully capture losses of these services that occur in the scenarios. The quantitative scenario models primarily capture the services that are perceived by society as more important—provisioning and regulating ecosystem services—and thus do not fully capture trade-offs of cultural and supporting services. Successful management policies will be those that incorporate lessons learned from prior decisions into future management actions. Managers should complement their actions with monitoring programs that, in addition to monitoring the short-term provisions of services, also monitor the long-term evolution of slowly changing variables. Policies can then be developed to take into account ES trade-offs at multiple spatial and temporal scales
Powering Up With Space-Time Wind Forecasting
Hering, Amanda S.
2010-03-01
The technology to harvest electricity from wind energy is now advanced enough to make entire cities powered by it a reality. High-quality, short-term forecasts of wind speed are vital to making this a more reliable energy source. Gneiting et al. (2006) have introduced a model for the average wind speed two hours ahead based on both spatial and temporal information. The forecasts produced by this model are accurate, and subject to accuracy, the predictive distribution is sharp, that is, highly concentrated around its center. However, this model is split into nonunique regimes based on the wind direction at an offsite location. This paper both generalizes and improves upon this model by treating wind direction as a circular variable and including it in the model. It is robust in many experiments, such as predicting wind at other locations. We compare this with the more common approach of modeling wind speeds and directions in the Cartesian space and use a skew-t distribution for the errors. The quality of the predictions from all of these models can be more realistically assessed with a loss measure that depends upon the power curve relating wind speed to power output. This proposed loss measure yields more insight into the true value of each models predictions. © 2010 American Statistical Association.
Discrete Space-Time: History and Recent Developments
Crouse, David
2017-01-01
Discussed in this work is the long history and debate of whether space and time are discrete or continuous. Starting from Zeno of Elea and progressing to Heisenberg and others, the issues with discrete space are discussed, including: Lorentz contraction (time dilation) of the ostensibly smallest spatial (temporal) interval, maintaining isotropy, violations of causality, and conservation of energy and momentum. It is shown that there are solutions to all these issues, such that discrete space is a viable model, yet the solution require strict non-absolute space (i.e., Mach's principle) and a re-analysis of the concept of measurement and the foundations of special relativity. In developing these solutions, the long forgotten but important debate between Albert Einstein and Henri Bergson concerning time will be discussed. Also discussed is the resolution to the Weyl tile argument against discrete space; however, the solution involves a modified version of the typical distance formula. One example effect of discrete space is then discussed, namely how it necessarily imposes order upon Wheeler's quantum foam, changing the foam into a gravity crystal and yielding crystalline properties of bandgaps, Brilluoin zones and negative inertial mass for astronomical bodies.
Spinorial space-time and the origin of Quantum Mechanics. The dynamical role of the physical vacuum
Gonzalez-Mestres, Luis
2016-11-01
Is Quantum Mechanics really and ultimate principle of Physics described by a set of intrinsic exact laws? Are standard particles the ultimate constituents of matter? The two questions appear to be closely related, as a preonic structure of the physical vacuum would have an influence on the properties of quantum particles. Although the first preon models were just « quark-like » and assumed preons to be direct constituents of the conventional « elementary » particles, we suggested in 1995 that preons could instead be constituents of the physical vacuum (the superbradyon hypothesis). Standard particles would then be excitations of the preonic vacuum and have substantially different properties from those of preons themselves (critical speed…). The standard laws of Particle Physics would be approximate expressions generated from basic preon dynamics. In parallel, the mathematical properties of space-time structures such as the spinoral space-time (SST) we introduced in 1996-97 can have strong implications for Quantum Mechanics and even be its real origin. We complete here our recent discussion of the subject by pointing out that: i) Quantum Mechanics corresponds to a natural set of properties of vacuum excitations in the presence of a SST geometry ; ii) the recently observed entanglement at long distances would be a logical property if preons are superluminal (superbradyons), so that superluminal signals and correlations can propagate in vacuum ; iii) in a specific description, the function of space-time associated to the extended internal structure of a spin-1/2 particle at very small distances may be incompatible with a continuous motion at space and time scales where the internal structure of vacuum can be felt. In the dynamics associated to iii), and using the SST approach to space-time, a contradiction can appear between macroscopic and microscopic space-times due to an overlap in the time variable directly related to the fact that a spinorial function takes
Space-Time-Isotopic Trends of Snake River Plain Basalts
Jean, M. M.; Hanan, B. B.; Shervais, J. W.
2010-12-01
The Snake River Plain (SRP) volcanic province is an 800 km track of basalt extending from the Owyhee Plateau to its current terminus, the Yellowstone Plateau. It is one of several late-Tertiary magmatic terranes that also include the Cascades magmatic arc, the Columbia River basalts, and the Oregon Plateau basalts; all of which are adjacent to the Basin and Range Province extensional system (Hughes and McCurry, 2002). This province represents the track of the Yellowstone plume and consists of basalt that is compositionally similar to ocean-island basalt. This basalt overlies a series of rhyolitic eruptive centers (overlapping caldera complexes, ignimbrites, and caldera-filling eruptions) that signal the arrival of the plume head (Christiansen, 2001) and herald the onset of plume-related rhyolitic and basaltic volcanism (Pierce et al., 2002). Observed within the SRP are two basalt types: the dominant low-K olivine tholeiites and less common high-K alkaline basalts. We report new Sr-, Nd-, and Pb-isotopic analyses of these two basalt types from all three SRP provinces: eastern, central, and western. Low-K tholeiites are enriched in 143Nd/144Nd and 86Sr/87Sr and forms a quasi-linear array in Pb-isotope space, along with Craters of the Moon and eastern SRP basalts. High-K lavas are found largely in the western plain, and have a uniquely different isotopic signature. They are depleted in 143Nd/144Nd and 86Sr/87Sr, relative to the low-K tholeiites, and plot closer to the BSE component of Zindler and Hart (1986). They also share the same Pb-isotopic space with high-K basalts from Smith Prairie (Boise River Group 2 of Vetter and Shervais, 1992). One low-K tholeiite - Eureka North, plots with these high alkali basalts. Mass balance models have demonstrated an increasing plume component from the Yellowstone caldera in the east to the craton edge in the west. The lavas analyzed in this study conform remarkably to this model. The mass fraction of plume component in western
Noutchegueme, N; Noutchegueme, Norbert; Tetsadjio, Mesmin Erick
2003-01-01
We prove, for the relativistic Boltzmann equation in the homogeneous case, on the Minkowski space-time, a global in time existence and uniqueness theorem. The method we develop extends to the cases of some curved space-times such as the flat Robertson-Walker space-time and some Bianchi type I space-times.
Timescape: a simple space-time interpolation geostatistical Algorithm
Ciolfi, Marco; Chiocchini, Francesca; Gravichkova, Olga; Pisanelli, Andrea; Portarena, Silvia; Scartazza, Andrea; Brugnoli, Enrico; Lauteri, Marco
2016-04-01
explored in many ways, including the extraction of time series at fixed locations and GIS layers at constant times, allowing for the inclusion of the model in the users' established workflow. The software requirements are relatively modest since it has been purposely designed for potential users in various research field with a limited computing power at their disposal. Any respectful modern PC or laptop can run it. Users however need a separate database for sample data and models storage because these can be quite bulky in terms of data output: a single model can be composed of several billions of voxels (three-dimensional discrete cells, a sort of 3D pixels). Running times range from a few minutes for sketch models to some days of evaluation for a full-size model, depending on the users' hardware and model size.
The squares of the dirac and spin-dirac operators on a riemann-cartan space(time)
Notte-Cuello, E. A.; Rodrigues, W. A.; Souza, Q. A. G.
2007-08-01
In this paper we introduce the Dirac and spin-Dirac operators associated to a connection on Riemann-Cartan space(time) and standard Dirac and spin-Dirac operators associated with a Levi-Civita connection on a Riemannian (Lorentzian) space(time) and calculate the squares of these operators, which play an important role in several topics of modern mathematics, in particular in the study of the geometry of moduli spaces of a class of black holes, the geometry of NS-5 brane solutions of type II supergravity theories and BPS solitons in some string theories. We obtain a generalized Lichnerowicz formula, decompositions of the Dirac and spin-Dirac operators and their squares in terms of the standard Dirac and spin-Dirac operators and using the fact that spinor fields (sections of a spin-Clifford bundle) have representatives in the Clifford bundle we present also a noticeable relation involving the spin-Dirac and the Dirac operators.
McDuffee, Ryan
2016-01-01
Recent observations of gravitational waves by the Laser Interferometer Gravitational-Wave Observatory (LIGO) has confirmed one of the last outstanding predictions in general relativity and in the process opened up a new frontier in astronomy and astrophysics. Additionally the observation of gravitational waves has also given us the data needed to deduce the physical properties of space time. Bredberg et al have shown in their 2011 paper titled From Navier-Stokes to Einstein, that for every solution of the incompressible Navier-Stokes equation in p + 1 dimensions, there is a uniquely associated dual" solution of the vacuum Einstein equations in p + 2 dimensions. The author shows that the physical properties of space time can be deduced using the recent measurements from the Laser Interferometer Gravitational-Wave Observatory and solutions from the incompressible Navier-Stokes equation.
Dai, De-Chang
2012-01-01
We study a retarded potential solution of a massless scalar field in curved space-time. In a special ansatz for a particle at rest whose magnitude of the (scalar) charge is changing with time, we found an exact analytic solution. The solution indicates that the phase velocity of the retarded potential of a non-moving scalar charge is position dependent, and may easily be greater than the speed of light at a given point. In the case of the Schwarzschild space-time, at the horizon, the phase velocity becomes infinitely faster than the coordinate speed of light at that point. Superluminal phase velocity is relatively common phenomenon, with the the phase velocity of the massive Klein-Gordon field as the best known example. We discuss why it is possible to have modes with superluminal phase velocity even for a massless field.
Zero Geometry, Zero Space Time, The Seeds of The Final Theory
Kambiz Afrasiabi
2011-01-01
Full Text Available Problem statement: Lack of understanding And scientific formulation of zero geometry and zero space-time and the truth about initiation conditions would continue to keep us all in dark and we would continue to create more theories defining our observations about the known universe which could Indeed be part of our illusionary perception of reality And as long as they continue to align themselves with our observations we will continue to obey and propagate them. Approach: Second law of thermodynamics which is considered to be the most fundamental law governing The known universe and its behavior and at all levels from micro to macro cosmos is itself subject to such flaws simply because it is nonexistent in zero space-time and it reaches infinity at leap out of zero state bordered by infinity wall (the outermost border of the leap universe in no time. This law dictates that in the known universe/post big bang universe which is around 13.4 billion light years old the index of instability which inversely correlates with free energy incessantly increases following its inception, though we are in dark regarding the initiation condition of the known universe and the relation of initiation condition with entropy and This needs to be understood, dissected and formulated Into the new physics on an urgent basis. Results: Big bang which has been proposed to give rise to the known universe presumably is the product of collision of two p-branes and this collision is expected to be similar in nature to the collision of biological p-branes In which case one p-brane impregnates the other and I have alluded to that in my previous publications; Following collision of cosmic p-branes the free energy of the impregnated p-brane increases from zero to infinity in no time and because the cosmic p-branes are the residents of zero geometry and zero space-time in which all the values are zero , i.e., free energy and entropy are paradoxically both zero and because p
Schild Action and Space-Time Uncertainty Principle in String Theory
Yoneya, T
1997-01-01
We show that the path-integral quantization of relativistic strings with the Schild action is essentially equivalent to the usual Polyakov quantization at critical space-time dimensions. We then present an interpretation of the Schild action which points towards a derivation of superstring theory as a theory of quantized space-time where the squared string scale, $\\ell_s^2 \\sim \\alpha'$, plays the role of the minimum quantum for space-time areas. A tentative approach towards such a goal is proposed, based on a microcanonical formulation of large N supersymmetric matrix model.
Generation and evaluation of space-Time trajectories of photovoltaic power
Golestaneh, Faranak; Gooi, Hoay Beng; Pinson, Pierre
2016-01-01
spatio-temporal dependencies in PV generation. Multivariate predictive distributions are modelled and space-time trajectories describing the potential evolution of forecast errors through successive lead-times and locations are generated. Discrimination ability of the relevant scoring rules...... on performance assessment of space-time trajectories of PV generation is also studied. Finally, the advantage of taking into account space-time correlations over probabilistic and point forecasts is investigated. The empirical investigation is based on the solar PV dataset of the Global Energy Forecasting...
An Approach to Integrate a Space-Time GIS Data Model with High Performance Computers
Wang, Dali [ORNL; Zhao, Ziliang [University of Tennessee, Knoxville (UTK); Shaw, Shih-Lung [ORNL
2011-01-01
In this paper, we describe an approach to integrate a Space-Time GIS data model on a high performance computing platform. The Space-Time GIS data model has been developed on a desktop computing environment. We use the Space-Time GIS data model to generate GIS module, which organizes a series of remote sensing data. We are in the process of porting the GIS module into an HPC environment, in which the GIS modules handle large dataset directly via parallel file system. Although it is an ongoing project, authors hope this effort can inspire further discussions on the integration of GIS on high performance computing platforms.
Displaying time series, spatial, and space-time data with R
Perpinan Lamigueiro, Oscar
2014-01-01
Code and Methods for Creating High-Quality Data GraphicsA data graphic is not only a static image, but it also tells a story about the data. It activates cognitive processes that are able to detect patterns and discover information not readily available with the raw data. This is particularly true for time series, spatial, and space-time datasets.Focusing on the exploration of data with visual methods, Displaying Time Series, Spatial, and Space-Time Data with R presents methods and R code for producing high-quality graphics of time series, spatial, and space-time data. Practical examples using
Exponential rational function method for space-time fractional differential equations
Aksoy, Esin; Kaplan, Melike; Bekir, Ahmet
2016-04-01
In this paper, exponential rational function method is applied to obtain analytical solutions of the space-time fractional Fokas equation, the space-time fractional Zakharov Kuznetsov Benjamin Bona Mahony, and the space-time fractional coupled Burgers' equations. As a result, some exact solutions for them are successfully established. These solutions are constructed in fractional complex transform to convert fractional differential equations into ordinary differential equations. The fractional derivatives are described in Jumarie's modified Riemann-Liouville sense. The exact solutions obtained by the proposed method indicate that the approach is easy to implement and effective.
Theoretical analysis of Casimir and thermal Casimir effect in stationary space-time
Zhang, Anwei
2017-10-01
We investigate Casimir effect as well as thermal Casimir effect for a pair of parallel perfectly plates placed in general stationary space-time background. It is found that the Casimir energy is influenced by the 00-component of metric and the corresponding quantity in dragging frame. We give a scheme to renormalize thermal correction to free energy in curved space-time. It is shown that the thermal corrections to Casimir thermodynamic quantities not only depend on the proper temperature and proper geometrical parameters of the plates, but also on the determinant of space-time metric.
Energy Balance of a Bose Gas in Curved Space-times
Matos, Tonatiuh; Bernal, Tula
2016-01-01
In the present work, we obtain a general energy balance equation for a boson gas in curved space-times that can be interpreted as the generalization of the corresponding first law of thermodynamics for the system. By using a 3+1 foliation of the space-time and performing a Madelung transformation, we rewrite the Klein-Gordon-Maxwell equations in a general curved space-time into its hydrodynamic version, where we can identify the different energy contributions of the system and separate them into the gravitational, quantum, electromagnetic and kinetic ones.
Nonuniqueness of Representations of Wave Equations in Lorentzian Space-Times
Beyer, Horst Reinhard
2012-01-01
This brief note wants to bring to attention that the formulation of physically reasonable initial-boundary value problems for wave equations in Lorentzian space-times is not unique, i.e., that there are inequivalent such formulations that lead to a different outcome of the stability discussion of the solutions. For demonstration, the paper uses the case of the wave equation on the right Rindler wedge in 2-dimensional Minkowski space. The used methods can be generalized to wave equations on stationary globally hyperbolic space-times with horizons in higher dimensions, such as Schwarzschild and Kerr space-times.
Analytical approximate solution for nonlinear space-time fractional Klein-Gordon equation
Khaled A.Gepreel; Mohamed S.Mohamed
2013-01-01
The fractional derivatives in the sense of Caputo and the homotopy analysis method are used to construct an approximate solution for the nonlinear space-time fractional derivatives Klein-Gordon equation.The numerical results show that the approaches are easy to implement and accurate when applied to the nonlinear space-time fractional derivatives KleinGordon equation.This method introduces a promising tool for solving many space-time fractional partial differential equations.This method is efficient and powerful in solving wide classes of nonlinear evolution fractional order equations.
Schild Action and Space-Time Uncertainty Principle in String Theory
Yoneya, Tamiaki
1997-01-01
We show that the path-integral quantization of relativistic strings with the Schild action is essentially equivalent to the usual Polyakov quantization at critical space-time dimensions. We then present an interpretation of the Schild action which points towards a derivation of superstring theory as a theory of quantized space-time where the squared string scale plays the role of the minimum quantum for space-time areas. A tentative approach towards such a goal is proposed, based on a microca...
Rodrigues da Silva, Vicente de P; Belo Filho, Adelgcio F; Rodrigues Almeida, Rafaela S; de Holanda, Romildo Morant; da Cunha Campos, João Hugo Baracuy
2016-02-15
The principle of maximum entropy can provide consistent basis to analyze water resources and geophysical processes in general. In this paper, we propose to assess the space-time variability of rainfall and streamflow in northeastern region of Brazil using the Shannon entropy. Mean values of marginal and relative entropies were computed for a 10-year period from 189 stations in the study area and entropy maps were then constructed for delineating annual and seasonal characteristics of rainfall and streamflow. The Mann-Kendall test was used to evaluate the long-term trend in marginal entropy as well as relative entropy for two sample stations. High degree of similarity was found between rainfall and streamflow, particularly during dry season. Both rainfall and streamflow variability can satisfactorily be obtained in terms of marginal entropy as a comprehensive measure of the regional uncertainty of these hydrological events. The Shannon entropy produced spatial patterns which led to a better understanding of rainfall and streamflow characteristics throughout the northeastern region of Brazil. The total relative entropy indicated that rainfall and streamflow carried the same information content at annual and rainy season time scales.
Different Approaches for Moller's Energy in the Kasner-type Space-time
Salti, M
2005-01-01
Considering the Moller energy definition in both Einstein's theory of general relativity and tele-parallel theory of gravity, we find the energy of the universe based on viscous Kasner-type metrics. The energy distribution which includes both the matter and gravitational field is found to be zero in both of these different gravitation theories and this result agrees with previous works of Cooperstock and Israelit, Rosen, Johri et al., Banerjee-Sen, Vargas who investigated the problem of the energy in Friedmann-Robertson-Walker universe in Einstein's theory of general relativity and Aydogdu-Salti who considered the same problem in tele-parallel gravity. In all of these works, they found that the energy of the Friedmann-Robertson-Walker space-time is zero. Our result is the same as obtained in the studies of Salti and Havare. They used the viscous Kasner-type metric and found total energy and momentum by using Bergmann-Thomson energy-momentum formulation in both general relativity and tele-parallel gravity. The...
Tetrahedral-Mesh Simulation of Turbulent Flows with the Space-Time Conservative Schemes
Chang, Chau-Lyan; Venkatachari, Balaji; Cheng, Gary C.
2015-01-01
Direct numerical simulations of turbulent flows are predominantly carried out using structured, hexahedral meshes despite decades of development in unstructured mesh methods. Tetrahedral meshes offer ease of mesh generation around complex geometries and the potential of an orientation free grid that would provide un-biased small-scale dissipation and more accurate intermediate scale solutions. However, due to the lack of consistent multi-dimensional numerical formulations in conventional schemes for triangular and tetrahedral meshes at the cell interfaces, numerical issues exist when flow discontinuities or stagnation regions are present. The space-time conservative conservation element solution element (CESE) method - due to its Riemann-solver-free shock capturing capabilities, non-dissipative baseline schemes, and flux conservation in time as well as space - has the potential to more accurately simulate turbulent flows using unstructured tetrahedral meshes. To pave the way towards accurate simulation of shock/turbulent boundary-layer interaction, a series of wave and shock interaction benchmark problems that increase in complexity, are computed in this paper with triangular/tetrahedral meshes. Preliminary computations for the normal shock/turbulence interactions are carried out with a relatively coarse mesh, by direct numerical simulations standards, in order to assess other effects such as boundary conditions and the necessity of a buffer domain. The results indicate that qualitative agreement with previous studies can be obtained for flows where, strong shocks co-exist along with unsteady waves that display a broad range of scales, with a relatively compact computational domain and less stringent requirements for grid clustering near the shock. With the space-time conservation properties, stable solutions without any spurious wave reflections can be obtained without a need for buffer domains near the outflow/farfield boundaries. Computational results for the
Solano, Rubén; Gómez-Barroso, Diana; Simón, Fernando; Lafuente, Sarah; Simón, Pere; Rius, Cristina; Gorrindo, Pilar; Toledo, Diana; Caylà, Joan A
2014-05-01
A retrospective, space-time study of whooping cough cases reported to the Public Health Agency of Barcelona, Spain between the years 2000 and 2011 is presented. It is based on 633 individual whooping cough cases and the 2006 population census from the Spanish National Statistics Institute, stratified by age and sex at the census tract level. Cluster identification was attempted using space-time scan statistic assuming a Poisson distribution and restricting temporal extent to 7 days and spatial distance to 500 m. Statistical calculations were performed with Stata 11 and SatScan and mapping was performed with ArcGis 10.0. Only clusters showing statistical significance (P <0.05) were mapped. The most likely cluster identified included five census tracts located in three neighbourhoods in central Barcelona during the week from 17 to 23 August 2011. This cluster included five cases compared with the expected level of 0.0021 (relative risk = 2436, P <0.001). In addition, 11 secondary significant space-time clusters were detected with secondary clusters occurring at different times and localizations. Spatial statistics is felt to be useful by complementing epidemiological surveillance systems through visualizing excess in the number of cases in space and time and thus increase the possibility of identifying outbreaks not reported by the surveillance system.
Exact solution of the space-time fractional coupled EW and coupled MEW equations
Raslan, K. R.; S. EL-Danaf, Talaat; K. Ali, Khalid
2017-07-01
In this paper, we obtained a traveling wave solution by using the Kudryashov method for the space-time fractional nonlinear partial differential equations. The method is used to obtain the exact solutions for different types of the space-time fractional nonlinear partial differential equations, such as the space-time fractional coupled equal width wave equation (CEWE) and the space-time fractional coupled modified equal width wave equation (CMEWE), which are the important soliton equations. Both equations are reduced to ordinary differential equations by use of the fractional complex transform and of the properties of the modified Riemann-Liouville derivative. We plot the exact solutions for these equations at different time levels.
Accelerating the discovery of space-time patterns of infectious diseases using parallel computing.
Hohl, Alexander; Delmelle, Eric; Tang, Wenwu; Casas, Irene
2016-11-01
Infectious diseases have complex transmission cycles, and effective public health responses require the ability to monitor outbreaks in a timely manner. Space-time statistics facilitate the discovery of disease dynamics including rate of spread and seasonal cyclic patterns, but are computationally demanding, especially for datasets of increasing size, diversity and availability. High-performance computing reduces the effort required to identify these patterns, however heterogeneity in the data must be accounted for. We develop an adaptive space-time domain decomposition approach for parallel computation of the space-time kernel density. We apply our methodology to individual reported dengue cases from 2010 to 2011 in the city of Cali, Colombia. The parallel implementation reaches significant speedup compared to sequential counterparts. Density values are visualized in an interactive 3D environment, which facilitates the identification and communication of uneven space-time distribution of disease events. Our framework has the potential to enhance the timely monitoring of infectious diseases.
Channel estimation for space-time trellis coded-OFDM systems based on nonoverlapping pilot structure
Sokoya, O
2008-09-01
Full Text Available The performance of space time trellis coded orthogonal frequency division multiplexing (STTC-OFDM) systems relies on accurate channel state information at the receiver for proper decoding. One method of obtaining channel state information...
Dyja, Robert; van der Zee, Kristoffer G
2016-01-01
We present an adaptive methodology for the solution of (linear and) non-linear time dependent problems that is especially tailored for massively parallel computations. The basic concept is to solve for large blocks of space-time unknowns instead of marching sequentially in time. The methodology is a combination of a computationally efficient implementation of a parallel-in-space-time finite element solver coupled with a posteriori space-time error estimates and a parallel mesh generator. This methodology enables, in principle, simultaneous adaptivity in both space and time (within the block) domains. We explore this basic concept in the context of a variety of time-steppers including $\\Theta$-schemes and Backward Differentiate Formulas. We specifically illustrate this framework with applications involving time dependent linear, quasi-linear and semi-linear diffusion equations. We focus on investigating how the coupled space-time refinement indicators for this class of problems affect spatial adaptivity. Final...
Space-time Block Codes Based on Quasi-Orthogonal Designs
李正权; 胡光锐; 单红梅
2004-01-01
A new space-time block codes based on quasi-orthogonal designs are put forward. First the channel model is formulated. Then the connection between orthogonal/quasiorthogonal designs and space-time block codes is explored.Finally we make simulations for the transmission of 4 bits/s/Hz and 6 bits/s/Hz using eight transmit antennas using the rate 3/4 quasi-orthogonal space-time block code and the rate 1/2 full-diversity orthogonal space-time block code.Simulation results show that full transmission rate is more important for very low signal noise ratio (SNR) and high bit error probability (BEP), while full diversity is more important for very high SNR and low BEP.
A VERTICAL LAYERED SPACE-TIME CODE AND ITS CLOSED-FORM BLIND SYMBOL DETECTION
Zhao Zheng; Yin Qinye; Zhang Hong; Feng Aigang
2003-01-01
Vertical layered space-time codes have demonstrated the enormous potential to accommodate rapid flow data. Thus far, vertical layered space-time codes assumed that perfect estimates of current channel fading conditions are available at the receiver. However, increasing the number of transmit antennas increases the required training interval and reduces the available time in which data may be transmitted before the fading coefficients change. In this paper, a vertical layered space-time code is proposed. By applying the subspace method to the layered space-time code, the symbols can be detected without training symbols and channel estimates at the transmitter or the receiver. Monte Carlo simulations show that performance can approach that of the detection method with the knowledge of the channel.
Reduced-Rank Space-Time Processing for Anti-Jamming GPS Receivers
ZHUANG Xuebin; CUI Xiaowei; LU Mingquan; FENG Zhenming
2009-01-01
In a jamming environment with multiple wideband and narrowband jammers, global positioning system (GPS) receivers can use space-time processing to efficiently suppress the jamming. However, the computational complexity of space-time algorithms restricts their application in practical GPS receivers. This paper describes a reduced-rank multi-stage nested Wiener filter (MSNWF) based on subspace decomposi-tion and Wiener filter (WF) to eliminate the effect of jamming in anti-jamming GPS receivers. A general sidelobe canceller (GSC) structure that is equivalent to the MSNWF is used to facilitate calculation of the optimal weights for the space-time processing. Simulation results demonstrate the satisfactory performance of the MSNWF to cancel jamming and the significant reduction in computational complexity by the re-duced-rank processing. The technique offers a feasible space-time processing solution for anti-jamming GPS receivers.
Axially Symmetric Null Dust Space-Time, Naked Singularity, and Cosmic Time Machine
Faizuddin Ahmed
2017-01-01
... the cylinder which has closed orbits. The space-time admits closed timelike curves (CTCs) which develop at some particular moment in a causally well-behaved manner and may represent a Cosmic Time Machine...
The Trade-offs with Space Time Cube Representation of Spatiotemporal Patterns
Kristensson, Per Ola; Anundi, Daniel; Bjornstad, Marius; Gillberg, Hanna; Haraldsson, Jonas; Martensson, Ingrid; Nordvall, Matttias; Stahl, Josefin
2007-01-01
Space time cube representation is an information visualization technique where spatiotemporal data points are mapped into a cube. Fast and correct analysis of such information is important in for instance geospatial and social visualization applications. Information visualization researchers have previously argued that space time cube representation is beneficial in revealing complex spatiotemporal patterns in a dataset to users. The argument is based on the fact that both time and spatial information are displayed simultaneously to users, an effect difficult to achieve in other representations. However, to our knowledge the actual usefulness of space time cube representation in conveying complex spatiotemporal patterns to users has not been empirically validated. To fill this gap we report on a between-subjects experiment comparing novice users error rates and response times when answering a set of questions using either space time cube or a baseline 2D representation. For some simple questions the error rat...
Fermions in Gödel-type background space-times with torsion and the Landau quantization
Garcia, G. Q.; de S. Oliveira, J. R.; Bakke, K.; Furtado, C.
2017-03-01
In this paper, we analyze Dirac fermions in Gödel-type background space-times with torsion. We also consider the Gödel-type space-times embedded in a topological defect background. We show that relativistic bound states solutions to the Dirac equation can be obtained by dealing with three cases of the Gödel-type solutions with torsion, where a cosmic string passes through these three cases of the space-time. We obtain the relativistic energy levels for all cases of the Gödel-type solutions with torsion with a cosmic string, where we show that there exists an analogy with the Landau levels for Dirac particles. We also show that the presence of torsion in the space-time yields new contributions to the relativistic spectrum of energies and that the presence of the topological defect modifies the degeneracy of the relativistic energy levels.
LES prediction of space-time correlations in turbulent shear flows
Li Guo; Dong Li; Xing Zhang; Guo-Wei He
2012-01-01
We compare the space-time correlations calculated from direct numerical simulation (DNS) and large-eddy simulation (LES) of turbulent channel flows.It is found from the comparisons that the LES with an eddy-viscosity subgrid scale (SGS) model over-predicts the space-time correlations than the DNS.The overpredictions are further quantified by the integral scales of directional correlations and convection velocities.A physical argument for the overprediction is provided that the eddy-viscosity SGS model alone does not includes the backscatter effects although it correctly represents the energy dissipations of SGS motions.This argument is confirmed by the recently developed elliptic model for space-time correlations in turbulent shear flows.It suggests that enstrophy is crucial to the LES prediction of spacetime correlations.The random forcing models and stochastic SGS models are proposed to overcome the overpredictions on space-time correlations.
K D Patil; S H Ghate; R V Saraykar
2001-04-01
We consider a collapsing spherically symmetric inhomogeneous dust cloud in higher dimensional space-time. We show that the central singularity of collapse can be a strong curvature or a weak curvature naked singularity depending on the initial density distribution.
Massey, Doreen, Power-geometries and the politics of space-time / [rezensiert von] Wolfgang Aschauer
Aschauer, Wolfgang
2008-01-01
Rezensiertes Werk: Power-geometries and the politics of space-time : Hettner-Lecture 1998 / with Doreen Massey. - Heidelberg : Dep. of Geography, Univ., 1999. - 112 S. : Ill. - (Hettner-Lectures ; 2) ISBN 3-88570-502-8
Melas, Evangelos
2017-07-01
The original Bondi-Metzner-Sachs (BMS) group B is the common asymptotic symmetry group of all asymptotically flat Lorentzian radiating 4-dim space-times. As such, B is the best candidate for the universal symmetry group of General Relativity (G.R.). In 1973, with this motivation, McCarthy classified all relativistic B-invariant systems in terms of strongly continuous irreducible unitary representations (IRS) of B. Here we introduce the analogue B(2, 1) of the BMS group B in 3 space-time dimensions. B(2, 1) itself admits thirty-four analogues both real in all signatures and in complex space-times. In order to find the IRS of both B(2, 1) and its analogues, we need to extend Wigner-Mackey's theory of induced representations. The necessary extension is described and is reduced to the solution of three problems. These problems are solved in the case where B(2, 1) and its analogues are equipped with the Hilbert topology. The extended theory is necessary in order to construct the IRS of both B and its analogues in any number d of space-time dimensions, d ≥3 , and also in order to construct the IRS of their supersymmetric counterparts. We use the extended theory to obtain the necessary data in order to construct the IRS of B(2, 1). The main results of the representation theory are as follows: The IRS are induced from "little groups" which are compact. The finite "little groups" are cyclic groups of even order. The inducing construction is exhaustive notwithstanding the fact that B(2, 1) is not locally compact in the employed Hilbert topology.
Inhomogeneous relativistic Boltzmann equation near vacuum in the Robertson-Walker space-time
Takou, Etienne
2016-01-01
In this paper, we consider the Cauchy problem for the relativistic Boltzmann equation with near vacuum initial data where the distribution function depends on the time, the position and the impulsion. The collision kernel considered here is for the hard potentials case and the background space-time in which the study is done is the Robertson-Walker space-time. Unique global (in time) mild solution is obtained in a suitable weighted space.
The Relativistic Boltzmann Equation on Bianchi Type I Space Time for Hard Potentials
Noutchegueme, Norbert; Takou, Etienne; Tchuengue, E. Kamdem
2017-08-01
In this paper, we consider the Cauchy problem for the spatially homogeneous relativistic Boltzmann equation with small initial data. The collision kernel considered here is for a hard potentials case. The background space-time in which the study is done is the Bianchi type I space-time. Under certain conditions made on the scattering kernel and on the metric, a uniqueness global (in time) solution is obtained in a suitable weighted functional space.