scholarly journals INEVITABILITY OF SPACE–TIME SINGULARITIES IN THE CANONICAL METRIC

2001 ◽  
Vol 16 (21) ◽  
pp. 1405-1411 ◽  
Author(s):  
J. PONCE DE LEON
Keyword(s):  
Intrinsic Property ◽  
Space Time ◽  
Field Equations ◽  
Time Section ◽  
Canonical Metrics ◽  
Canonical Metric ◽  
Matter Theory ◽  
Time Singularities ◽  
Coordinate Singularity ◽  
Singular Hypersurface

We discuss the question of whether the existence of singularities is an intrinsic property of 4D space–time. Our hypothesis is that singularities in 4D are induced by the separation of space–time from the other dimensions. We examine this hypothesis in the context of the so-called canonical or warp metrics in 5D. These metrics are popular because they provide a clean separation between the extra dimension and space–time. We show that the space–time section, in these metrics, inevitably becomes singular for some finite (nonzero) value of the extra coordinate. This is true for all canonical metrics that are solutions of the field equations in space–time-matter theory. This is a coordinate singularity in 5D, but appears as a physical one in 4D. At this singular hypersurface, the determinant of the space–time metric becomes zero and the curvature of the space–time blows up to infinity. These results are consistent with our hypothesis.

scholarly journals An Approach to Colliding Plane Waves in General Relativity

2021 ◽  
Vol 9 (12) ◽  
pp. 981-988
Author(s):  
Dr. Shailendra Kumar Srivastava
Keyword(s):  
General Relativity ◽  
Plane Waves ◽  
Space Time ◽  
Theory Of Relativity ◽  
Field Equations ◽  
Vast Number ◽  
Gravitational Fields ◽  
Time Singularities ◽  
Linearized Theory ◽  
High Degree

Abstract: For many years after Einstein proposed his general theory of relativity, only a few exact solutions were known. Today the situation is completely different, and we now have a vast number of such solutions. However, very few are well understood in the sense that they can be clearly interpreted as the fields of real physical sources. The obvious exceptions are the Schwarzschild and Kerr solutions. These have been very thoroughly analysed, and clearly describe the gravitational fields surrounding static and rotating black holes respectively. In practice, one of the great difficulties of relating the particular features of general relativity to real physical problems, arises from the high degree of non-linearity of the field equations. Although the linearized theory has been used in some applications, its use is severely limited. Many of the most interesting properties of space-time, such as the occurrence of singularities, are consequences of the non-linearity of the equations. Keywords: General Relativity , Space-Time, Singularities, Non-linearity of the Equations.

scholarly journals Cosmic acceleration via space-time-matter theory

2019 ◽  
Vol 34 (36) ◽  
pp. 1950296
Author(s):  
Raziyeh Zaregonbadi
Keyword(s):  
State Parameter ◽  
Space Time ◽  
Cosmic Acceleration ◽  
Late Time ◽  
Field Equations ◽  
Deviation Equation ◽  
Matter Theory ◽  
Induced Field ◽  
Vacuum Spacetime ◽  
The Universe

We consider the space-time-matter theory (STM) in a 5D vacuum spacetime with a generalized FLRW metric to investigate the late-time acceleration of the universe. For this purpose, we derive the 4D induced field equations and obtain the evolution of the state parameter with respect to the redshift. Then, we show that with consideration of the extra dimension scale factor to be a linear function of redshift, this leads to a model which gives an accelerating phase in the universe. Moreover, we derive the geodesic deviation equation in the STM theory to study the relative acceleration of the parallel geodesics of this spacetime, and also, obtain the observer area-distance as a measurable quantity to compare this theory with two other models.

Field equations in the neighbourhood of a particle in a conformal theory of gravitation. II

1969 ◽  
Vol 313 (1512) ◽  
pp. 71-82 ◽  
Keyword(s):  
Local Geometry ◽  
Field Equations ◽  
Schwarzschild Solution ◽  
Conformal Theory ◽  
Conformally Invariant ◽  
Coordinate Singularity ◽  
Previous Solution ◽  
Theory Of Gravitation ◽  
Spherically Symmetric Metric ◽  
Radial Variable

The field equations in the neighbourhood of a particle for a spherically symmetric metric in the conformal theory of gravitation put forward by Hoyle & Narlikar are examined. As the theory is conformally invariant, one can use different but physically equivalent conformal frames to study the equations. Previously these equations were studied in a conformal frame which, though suitable far away from the isolated particle, turns out not to be suitable in the neighbourhood of the particle. In the present paper a solution in a conformal frame is obtained that is suitable for considering regions near the particle. The solution thus obtained differs from the previous one in several respects. For example, it has no coordinate singularity for any non-zero value of the radial variable, unlike the previous solution or the Schwarzschild solution. It is also shown with the use of this solution that in this theory distant matter has an effect on local geometry.

scholarly journals Post-Newtonian limit: second-order Jefimenko equations

2020 ◽  
Vol 80 (7) ◽  
Author(s):  
David Pérez Carlos ◽  
Augusto Espinoza ◽  
Andrew Chubykalo
Keyword(s):  
Linear Equations ◽  
Space Time ◽  
Second Order ◽  
Field Equations ◽  
Gravitational Fields ◽  
Mass Distributions ◽  
Minkowski Space Time ◽  
Theory Of Gravitation ◽  
Gravity Probe ◽  
Gravitational Equations

Abstract The purpose of this paper is to get second-order gravitational equations, a correction made to Jefimenko’s linear gravitational equations. These linear equations were first proposed by Oliver Heaviside in [1], making an analogy between the laws of electromagnetism and gravitation. To achieve our goal, we will use perturbation methods on Einstein field equations. It should be emphasized that the resulting system of equations can also be derived from Logunov’s non-linear gravitational equations, but with different physical interpretation, for while in the former gravitation is considered as a deformation of space-time as we can see in [2–5], in the latter gravitation is considered as a physical tensor field in the Minkowski space-time (as in [6–8]). In Jefimenko’s theory of gravitation, exposed in [9, 10], there are two kinds of gravitational fields, the ordinary gravitational field, due to the presence of masses, at rest, or in motion and other field called Heaviside field due to and acts only on moving masses. The Heaviside field is known in general relativity as Lense-Thirring effect or gravitomagnetism (The Heaviside field is the gravitational analogous of the magnetic field in the electromagnetic theory, its existence was proved employing the Gravity Probe B launched by NASA (See, for example, [11, 12]). It is a type of gravitational induction), interpreted as a distortion of space-time due to the motion of mass distributions, (see, for example [13, 14]). Here, we will present our second-order Jefimenko equations for gravitation and its solutions.

scholarly journals SPACE–TIME STRUCTURE AND SPINOR GEOMETRY

2008 ◽  
Vol 50 (2) ◽  
pp. 143-176 ◽  
Author(s):  
GEORGE SZEKERES ◽  
LINDSAY PETERS
Keyword(s):  
Cosmological Solution ◽  
Space Time ◽  
Time Structure ◽  
Variation Principle ◽  
Field Equations ◽  
Covering Group ◽  
Space Time Structure ◽  
Spinor Geometry ◽  
Complete Set ◽  
Particle Solution

AbstractThe structure of space–time is examined by extending the standard Lorentz connection group to its complex covering group, operating on a 16-dimensional “spinor” frame. A Hamiltonian variation principle is used to derive the field equations for the spinor connection. The result is a complete set of field equations which allow the sources of the gravitational and electromagnetic fields, and the intrinsic spin of a particle, to appear as a manifestation of the space–time structure. A cosmological solution and a simple particle solution are examined. Further extensions to the connection group are proposed.

DESITTER GAUGE THEORY OF GRAVITATION

2003 ◽  
Vol 14 (01) ◽  
pp. 41-48 ◽  
Author(s):  
G. ZET ◽  
V. MANTA ◽  
S. BABETI
Keyword(s):  
Gauge Theory ◽  
Riemann Tensor ◽  
Space Time ◽  
Point Of View ◽  
Field Equations ◽  
Minkowski Space Time ◽  
Strength Tensor ◽  
Group A ◽  
Theory Of Gravitation ◽  
Tensor Formula

A deSitter gauge theory of gravitation over a spherical symmetric Minkowski space–time is developed. The "passive" point of view is adapted, i.e., the space–time coordinates are not affected by group transformations; only the fields change under the action of the symmetry group. A particular ansatz for the gauge fields is chosen and the components of the strength tensor are computed. An analytical solution of Schwarzschild–deSitter type is obtained in the case of null torsion. It is concluded that the deSitter group can be considered as a "passive" gauge symmetry for gravitation. Because of their complexity, all the calculations, inclusive of the integration of the field equations, are performed using an analytical program conceived in GRTensorII for MapleV. The program allows one to compute (without using a metric) the strength tensor [Formula: see text], Riemann tensor [Formula: see text], Ricci tensor [Formula: see text], curvature scalar [Formula: see text], field equations, and the integration of these equations.

scholarly journals A MAXWELL-LIKE FORMULATION OF GRAVITATIONAL THEORY IN MINKOWSKI SPACE–TIME

2007 ◽  
Vol 16 (06) ◽  
pp. 1027-1041 ◽  
Author(s):  
EDUARDO A. NOTTE-CUELLO ◽  
WALDYR A. RODRIGUES
Keyword(s):  
Gravitational Field ◽  
Minkowski Space ◽  
Gravitational Theory ◽  
Space Time ◽  
Lorentzian Geometry ◽  
Field Equations ◽  
Yang Mills ◽  
Minkowski Space Time ◽  
Clifford Bundle ◽  
Gauge Fixing

Using the Clifford bundle formalism, a Lagrangian theory of the Yang–Mills type (with a gauge fixing term and an auto interacting term) for the gravitational field in Minkowski space–time is presented. It is shown how two simple hypotheses permit the interpretation of the formalism in terms of effective Lorentzian or teleparallel geometries. In the case of a Lorentzian geometry interpretation of the theory, the field equations are shown to be equivalent to Einstein's equations.

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