Invariant solutions of Einstein field equations in pure radiation fields

2021 ◽  
Author(s):  
Sachin Kumar ◽  
Divya Jyoti
Keyword(s):  
Invariant Solutions ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Pure Radiation ◽  
Radiation Fields

Exact solutions of the field equations: twist-free pure radiation fields

1962 ◽  
Vol 270 (1342) ◽  
pp. 328-334 ◽  
Keyword(s):  
General Relativity ◽  
Exact Solutions ◽  
Radiation Field ◽  
Relativity Theory ◽  
Vacuum Field ◽  
Field Equations ◽  
General Relativity Theory ◽  
Pure Radiation ◽  
Radiation Fields ◽  
Null Congruence

This note is intended to give a rough survey of the results obtained in the study of twist-free pure radiation fields in general relativity theory. Here we are using the following Definition. A space-time ( V 4 of signature +2) is called a pure radiation field if it contains a distortion-free geodetic null congruence (a so-called ray congruence ), and if it satisfies certain field equations which we will specify below (e.g. Einstein’s vacuum-field equations). A (null) congruence is called twist-free if it is hypersurface-orthogonal (or ‘normal’). The results listed below were obtained by introducing special (‘canonical’) co-ordinates adapted to the ray congruence. Detailed proofs were given by Robinson & Trautman (1962) and by Jordan, Kundt & Ehlers (1961) (see also Kundt 1961). For the sake of completeness we include in our survey the subclass of expanding fields, and make use of some formulae first obtained by Robinson & Trautman.

scholarly journals Some pure radiation filds in general relativity

1980 ◽  
Vol 21 (4) ◽  
pp. 464-473 ◽  
Author(s):  
R. P. Akabari ◽  
U. K. Dave ◽  
L. K. Patel
Keyword(s):  
General Relativity ◽  
General Solution ◽  
Einstein’S Field Equations ◽  
Field Equations ◽  
Pure Radiation ◽  
Radiation Fields ◽  
Einstein's Field Equations

AbstractA Demianski-type metric investigated in connection with Einstein's field equations corresponding to pure radiation fields. With aid of complex vectorical formalism, a general solution of these fiel equations is obtained. The solution is algebraically spcial. A particular case of the solution is considered which includes many known solutions; among them are the raiationg versions of some of Kinnersley's solutions.

INVARIANT SOLUTIONS OF EINSTEIN FIELD EQUATION FOR NONCONFORMALLY FLAT FLUID SPHERES OF EMBEDDING CLASS ONE

2010 ◽  
Vol 25 (20) ◽  
pp. 3993-4000 ◽  
Author(s):  
SACHIN KUMAR ◽  
PRATIBHA ◽  
Y. K. GUPTA
Keyword(s):  
Field Equation ◽  
Einstein Field Equation ◽  
Invariant Solutions ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Free Interface ◽  
Lie Group Of Transformations ◽  
Embedding Class One ◽  
Perfect Fluids ◽  
Fluid Spheres

In the present paper, nonconformal spherical symmetric perfect fluid solutions to Einstein field equations are obtained by using the invariance of the equations under the Lie group of transformations and some new solutions of this category are obtained satisfying the reality conditions like ρ ≥ p ≥ 0, ρr < 0, pr < 0 (p and ρ being pressure and energy-density respectively) in the region 0 < r < a. Such fluids do not represent isolated fluid spheres as pressure free interface is not possible for nonconformally perfect fluids of class one.

Radiating Demianski-type metrics and the Einstein-Maxwell fields

1988 ◽  
Vol 30 (1) ◽  
pp. 120-126 ◽  
Author(s):  
L. K. Patel ◽  
R. P. Akabari ◽  
U. K. Dave
Keyword(s):  
Exact Solutions ◽  
Electromagnetic Fields ◽  
Maxwell Field ◽  
Field Equations ◽  
Pure Radiation ◽  
Radiation Fields ◽  
Maxwell Fields

AbstractA Demianski-type metric is investigated in connection with the Einstein-Maxwell fields. Using complex vectorial formalism, some exact solutions of Einstein-Maxwell field equations for source-free electromagnetic fields plus pure radiation fields are obtained. The radiating Demianski solution, the Debney-Kerr-Schild solution and the Brill solution are derived as particular cases.

scholarly journals Does general relativity highlight necessary connections in nature?

Synthese ◽  
2021 ◽  
Author(s):  
Antonio Vassallo
Keyword(s):  
General Relativity ◽  
Laws Of Nature ◽  
Coupling Mechanism ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Bianchi Identities ◽  
Physical Role ◽  
General Relativistic ◽  
Differential Relations ◽  
Necessary Connections

AbstractThe dynamics of general relativity is encoded in a set of ten differential equations, the so-called Einstein field equations. It is usually believed that Einstein’s equations represent a physical law describing the coupling of spacetime with material fields. However, just six of these equations actually describe the coupling mechanism: the remaining four represent a set of differential relations known as Bianchi identities. The paper discusses the physical role that the Bianchi identities play in general relativity, and investigates whether these identities—qua part of a physical law—highlight some kind of a posteriori necessity in a Kripkean sense. The inquiry shows that general relativistic physics has an interesting bearing on the debate about the metaphysics of the laws of nature.

scholarly journals Mass-radius relation of compact objects

2019 ◽  
Vol 15 (S356) ◽  
pp. 383-384
Author(s):  
Seman Abaraya ◽  
Tolu Biressa
Keyword(s):  
Numerical Analysis ◽  
Equation Of State ◽  
Compact Objects ◽  
Mass Limit ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Formation And Evolution ◽  
Active Research ◽  
Compact Sources ◽  
Astrophysical Research

AbstractCompact objects are of great interest in astrophysical research. There are active research interests in understanding better various aspects of formation and evolution of these objects. In this paper we addressed some problems related to the compact objects mass limit. We employed Einstein field equations (EFEs) to derive the equation of state (EoS). With the assumption of high densities and low temperature of compact sources, the derived equation of state is reduced to polytropic kind. Studying the polytropic equations we obtained similar physical implications, in agreement to previous works. Using the latest version of Mathematica-11 in our numerical analysis, we also obtained similar results except slight differences in accuracy.

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