Showing papers on "Mathematics of general relativity published in 2016"
TL;DR: In this article, the authors studied compact stars in Fab Four gravity, which includes as special cases general relativity ("George"), Einstein-dilaton-Gauss-Bonnet gravity ("Ringo"), theories with a nonminimal coupling with the Einstein tensor ("John") and theories involving the double-dual of the Riemann tensor (Paul).
Abstract: Horndeski's theory of gravity is the most general scalar-tensor theory with a single scalar whose equations of motion contain at most second-order derivatives. A subsector of Horndeski's theory known as "Fab Four" gravity allows for dynamical self-tuning of the quantum vacuum energy, and therefore it has received particular attention in cosmology as a possible alternative to the $\Lambda$CDM model. Here we study compact stars in Fab Four gravity, which includes as special cases general relativity ("George"), Einstein-dilaton-Gauss-Bonnet gravity ("Ringo"), theories with a nonminimal coupling with the Einstein tensor ("John") and theories involving the double-dual of the Riemann tensor ("Paul"). We generalize and extend previous results in theories of the John class and were not able to find realistic compact stars in theories involving the Paul class.
91 citations
Book•
11 Feb 2016TL;DR: The history of attempts to algebraically extend General Relativity is reviewed in this paper, where the philosophy of the pseudo-complex extension is introduced and the basic assumptions, including for example a generalized variational principle and how to map to real observables.
Abstract: The history of of attempts to algebraically extend General Relativity is reviewed. The philosophy of the pseudo-complex extension is introduced and the basic assumptions, including for example a generalized variational principle and how to map to real observables. The appearance of a minimal length and the advantages of the pseudo-complex theory are discussed.
71 citations
TL;DR: An alternative approach to the theory of General Relativity (GR) is reviewed in this article, which is motivated by a range of serious theoretical issues inflicting the theory, such as the cosmological constant problem, presence of non-Machian solutions, problems related with the energy-stress tensor T i k and unphysical solutions.
Abstract: An alternative approach to Einstein’s theory of General Relativity (GR) is reviewed, which is motivated by a range of serious theoretical issues inflicting the theory, such as the cosmological constant problem, presence of non-Machian solutions, problems related with the energy-stress tensor T i k and unphysical solutions. The new approach emanates from a critical analysis of these problems, providing a novel insight that the matter fields, together with the ensuing gravitational field, are already present inherently in the spacetime without taking recourse to T i k . Supported by lots of evidence, the new insight revolutionizes our views on the representation of the source of gravitation and establishes the spacetime itself as the source, which becomes crucial for understanding the unresolved issues in a unified manner. This leads to a new paradigm in GR by establishing equation R i k = 0 as the field equation of gravitation plus inertia in the very presence of matter.
51 citations
01 Jan 2016
TL;DR: The mass and motion in general relativity is universally compatible with any devices to read as mentioned in this paper and it is available in our book collection and an online access to it is set as public so you can get it instantly.
Abstract: Thank you very much for downloading mass and motion in general relativity. Maybe you have knowledge that, people have search hundreds times for their chosen readings like this mass and motion in general relativity, but end up in infectious downloads. Rather than enjoying a good book with a cup of tea in the afternoon, instead they are facing with some infectious virus inside their laptop. mass and motion in general relativity is available in our book collection an online access to it is set as public so you can get it instantly. Our books collection spans in multiple countries, allowing you to get the most less latency time to download any of our books like this one. Merely said, the mass and motion in general relativity is universally compatible with any devices to read.
40 citations
TL;DR: In this paper, a geometrical interpretation of Yang-Mills theory is presented, and the analogies and disanalogies between Yang-mills theory and general relativity are considered.
Abstract: I articulate and discuss a geometrical interpretation of Yang–Mills theory. Analogies and disanalogies between Yang–Mills theory and general relativity are also considered.
35 citations
TL;DR: In this article, the authors investigated the properties of the generalized quasi-Einstein spacetime G(Q E)4 under certain conditions and proved the existence of the Ricci tensor and the shear tensor in this spacetime.
Abstract: The aim of this paper is to investigate some geometric and physical properties of the generalized quasi Einstein spacetime G(Q E)4 under certain conditions. Firstly, we prove the existence of G(Q E)4 by constructing a non trivial example. Then it is proved that the G(Q E)4 spacetime with the conditions \(\mathcal {B}\cdot S=L_{S}Q(g,S)\), where \(\mathcal {B}\) denotes the Ricci tensor or the concircular curvature tensor is an \(N(\frac {a-b}{3})\)-quasi Einstein spacetime and in a G(Q E)4 spacetime with C ⋅ S = 0, where C is the conformal curvature tensor, a − b is an eigenvalue of the Ricci operator. Then, we deal with the Ricci recurrent G(Q E)4 spacetime and prove that in this spacetime, the acceleration vector and the vorticity tensor vanish; but this spacetime has the non-vanishing expansion scalar and the shear tensor. Moreover, it is shown that every Ricci recurrent G(Q E)4 is Weyl compatible, purely electric spacetime and its possible Petrov types are I or D.
31 citations
TL;DR: In this article, the authors discuss what they take to be three possible misconceptions in the foundations of general relativity, relating to: (a) the interpretation of the weak equivalence principle and the relationship between gravity and inertia; (b) the connection between gravitational redshift results and spacetime curvature; and (c) the ability to transform away gravity in local inertial coordinate systems.
Abstract: We discuss what we take to be three possible misconceptions in the foundations of general relativity, relating to: (a) the interpretation of the weak equivalence principle and the relationship between gravity and inertia; (b) the connection between gravitational redshift results and spacetime curvature; and (c) the Einstein equivalence principle and the ability to “transform away” gravity in local inertial coordinate systems.
31 citations
TL;DR: In this article, the conceptual basis of curved spacetime gravity can be simply and correctly presented, and that the spatial curvature of a deformed elastic sheet is very different from the spacetime curvature underlying gravity.
Abstract: The belief that curved spacetime gravity cannot be simply and correctly presented results in such misleading presentations as elastic two-dimensional sheets deformed as they support heavy objects. This article attempts to show that the conceptual basis of curved spacetime gravity can be simply and correctly presented, and that the spatial curvature of a deformed elastic sheet is very different from the spacetime curvature underlying gravity. This article introduces the idea of a “splittable” spacetime that has spatial curvature, but is missing most of the manifestations of gravity. A section in which no mathematics is used is directed at students who have studied no more than introductory physics. A separate section, for students who have taken only an introductory course in general relativity, gives mathematical arguments centering on splittable spacetimes.
24 citations
TL;DR: In this article, the authors verify the consistency of the Godel-type solutions within the four-dimensional Chern-Simons modified gravity with the non-dynamical ChernSimons coefficient, for different forms of matter including dust, fluid, scalar field and electromagnetic field.
Abstract: We verify the consistency of the Godel-type solutions within the four-dimensional Chern-Simons modified gravity with the non-dynamical Chern-Simons coefficient, for different forms of matter including dust, fluid, scalar field and electromagnetic field, and the related causality issues. Unlike the general relativity, the vacuum solution turns out to be possible in our theory. Another essentially new result of our theory having no analogue in the general relativity consists in the existence of the hyperbolic causal solutions for the physically well-motivated matter.
17 citations
TL;DR: The Born-Infeld theory of the gravitational field formulated in Weitzenbock spacetime is studied in detail in this paper, where the action, constructed quadratically upon the torsion two-form, reduces to Einstein gravity in the low field limit where the Born-infeld constant λ goes to infinity.
16 citations
TL;DR: In this article, the authors study the properties of anti-de-Sitter spacetime and show that the spacetime is not a self-contained world, but rather a chaotic and non-self-contained space, where one finds superluminal velocities of light and particles.
Abstract: Anti-de Sitter spacetime is important in general relativity and modern field theory. We review its geometrical features and properties of light signals and free particles moving in it. By applying only the elementary tools of tensor calculus, we derive ab initio of all these properties and show that they are really weird. One finds superluminal velocities of light and particles, infinite particle energy necessary to escape at infinite distance and spacetime regions inaccessible by a free fall, though reachable by an accelerated spaceship. Radial timelike geodesics are identical to the circular ones and actually all timelike geodesics are identical to one circle in a fictitious five-dimensional space. Employing the latter space, one is able to explain these bizarre features of anti-de Sitter spacetime; in this sense the spacetime is not self-contained. This is not a physical world.
TL;DR: In this paper, a correspondence between general relativity with diffeomorphism invariance and scalar field theories with Galilean invariance was established, and it was shown that the requirement of first-order Palatini formalism uniquely determines the Galileon models with second-order field equations.
Abstract: We establish a correspondence between general relativity with diffeomorphism invariance and scalar field theories with Galilean invariance: notions such as the Levi-Civita connection and the Riemann tensor have a Galilean counterpart. This suggests Galilean theories as the unique nontrivial alternative to gauge theories (including general relativity). Moreover, it is shown that the requirement of first-order Palatini formalism uniquely determines the Galileon models with second-order field equations, similar to the Lovelock gravity theories. Possible extensions are discussed.
Dissertation•
18 Apr 2016
TL;DR: The Unruh effect in Rindler space and the entanglement structure of the Minkowski vacuum were discussed in this article. But they did not consider Euclidean time.
Abstract: 1 Lecture I 1.1 Rindler space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 The Unruh effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Euclidean time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Euclidean time in Rindler space and the entanglement structure of the Minkowski vacuum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
01 Jan 2016
Abstract: Thank you very much for downloading lecture notes on symmetries and curvature structure in general relativity. Maybe you have knowledge that, people have look numerous times for their chosen novels like this lecture notes on symmetries and curvature structure in general relativity, but end up in harmful downloads. Rather than enjoying a good book with a cup of coffee in the afternoon, instead they juggled with some malicious bugs inside their desktop computer.
TL;DR: In this paper, the authors explore two methods for obtaining solutions for uniformly accelerated motion in general curved spacetime and provide an example in Schwarzschild spacetime, where the solution is based on a solution in the Euclidean plane.
Abstract: We explore two methods for obtaining solutions for uniformly accelerated motion in general curved spacetime. We provide an example in Schwarzschild spacetime.
TL;DR: Within the theory of General Relativity, the solution and range of applicability of the standard geodesic deviation equation in highly symmetric spacetimes have been investigated in this article, where the solution is used to model satellite orbit constellations and their deviations around a spherically symmetric Earth model.
Abstract: Within the theory of General Relativity, we study the solution and range of applicability of the standard geodesic deviation equation in highly symmetric spacetimes In the Schwarzschild spacetime, the solution is used to model satellite orbit constellations and their deviations around a spherically symmetric Earth model We investigate the spatial shape and orbital elements of perturbations of circular reference curves In particular, we reconsider the deviation equation in Newtonian gravity and then determine relativistic effects within the theory of General Relativity by comparison The deviation of nearby satellite orbits, as constructed from exact solutions of the underlying geodesic equation, is compared to the solution of the geodesic deviation equation to assess the accuracy of the latter Furthermore, we comment on the so-called Shirokov effect in the Schwarzschild spacetime and limitations of the first order deviation approach
01 Jan 2016
01 Jan 2016
TL;DR: In this article, some properties of generalized quasi-Einstein manifold spacetimes have been studied and two non-trivial examples have been constructed to prove the existence of generalized quasi-einstein manifolds.
Abstract: Quasi Einstein manifold is a simple and natural generalization of Einstein manifold. The object of the present paper is to study some properties of generalized quasi Einstein manifolds. We also discuss $G(QE)_{4}$ with space-matter tensor and some properties related to it. Two non-trivial examples have been constructed to prove the existence of generalized quasi Einstein spacetimes.
Posted Content•
TL;DR: In this paper, the role of consistency with causality and quantum mechanics in determining the properties of gravitation was examined, and two different classes of interacting theories of massless spin 2 particles were constructed.
Abstract: We examine the role of consistency with causality and quantum mechanics in determining the properties of gravitation. We begin by constructing two different classes of interacting theories of massless spin 2 particles -- gravitons. One involves coupling the graviton with the lowest number of derivatives to matter, the other involves coupling the graviton with higher derivatives to matter, making use of the linearized Riemann tensor. The first class requires an infinite tower of terms for consistency, which is known to lead uniquely to general relativity. The second class only requires a finite number of terms for consistency, which appears as a new class of theories of massless spin 2. We recap the causal consistency of general relativity and show how this fails in the second class for the special case of coupling to photons, exploiting related calculations in the literature. In an upcoming publication [1] this result is generalized to a much broader set of theories. Then, as a causal modification of general relativity, we add light scalar particles and recap the generic violation of universal free-fall they introduce and its quantum resolution. This leads to a discussion of a special type of scalar-tensor theory; the $F(\mathcal{R})$ models. We show that, unlike general relativity, these models do not possess the requisite counterterms to be consistent quantum effective field theories. Together this helps to remove some of the central assumptions made in deriving general relativity.
01 Jan 2016
TL;DR: In this article, a systematic review of the theoretical framework, major predictions, experimental evidences of general relativity and its implications to other branches of science is presented, and the review concludes that the Newtonian law of gravity is built upon the Keplers laws and has stood hundreds of years' test by scientific research and engineering practice.
Abstract: This article gives a systematic review of the theoretical framework, major predictions, experimental evidences of general relativity and its implications to other branches of science. It has been pointed out that, other than the (0,0) component of Einstein’s tensor field equation which reduces to the Newtonian law of gravitation under linear approximation, all other components either lead to divergence, or are in conflict with the fundamental postulation of relativity that no speed should exceed the speed of light, or defies physical interpretation. The review gives a detailed analysis of the three classical evidences of general relativity and has shown that none of these experimental evidences can stand scrutiny. The article also analyzed the two recent experiments (BICEP2 and LIGO) that claimed to have found experimental evidences of gravitational wave and black hole, and demonstrated their fallacies. It has been pointed out that the principle of relativity demands that any viable theory must have translational as well as rotational relativity, which requires general relativity to have a rotational transformation that can transform the Schwarzschild metric into the Kerr metric and vice versa. Calculations show that a general rotational transformation is in conflict with one of the fundamental postulations of relativity—no speed should exceed the speed of light, i.e., general relativity violates the principle of relativity. The article also gives a thorough analysis of one of the most important concept of general relativity—gravity comes from the curvature of space time, and gravity warps the space time. It has been pointed out that the curving of a geodesic is merely the bending of the trajectory of an object moving in gravitational field, which is not the curving of the space time itself. Moreover, the field equation describes the shape of equipotential, the curving of which is not the curving of space time either. The measure of curvature of space time is the Riemann curvature scalar R. Calculations show that the Riemann curvature and Ricii tensor of both the Schwarzschild metric and the Kerr metric—the only two known analytical solutions to Einstein’s field equation, vanish, which means that the space time is flat. The concept that gravity comes from the curvature of space time and gravity warps the space time is invalid. The review concludes that the Newtonian law of gravity is built upon the Keplers laws that represent enormous results of observational astronomy and has stood hundreds of years’ test by scientific research and engineering practice. It is still been checked every day by science and engineering, and has never failed the test. On the other hand, Einstein’s general relativity has a multitude of unsolvable inconsistencies in its fundamental postulations, theoretical framework, experimental tests, and it is completely powerless in practical applications. It is therefore incorrect to say that the Newtonian law of gravitation is only
TL;DR: In this article, the energy concept in the case of a continuum or a system of fields is reviewed, and the definitions of the canonical and Hilbert energymomentum tensors from a Lagrangian through the principle of stationary action in a general spacetime.
Abstract: We review the energy concept in the case of a continuum or a system of fields. First, we analyze the emergence of a true local conservation equation for the energy of a continuous medium, taking the example of an isentropic continuum in Newtonian gravity. Next, we consider a continuum or a system of fields in special relativity: we recall that the conservation of the energy-momentum tensor contains two local conservation equations of the same kind as before. We show that both of these equations depend on the reference frame, and that, however, they can be given a rigorous meaning. Then we review the definitions of the canonical and Hilbert energy-momentum tensors from a Lagrangian through the principle of stationary action in a general spacetime. Using relatively elementary mathematics, we prove precise results regarding the definition of the Hilbert tensor field, its uniqueness, and its tensoriality. We recall the meaning of its covariant conservation equation. We end with a proof of uniqueness of the energy density and flux, when both depend polynomially of the fields.
TL;DR: In this article, the simplest variant of gauge gravitation theory in Riemann-Cartan spacetime leading to the solution of the problem of cosmological singularity and dark energy problem is investigated.
Abstract: The simplest variant of gauge gravitation theory in Riemann-Cartan spacetime leading to the solution of the problem of cosmological singularity and dark energy problem is investigated. It is shown that this theory by certain restrictions on indefinite parameters of gravitational Lagrangian in the case of usual gravitating systems leads to Einstein gravitational equations with effective cosmological constant.
01 Jan 2016
TL;DR: The geometry of spacetime as mentioned in this paper is an introduction to special and general relativity, but it is not suitable for reading in a classroom environment, as it is unsuitable for children's reading.
Abstract: Thank you very much for reading geometry of spacetime an introduction to special and general relativity. Maybe you have knowledge that, people have look hundreds times for their chosen readings like this geometry of spacetime an introduction to special and general relativity, but end up in infectious downloads. Rather than enjoying a good book with a cup of coffee in the afternoon, instead they juggled with some harmful bugs inside their computer.
TL;DR: In this article, a brief discussion of situation before the completion of special relativity (Le Verrier's discovery of the Mercury perihelion advance anomaly, Michelson-Morley experiment, Eotvos experiment, Newcomb's improved observation of the Newcomb-Newcomb-Eisenstein divergence, the proposals of various new gravity theories and the development of tensor analysis and differential geometry) is given.
Abstract: This short exposition starts with a brief discussion of situation before the completion of special relativity (Le Verrier’s discovery of the Mercury perihelion advance anomaly, Michelson–Morley experiment, Eotvos experiment, Newcomb’s improved observation of Mercury perihelion advance, the proposals of various new gravity theories and the development of tensor analysis and differential geometry) and accounts for the main conceptual developments leading to the completion of the general relativity (CGR): gravity has finite velocity of propagation; energy also gravitates; Einstein proposed his equivalence principle and deduced the gravitational redshift; Minkowski formulated the special relativity in four-dimentional spacetime and derived the four-dimensional electromagnetic stress–energy tensor; Einstein derived the gravitational deflection from his equivalence principle; Laue extended Minkowski’s method of constructing electromagnetic stress-energy tensor to stressed bodies, dust and relativistic fluids; A...
Posted Content•
TL;DR: In this article, the authors recast Einstein's equations and spacetime curvatures in the extended Kerr-Schild form and discussed their properties, illustrated with simple examples, in the context of general relativity.
Abstract: We study in some detail the "extended Kerr-Schild" formulation of general relativity, which decomposes the gauge-independent degrees of freedom of a generic metric into two arbitrary functions and the choice of a flat background tetrad. We recast Einstein's equations and spacetime curvatures in the extended Kerr-Schild form and discuss their properties, illustrated with simple examples.
TL;DR: In this article, the concept of timespace manifold is introduced and the fundamental concepts of global relativity theory with respect to this general situation are defined, including affine connection, parallel transport, curvature tensor, and Einstein equation.
Abstract: In this paper we introduce the concept of timespace manifold. We study the affine connection, parallel transport, curvature tensor, and Einstein equation, respectively. In the case homogeneous, a time-space manifold with such tangent spaces which have a certain fixed time-space structure. We redefine the fundamental concepts of global relativity theory with respect to this general situation.
TL;DR: In this article, the authors studied the dynamics of self-gravitating fluids bounded by spherically symmetric surface in the background of f (G) gravity and found that their results are consistent with general relativity for constant f (g) model (regular distribution of dark energy in the universe).
Abstract: We study the dynamics of self-gravitating fluids bounded by spherically symmetric surface in the background of f (G) gravity. The link between physical and geometrical variables, such as anisotropy, density inhomogeneity, dissipation, the Weyl tensor, expansion scalar, shear tensor and modified (Gauss-Bonnet) curvature terms, is given. We also investigate some particular fluid models according to various dynamical conditions. It is found that our results are consistent with general relativity for constant f (G) model (regular distribution of dark energy in the universe). Any other choice of the model leads to irregular distribution of dark energy and deviates from general relativity.
01 Jan 2016
TL;DR: In this article, the authors present a book collection of geometry relativity and the fourth dimension, which is universally compatible with any devices to read and save in multiple locations, allowing to get the most less latency time to download any of our books like this one.
Abstract: Thank you very much for downloading geometry relativity and the fourth dimension. Maybe you have knowledge that, people have look numerous times for their favorite books like this geometry relativity and the fourth dimension, but end up in harmful downloads. Rather than enjoying a good book with a cup of tea in the afternoon, instead they are facing with some infectious bugs inside their desktop computer. geometry relativity and the fourth dimension is available in our book collection an online access to it is set as public so you can get it instantly. Our books collection saves in multiple locations, allowing you to get the most less latency time to download any of our books like this one. Merely said, the geometry relativity and the fourth dimension is universally compatible with any devices to read.
TL;DR: In this paper, the authors compare the Herglotz-Mie-Born understanding that the canonical tensor was conserved due to translation symmetries, a result with roots in Lagrange, Hamilton and Jacobi, with the Entwurf Lagrangian.
Abstract: Recent work on the history of General Relativity by Renn, Sauer, Janssen et al. shows that Einstein found his field equations partly by a physical strategy including the Newtonian limit, the electromagnetic analogy, and energy conservation. Such themes are similar to those later used by particle physicists. How do Einstein's physical strategy and the particle physics derivations compare? What energy-momentum complex(es) did he use and why? Did Einstein tie conservation to symmetries, and if so, to which? Einstein used an identity from his assumed linear coordinate covariance x'= Mx to relate it to the canonical tensor. Usually he avoided using matter Euler-Lagrange equations and so was not well positioned to use or reinvent the Herglotz-Mie-Born understanding that the canonical tensor was conserved due to translation symmetries, a result with roots in Lagrange, Hamilton and Jacobi. Whereas Mie and Born were concerned about the canonical tensor's asymmetry, Einstein did not need to worry because his Entwurf Lagrangian is modeled not so much on Maxwell's theory as on a scalar theory. As a result, it also has 3 ghosts, failing a 1920s-30s a priori particle physics stability test with antecedents in Lagrange's and Dirichlet's stability work.
This critique of the Entwurf theory can be compared with Einstein's 1915 critique of his Entwurf theory for not admitting rotating coordinates and not getting Mercury's perihelion right.
Particle physics also can be useful in the historiography of gravity and space-time. This topic can be a useful case study in the history of science on recently reconsidered questions of presentism, whiggism and the like.