Some solutions of Einstein's equations in general relativity

1968 ◽  
Vol 64 (1) ◽  
pp. 167-170 ◽  
Author(s):  
J. J. J. Marek
Keyword(s):  
General Relativity ◽  
Existence Of Solutions ◽  
Empty Space ◽  
Stationary Solutions ◽  
Einstein’S Equations ◽  
Field Equations ◽  
Einstein's Equations ◽  
New Class

AbstractA new class of axi-symmetric stationary solutions of Einstein's empty space field equations is obtained. Non-existence of solutions of certain other classes is proved.

Some spherical gravitational waves in general relativity

1962 ◽  
Vol 265 (1323) ◽  
pp. 463-473 ◽  
Keyword(s):  
General Relativity ◽  
Gravitational Waves ◽  
Empty Space ◽  
Einstein Equations ◽  
Einstein’S Equations ◽  
Killing Field ◽  
Einstein's Equations ◽  
Outgoing Radiation ◽  
Null Curves

Einstein's equations for empty space are solved for the class of metrics which admit a family of hypersurface-orthogonal, non-shearing, diverging null curves. Some of these metrics may be considered as representing a simple kind of spherical, outgoing radiation. (Among them are solutions admitting no Killing field whatsoever.) Examples of solutions to the Maxwell-Einstein equations with a similar geometry are also given.

THE EQUIVALENCE PROBLEM IN TELEPARALLEL GRAVITY

2002 ◽  
Vol 17 (29) ◽  
pp. 4161-4166
Author(s):  
J. FONSECA
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Equivalence Problem ◽  
Teleparallel Gravity ◽  
Alternative Formulation ◽  
Einstein’S Equations ◽  
Field Equations ◽  
Einstein's Equations ◽  
Invariant Description ◽  
Torsion Free

The teleparallel equivalent of general relativity (TEGR) is an alternative formulation of Einstein's equations in the framework of Riemann-Cartan spacetimes. The gravitational field can be described either by the curvature of the torsion-free connection of general relativity (GR) or by the torsion of the curvature-free connection of the TEGR. Both in GR and TEGR the freedom in the choice of coordinates gives rise to the equivalence problem of deciding whether two solutions of the field equations are the same. This problem is solved by means of a invariant description of the gravitational field. We investigate whether the equivalence between GR and TEGR also holds at the level of these invariant descriptions. We show that the GR description assures equivalence in TEGR only in very special situations. These results are illustrated on teleparallel spacetimes with torsion and Gödel metric.

scholarly journals CLASSICAL TRACE ANOMALY

2005 ◽  
Vol 14 (07) ◽  
pp. 1233-1250 ◽  
Author(s):  
M. FARHOUDI
Keyword(s):  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Second Order ◽  
Alternative Form ◽  
Mathematical Form ◽  
Einstein’S Field Equations ◽  
Einstein’S Equations ◽  
Field Equations ◽  
Einstein's Equations ◽  
Trace Anomaly

We seek an analogy of the mathematical form of the alternative form of Einstein's field equations for Lovelock's field equations. We find that the price for this analogy is to accept the existence of the trace anomaly of the energy–momentum tensor even in classical treatments. As an example, we take this analogy to any generic second order Lagrangian and exactly derive the trace anomaly relation suggested by Duff. This indicates that an intrinsic reason for the existence of such a relation should perhaps be, classically, somehow related to the covariance of the form of Einstein's equations.

scholarly journals Plane Symmetric Solutions of a Scalar-Tensor Theory of Gravitation

1977 ◽  
Vol 30 (1) ◽  
pp. 109 ◽  
Author(s):  
DRK Reddy
Keyword(s):  
General Relativity ◽  
Empty Space ◽  
Scalar Fields ◽  
Scalar Tensor Theory ◽  
Field Equations ◽  
Plane Symmetric ◽  
Zero Mass ◽  
Tensor Theory ◽  
Special Cases ◽  
Theory Of Gravitation

Plane symmetric solutions of a scalar-tensor theory proposed by Dunn have been obtained. These solutions are observed to be similar to the plane symmetric solutions of the field equations corresponding to zero mass scalar fields obtained by Patel. It is found that the empty space-times of general relativity discussed by Taub and by Bera are obtained as special cases.

Physics as an Art Form

2018 ◽  
pp. 1-4
Author(s):  
Alvaro De Rújula
Keyword(s):  
General Relativity ◽  
Laws Of Nature ◽  
Space Time ◽  
Einstein’S Equations ◽  
Einstein's Equations ◽  
Ockham’S Razor ◽  
Art Form ◽  
Ockham's Razor ◽  
The Universe ◽  
The Way

Beauty and simplicity, a scientist’s view. A first encounter with Einstein’s equations of General Relativity, space-time, and Gravity. Ockham’s Razor. Why the Universe is the way it is: The origin of the laws of Nature.

Approximate solutions of the general relativity field equations with a scalar meson field

1963 ◽  
Vol 59 (4) ◽  
pp. 739-741 ◽  
Author(s):  
J. Hyde
Keyword(s):  
General Relativity ◽  
Scalar Meson ◽  
Empty Space ◽  
Approximate Solutions ◽  
Spherically Symmetric ◽  
Coordinate Transformations ◽  
Field Equations ◽  
Spherically Symmetric Solution ◽  
Image Position ◽  
Scalar Meson Field

It was shown by Birkhoff ((1), p. 253) that every spherically symmetric solution of the field equations of general relativity for empty space,may be reduced, by suitable coordinate transformations, to the static Schwarzschild form:where m is a constant. This result is known as Birkhoff's theorem and excludes the possibility of spherically symmetric gravitational radiation. Different proofs of the theorem have been given by Eiesland(2), Tolman(3), and Bonnor ((4), p. 167).

Derivation of Generalized Einstein's Equations of Gravitation Based on a Mechanical Model of Vacuum and a Sink Flow Model of Particles

2019 ◽  
Author(s):  
Xiao-Song Wang
Keyword(s):  
General Relativity ◽  
Mechanical Model ◽  
Reference Frames ◽  
Flow Model ◽  
Weak Field ◽  
Einstein’S Equations ◽  
Previous Theory ◽  
Metric Tensor ◽  
Einstein's Equations ◽  
Definition Of

J. C. Maxwell, B. Riemann and H. Poincar$\acute{e}$ have proposed the idea that all microscopic particles are sink flows in a fluidic aether. Following this research program, a previous theory of gravitation based on a mechanical model of vacuum and a sink flow model of particles is generalized by methods of special relativistic continuum mechanics. In inertial reference frames, we construct a tensorial potential which satisfies the wave equation. Inspired by the equation of motion of a test particle, a definition of a metric tensor of a Riemannian spacetime is introduced. Applying Fock's theorem, generalized Einstein's equations in inertial systems are derived based on some assumptions. These equations reduce to Einstein's equations in case of weak field in harmonic reference frames. In some special non-inertial reference frames, generalized Einstein's equations are derived based on some assumptions. If the field is weak and the reference frame is quasi-inertial, these generalized Einstein's equations reduce to Einstein's equations. Thus, this theory may also explains all the experiments which support the theory of general relativity. There exists some differences between this theory and Einstein's theory of general relativity.

scholarly journals ON THE ENERGY–MOMENTUM FLUX IN GÖDEL-TYPE MODELS

2013 ◽  
Vol 28 (10) ◽  
pp. 1350039 ◽  
Author(s):  
S. C. ULHOA ◽  
A. F. SANTOS ◽  
R. G. G. AMORIM
Keyword(s):  
General Relativity ◽  
Total Pressure ◽  
Momentum Flux ◽  
Einstein’S Equations ◽  
Einstein's Equations ◽  
Cartesian Coordinates ◽  
Stationary Observer

In this paper, we work in the context of Teleparallelism Equivalent to General Relativity (TEGR) in order to construct the energy–momentum flux for Gödel-type solutions of Einstein's equations. We use an stationary observer, which is settled by the tetrad choice, to obtain the gravitational pressure for each direction of space in cartesian coordinates. Then, we write down the total pressure for each direction in terms of the pressure of the fluid, thus we are able to identify the role of the gravitational pressure.

Cylindrically symmetric relativistic fluids and the purely electric Weyl tensor

2015 ◽  
Vol 12 (10) ◽  
pp. 1550103 ◽  
Author(s):  
Rajesh Kumar ◽  
S. K. Srivastava ◽  
V. C. Srivastava
Keyword(s):  
General Relativity ◽  
Energy Density ◽  
Weyl Tensor ◽  
Einstein’S Equations ◽  
Relativistic Fluids ◽  
Einstein's Equations ◽  
Cylindrically Symmetric ◽  
Expansion Scalar

In General Relativity (GR), the analysis of electric and magnetic Weyl tensors has been studied by various authors. The present study deals with cylindrically symmetric relativistic fluids in GR characterized by the vanishing of magnetic Weyl tensor-purely electric (PE) fields. A very new assumption has been adapted to solve the Einstein's equations and the obtained solution is shearing at all. We signified the importance of PE fields in the context of expansion scalar, energy density, shear and acceleration.

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