NONSTATIC SPHERICALLY SYMMETRIC SPACE–TIME AND GLOBAL MONOPOLE

1998 ◽  
Vol 13 (08) ◽  
pp. 1221-1228
Author(s):  
SUBENOY CHAKRABORTY ◽  
LALIT BISWAS
Keyword(s):  
Symmetric Space ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Space Time ◽  
Einstein Equations ◽  
Symmetric Model ◽  
Spherically Symmetric ◽  
Global Monopole ◽  
Spherically Symmetric Model

Under the assumption of functional separability of the metric coefficients, we have solved the Einstein equations for nonstatic spherically symmetric model. The energy–momentum tensor for the monopole configuration is taken in the form [Formula: see text]. Also the trajectories have been studied in different situations.

MØLLER ENERGY–MOMENTUM COMPLEX FOR HIGHER-DIMENSIONAL SPHERICALLY SYMMETRIC SPACETIME IN GENERAL RELATIVITY

2012 ◽  
Vol 27 (40) ◽  
pp. 1250231 ◽  
Author(s):  
HÜSNÜ BAYSAL
Keyword(s):  
General Relativity ◽  
Momentum Density ◽  
Momentum Tensor ◽  
Symmetric Model ◽  
Spherically Symmetric ◽  
Higher Dimensional ◽  
Energy And Momentum ◽  
Momentum Complex ◽  
Spherically Symmetric Metric ◽  
Spherically Symmetric Model

We have calculated the total energy–momentum distribution associated with (n+2)-dimensional spherically symmetric model of the universe by using the Møller energy–momentum definition in general relativity (GR). We have found that components of Møller energy and momentum tensor for given spacetimes are different from zero. Also, we are able to get energy and momentum density of various well-known wormholes and black hole models by using the (n+2)-dimensional spherically symmetric metric. Also, our results have been discussed and compared with the results for four-dimensional spacetimes in literature.

Weyl static axially symmetric field equations in modified f(T) gravity

2017 ◽  
Vol 14 (04) ◽  
pp. 1750053 ◽  
Author(s):  
Saeed Nayeh ◽  
Mehrdad Ghominejad
Keyword(s):  
General Relativity ◽  
Symmetric Space ◽  
Energy Momentum Tensor ◽  
Radial Component ◽  
Momentum Tensor ◽  
Space Time ◽  
Axially Symmetric ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Torsion Scalar

In this paper, we obtain the field equations of Weyl static axially symmetric space-time in the framework of [Formula: see text] gravity, where [Formula: see text] is torsion scalar. We will see that, for [Formula: see text] related to teleparallel equivalent general relativity, these equations reduce to Einstein field equations. We show that if the components of energy–momentum tensor are symmetric, the scalar torsion must be either constant or only a function of radial component [Formula: see text]. The solutions of some functions [Formula: see text] in which [Formula: see text] is a function of [Formula: see text] are obtained.

scholarly journals Classical Polymerization of the Schwarzschild Metric

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Babak Vakili
Keyword(s):  
Energy Momentum Tensor ◽  
Vacuum Solution ◽  
Equations Of Motion ◽  
Hamiltonian Function ◽  
Momentum Tensor ◽  
Einstein Equations ◽  
Spherically Symmetric ◽  
Schwarzschild Black Hole ◽  
Schwarzschild Metric ◽  
Similarities And Differences

We study a spherically symmetric setup consisting of a Schwarzschild metric as the background geometry in the framework of classical polymerization. This process is an extension of the polymeric representation of quantum mechanics in such a way that a transformation maps classical variables to their polymeric counterpart. We show that the usual Schwarzschild metric can be extracted from a Hamiltonian function which in turn gets modifications due to the classical polymerization. Then, the polymer corrected Schwarzschild metric may be obtained by solving the polymer-Hamiltonian equations of motion. It is shown that while the conventional Schwarzschild space-time is a vacuum solution of the Einstein equations, its polymer-corrected version corresponds to an energy-momentum tensor that exhibits the features of dark energy. We also use the resulting metric to investigate some thermodynamical quantities associated with the Schwarzschild black hole, and in comparison with the standard Schwarzschild metric the similarities and differences are discussed.

scholarly journals Spinors in Cylindrically Symmetric Space–Time

Universe ◽  
2020 ◽  
Vol 6 (9) ◽  
pp. 152
Author(s):  
Bijan Saha
Keyword(s):  
Gravitational Field ◽  
Symmetric Space ◽  
Spinor Field ◽  
Bianchi Type ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Space Time ◽  
Type I ◽  
Nonlinear Spinor ◽  
Cylindrically Symmetric

We studied the behavior of nonlinear spinor field within the scope of a static cylindrically symmetric space–time. It is found that the energy-momentum tensor (EMT) of the spinor field in this case possesses nontrivial non-diagonal components. The presence of non-diagonal components of the EMT imposes three-way restrictions either on the space–time geometry or on the components of the spinor field or on both. It should be noted that the analogical situation occurs in cosmology when the nonlinear spinor field is exploited as a source of gravitational field given by the Bianchi type-I cosmological model.

scholarly journals Static spherically symmetric space-time and nonlinear spinor field

2020 ◽  
pp. 1-13
Author(s):  
Saha Bijan
Keyword(s):  
Symmetric Space ◽  
Spinor Field ◽  
Space Time ◽  
Einstein Equations ◽  
Spherically Symmetric ◽  
Nonlinear Spinor ◽  
Simple Method ◽  
Spinor Fields

We studied nonlinear spinor fields in the framework of a static spherically symmetric space-time. In doing so we have suggested a rather simple method to solve the corresponding Einstein equations. As an example, a nonlinear spinor field was considered. The corresponding equations were solved analytically and numerically.

scholarly journals PECULIAR ANISOTROPIC STATIONARY SPHERICALLY SYMMETRIC SOLUTION OF EINSTEIN EQUATIONS

2012 ◽  
Vol 27 (09) ◽  
pp. 1250044 ◽  
Author(s):  
EMANUEL GALLO ◽  
OSVALDO M. MORESCHI
Keyword(s):  
Dark Matter ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Einstein Equations ◽  
Spherically Symmetric ◽  
Gravitational Lenses ◽  
Field Equations ◽  
Spherically Symmetric Solution ◽  
Stress Energy ◽  
Stress Energy Momentum Tensor

Motivated by studies on gravitational lenses, we present an exact solution of the field equations of general relativity, which is static and spherically symmetric, has no mass but has a nonvanishing spacelike components of the stress–energy–momentum tensor. In spite of its strange nature, this solution has nontrivial descriptions of gravitational effects. We show that the main aspects found in the dark matter phenomena can be satisfactorily described by this geometry. We comment on the relevance it could have to consider nonvanishing spacelike components of the stress–energy–momentum tensor ascribed to dark matter.

CASIMIR EFFECT FOR THE ROBIN SURFACES IN STATIC ROBERTSON–WALKER SPACE–TIME

2011 ◽  
Vol 20 (02) ◽  
pp. 161-168 ◽  
Author(s):  
MOHAMMAD R. SETARE ◽  
M. DEHGHANI
Keyword(s):  
Scalar Field ◽  
Energy Momentum Tensor ◽  
Casimir Effect ◽  
Vacuum Expectation ◽  
Robin Boundary Condition ◽  
Momentum Tensor ◽  
Space Time ◽  
Conformally Invariant ◽  
Time Space ◽  
Robin Boundary

We investigate the energy–momentum tensor for a massless conformally coupled scalar field in the region between two curved surfaces in k = -1 static Robertson–Walker space–time. We assume that the scalar field satisfies the Robin boundary condition on the surfaces. Robertson–Walker space–time space is conformally related to Rindler space; as a result we can obtain vacuum expectation values of the energy–momentum tensor for a conformally invariant field in Robertson–Walker space–time space from the corresponding Rindler counterpart by the conformal transformation.

The Einstein pseudo-tensor and the flux integral for perturbed static space-times

1991 ◽  
Vol 435 (1895) ◽  
pp. 645-657 ◽  
Keyword(s):  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Einstein Equations ◽  
Second Variation ◽  
Common Procedure ◽  
Static Vacuum ◽  
Linear Perturbations ◽  
Maxwell Space ◽  
The Common ◽  
Static Space

The flux integral for axisymmetric polar perturbations of static vacuum space-times, derived in an earlier paper directly from the relevant linearized Einstein equations, is rederived with the aid of the Einstein pseudo-tensor by a simple algorism. A similar earlier effort with the aid of the Landau–Lifshitz pseudo-tensor failed. The success with the Einstein pseudo-tensor is due to its special distinguishing feature that its second variation retains its divergence-free property provided only the equations governing the static space-time and its linear perturbations are satisfied. When one seeks the corresponding flux integral for Einstein‒Maxwell space-times, the common procedure of including, together with the pseudo-tensor, the energy‒momentum tensor of the prevailing electromagnetic field fails. But, a prescription due to R. Sorkin, of including instead a suitably defined ‘Noether operator’, succeeds.

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