scholarly journals ENERGY DISTRIBUTION OF THE EINSTEIN–KLEIN–GORDON SYSTEM FOR A STATIC SPHERICALLY SYMMETRIC SPACE–TIME IN (2+1) DIMENSIONS

2006 ◽  
Vol 21 (13n14) ◽  
pp. 2853-2861 ◽  
Author(s):  
I. RADINSCHI ◽  
TH. GRAMMENOS
Keyword(s):  
Exact Solution ◽  
Momentum Density ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Spherically Symmetric ◽  
Field Equations ◽  
Density Distributions ◽  
Klein Gordon ◽  
Energy And Momentum ◽  
Momentum Complex

We use Møller's energy–momentum complex in order to explicitly compute the energy and momentum density distributions for an exact solution of Einstein's field equations with a negative cosmological constant, minimally coupled to a static massless scalar field in a static, spherically symmetric background in (2+1) dimensions.

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.

scholarly journals ENERGY AND MOMENTUM DISTRIBUTIONS OF THE MAGNETIC SOLUTION TO (2+1) EINSTEIN–MAXWELL GRAVITY

2005 ◽  
Vol 20 (23) ◽  
pp. 1741-1751 ◽  
Author(s):  
TH. GRAMMENOS
Keyword(s):  
Magnetic Field ◽  
Maxwell Equations ◽  
Three Dimensional ◽  
Momentum Density ◽  
Radial Magnetic Field ◽  
Density Distributions ◽  
Static Gravitational Field ◽  
Energy And Momentum ◽  
Momentum Complex ◽  
The Magnetic Field

We use Møller's energy–momentum complex in order to explicitly evaluate the energy and momentum density distributions associated with the three-dimensional magnetic solution to the Einstein–Maxwell equations. The magnetic spacetime under consideration is a one-parametric solution describing the distribution of a radial magnetic field in a three-dimensional AdS background, and representing the superposition of the magnetic field with a 2+1 Einstein static gravitational field.

ANOTHER “COSMOLOGICAL” CONSTANT

1992 ◽  
Vol 07 (06) ◽  
pp. 1287-1308 ◽  
Author(s):  
INGEMAR BENGTSSON ◽  
PETER PELDÁN
Keyword(s):  
Riemannian Geometry ◽  
Nonrelativistic Limit ◽  
Space Time ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Spherically Symmetric ◽  
Basic Variable ◽  
Field Equations ◽  
Tetrad Formalism ◽  
Spherically Symmetric Solutions

Capovilla, Jacobson and Dell have found a one-parameter family of field equations which coincides with Einstein’s equations when the parameter is set to zero. The basic variable is an SO(3) vector potential. For generic values of the parameter, we show that the solutions of the field equations may be interpreted in terms of Riemannian geometry. The space-time metric is expressible in terms of the field strengths. The connection between the SO(3) fibers and the tangent space of space-time is not that of the tetrad formalism. The metric is not Ricci flat. Coupling to a massless scalar field is given as an example of matter couplings. Spherically symmetric solutions are given. In the nonrelativistic limit there is a deviation from Newton’s inverse square law, and this is used to set an observational bound on the parameter.

scholarly journals PERTURBED SELF-SIMILAR MASSLESS SCALAR FIELD IN SPHERICALLY SYMMETRIC SPACE–TIMES

2007 ◽  
Vol 22 (25) ◽  
pp. 4695-4708
Author(s):  
M. SHARIF
Keyword(s):  
Scalar Field ◽  
Symmetric Space ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Spherically Symmetric ◽  
Field Equations ◽  
Self Similarity ◽  
Linear Perturbations ◽  
Self Similar ◽  
Scalar Field Equations

In this paper, we investigate the linear perturbations of the spherically symmetric space–times with kinematic self-similarity of the second kind. The massless scalar field equations are solved which yield the background and an exact solutions for the perturbed equations. We discuss the boundary conditions of the resulting perturbed solutions. The possible perturbation modes turn out to be stable as well as unstable. The analysis leads to the conclusion that there does not exist any critical solution.

scholarly journals Static solutions in the Freund – Nambu scalar-tensor theory of gravitation

2021 ◽  
Vol 57 (4) ◽  
pp. 464-469
Author(s):  
Yu. P. Vyblyi ◽  
O. G. Kurguzova
Keyword(s):  
Einstein Equations ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Spherically Symmetric ◽  
Scalar Tensor Theory ◽  
Axially Symmetric ◽  
Field Equations ◽  
Tensor Theory ◽  
Static Solutions ◽  
Theory Of Gravitation

Herein, the system of Einstein equations and the equation of the Freund – Nambu massless scalar field for static spherically symmetric and axially symmetric fields are considered. It is shown that this system of field equations decouples into gravitational and scalar subsystems. In the second post-Newtonian approximation, the solutions for spherically symmetric and slowly rotating sources are obtained. The application of the obtained solutions to astrophysical problems is discussed.

scholarly journals Janis–Newman–Winicour and Wyman Solutions are the Same

1997 ◽  
Vol 12 (27) ◽  
pp. 4831-4835 ◽  
Author(s):  
K. S. Virbhadra
Keyword(s):  
Exact Solution ◽  
Scalar Field ◽  
Total Energy ◽  
Space Time ◽  
Massless Scalar ◽  
Spherically Symmetric ◽  
Scalar Equations

We show that the well-known most general static and spherically symmetric exact solution to the Einstein-massless scalar equations given by Wyman is the same as one found by Janis, Newman and Winicour several years ago. We obtain the energy associated with this space–time and find that the total energy for the case of the purely scalar field is zero.

scholarly journals COLLAPSING SCALAR FIELD WITH KINEMATIC SELF-SIMILARITY OF THE SECOND KIND IN (2+1) GRAVITY

2005 ◽  
Vol 14 (06) ◽  
pp. 1049-1061 ◽  
Author(s):  
R. CHAN ◽  
M. F. A. DA SILVA ◽  
J. F. VILLAS DA ROCHA ◽  
ANZHONG WANG
Keyword(s):  
Black Holes ◽  
Scalar Field ◽  
Gravitational Collapse ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Field Equations ◽  
Self Similarity ◽  
Global Properties ◽  
Scalar Field Equations

All the (2+1)-dimensional circularly symmetric solutions with kinematic self-similarity of the second kind to the Einstein-massless-scalar field equations are found and their local and global properties are studied. It is found that some of them represent gravitational collapse of a massless scalar field, in which black holes are always formed.

scholarly journals Wormholes in Wyman's solution

2014 ◽  
Vol 23 (11) ◽  
pp. 1450086 ◽  
Author(s):  
J. B. Formiga ◽  
T. S. Almeida
Keyword(s):  
Scalar Field ◽  
General Solution ◽  
Detailed Analysis ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Human Beings ◽  
Einstein Field Equations ◽  
Field Equations

The most general solution of the Einstein field equations coupled with a massless scalar field is known as Wyman's solution. This solution is also present in the Brans–Dicke theory and, due to its importance, it has been studied in detail by many authors. However, this solutions has not been studied from the perspective of a possible wormhole. In this paper, we perform a detailed analysis of this issue. It turns out that there is a wormhole. Although we prove that the so-called throat cannot be traversed by human beings, it can be traversed by particles and bodies that can last long enough.

Joule–Thomson expansion and quasinormal modes of regular non-minimal magnetic black hole

2020 ◽  
Vol 35 (36) ◽  
pp. 2050298
Author(s):  
Abdul Jawad ◽  
Muhammad Yasir ◽  
Shamaila Rani
Keyword(s):  
Black Hole ◽  
Mass Formula ◽  
Quasinormal Modes ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Thomson Effect ◽  
First Order ◽  
Thermodynamical Parameters ◽  
Klein Gordon ◽  
Tortoise Coordinate

The Joule–Thomson effect and quasinormal modes (QNM) onto regular non-minimal magnetic charged black hole with a cosmological constant are being investigated. For this purpose, we extract some thermodynamical parameters such as pressure [Formula: see text] and mass [Formula: see text] in the presence of magnetic [Formula: see text] as well as electric [Formula: see text] charge. These parameters lead to inversion temperature [Formula: see text], pressure [Formula: see text] and corresponding isenthalpic curves. We introduce the tortoise coordinate and the Klein–Gordon wave equation which leads to the second-order ordinary Schrödinger equation. We find out the complex frequencies of QNMs through the massless scalar field perturbation which satisfy boundary conditions by using the first-order Wentzel–Kramers–Brillouin (WKB) technique.

scholarly journals Observables in terms of connection and curvature variables for Einstein’s equations with two commuting Killing vectors

2015 ◽  
Vol 471 (2183) ◽  
pp. 20150350
Author(s):  
P. Kordas
Keyword(s):  
Transition Matrix ◽  
Momentum Density ◽  
Transition Matrices ◽  
Einstein’S Equations ◽  
Integrals Of Motion ◽  
Einstein's Equations ◽  
Killing Vectors ◽  
Klein Gordon ◽  
Quantum Operators ◽  
Energy And Momentum

Einstein’s equations with two commuting Killing vectors and the associated Lax pair are considered. The equations for the connection A ( ς , η , γ )= Ψ , γ Ψ −1 , where γ the variable spectral parameter are considered. A transition matrix T = A ( ς , η , γ ) A −1 ( ξ , η , γ ) for A is defined relating A at ingoing and outgoing light cones. It is shown that it satisfies equations familiar from integrable PDE theory. A transition matrix on ς = constant is defined in an analogous manner. These transition matrices allow us to obtain a hierarchy of integrals of motion with respect to time, purely in terms of the trace of a function of the connections g , ς g −1 and g , η g −1 . Furthermore, a hierarchy of integrals of motion in terms of the curvature variable B = A , γ A −1 , involving the commutator [ A (1), A (−1)], is obtained. We interpret the inhomogeneous wave equation that governs σ = lnN , N the lapse, as a Klein–Gordon equation, a dispersion relation relating energy and momentum density, based on the first connection observable and hence this first observable corresponds to mass. The corresponding quantum operators are ∂/∂ t , ∂/∂ z and this means that the full Poincare group is at our disposal.

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