scholarly journals Final fate of Kantowski–Sachs gravitational collapse

2020 ◽  
Vol 18 (01) ◽  
pp. 2150016
Author(s):  
Brisa Terezón ◽  
Miguel De Campos
Keyword(s):  
Gravitational Collapse ◽  
Fundamental Question ◽  
Relativity Theory ◽  
Anisotropic Universe ◽  
Field Equations ◽  
General Relativity Theory ◽  
Petrov Classification ◽  
Curvature Parameter ◽  
Arbitrary Curvature ◽  
Spatial Section

Although it is not a fundamental question, determining exact and general solutions for a given theory has advantages over a numerical integration in many specific cases. Of course, respecting the peculiarities of the problem. Revisiting the integration of the General Relativity Theory field equations for the Kantowski–Sachs spacetime describes a homogeneous but anisotropic universe whose spatial section has the topology of [Formula: see text], we integrate the equations for arbitrary curvature parameter and write the solutions considering the process of gravitational collapse. We took the opportunity and made some comments involving some features of the model such as energy density, shear, viscosity and the production of gravitational waves via Petrov classification.

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.

On the relativistic interpretation of astronomical observations

1959 ◽  
Vol 252 (1271) ◽  
pp. 476-487 ◽  
Keyword(s):  
Differential Equation ◽  
General Relativity ◽  
Apparent Motion ◽  
Flat Space ◽  
Frame Of Reference ◽  
Relativity Theory ◽  
General Relativity Theory ◽  
Astronomical Observations ◽  
Basic Ideas ◽  
Arbitrary Curvature

The basic ideas of apparent motion are formulated within the framework of general relativity theory. This requires the introduction of a dynamically meaningful frame of reference. A differential equation characterizing motion relative to this frame in a space of arbitrary curvature is formulated and its solutions for nearly flat space-time are obtained. These solutions are compared with the results of classical and special relativistic theory.

scholarly journals On Hilbert's world-function

1927 ◽  
Vol 113 (765) ◽  
pp. 496-511 ◽  
Keyword(s):  
Dynamical System ◽  
General Relativity ◽  
Minimum Principle ◽  
Relativity Theory ◽  
Field Equations ◽  
General Relativity Theory ◽  
Least Action ◽  
Principle Of Least Action ◽  
The Universe ◽  
World Function

The well-known theorem that the motion of any conservative dynamical system can be determined from the “Principle of Least Action” or “Hamilton’s Principle” was carried over into General Relativity-Theory in 1915 by Hilbert, who showed that the field-equations of gravitation can be deduced very simply from a minimum-principle. Hilbert generalised his ideas into the assertion that all physical happenings (gravitational electrical, etc.) in the universe are determined by a scalar “world-function” H, being, in fact, such as to annul the variation of the integral ∫∫∫∫H√(−g)dx 0 dx 1 dx 2 dx 3 where ( x 0 , x 1 , x 2 , x 3 ) are the generalised co-ordinates which specify place and time, and g is (in the usual notation of the relativity-theory) the determinant of the gravitational potentials g v q , which specify the metric by means of the equation dx 2 = ∑ p, q g vq dx v dx q . In Hilbert’s work, the variation of the above integral was supposed to be due to small changes in the g vq 's and in the electromagnetic potentials, regarded as functions of x 0 , x 1 , x 2 , x 3 .

Massive and massless scalar field models for Kaluza–Klein universe in f(R, T) gravity

2019 ◽  
Vol 34 (11) ◽  
pp. 1950066 ◽  
Author(s):  
Can Aktaş
Keyword(s):  
Scalar Field ◽  
Cosmological Term ◽  
Relativity Theory ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Field Equations ◽  
General Relativity Theory ◽  
Text Model ◽  
The Universe ◽  
Kaluza Klein

In this research, we have investigated the behavior of massive and massless scalar field (SF) models (normal and phantom) for Kaluza–Klein universe in [Formula: see text] gravity with cosmological term ([Formula: see text]). To obtain field equations, we have used [Formula: see text] model given by Harko et al. [Phys. Rev. D 84, 024020 (2011)] and anisotropy feature of the universe. Finally, we have discussed our results in [Formula: see text] and General Relativity Theory (GRT) with various graphics.

Non-linear Lagrangians and Palatine's device

1960 ◽  
Vol 56 (4) ◽  
pp. 396-400 ◽  
Author(s):  
H. A. Buchdahl
Keyword(s):  
General Relativity ◽  
Relativity Theory ◽  
Field Equations ◽  
General Relativity Theory ◽  
Invariant Action ◽  
Action Integral ◽  
Independent Variation ◽  
Non Linear

ABSTRACTField equations in general relativity theory have sometimes been generated by subjecting, in an invariant action integral, the components of linear connexion and the components of a covariant tensor of valence 2 to independent variation. The conceptual objections to this process, and some of the manifold formal difficulties inherent in it, are discussed in some detail. At the same time certain results obtained elsewhere are strengthened and in part corrected.

scholarly journals Reciprocal Static Solutions of the Equations of the Gravitational Field

1956 ◽  
Vol 9 (1) ◽  
pp. 13 ◽  
Author(s):  
HA Buchdahl
Keyword(s):  
General Relativity ◽  
Equation Of State ◽  
Relativity Theory ◽  
Field Equations ◽  
General Relativity Theory ◽  
Remarkable Property ◽  
Reciprocal Transformation ◽  
Total Energy Density ◽  
Static Solutions ◽  
Line Elements

This paper deals with reciprocal static line-elements, previously defined by the author, the condition that their Ricci tensors vanish being no longer imposed. If the indices i, k run from 1 to n with the exception of the fixed index a (the line-elements being static with respect to xa) a certain quantity appears with the remarkable property that in a reciprocal transformation is invariant, whilst merely changes sign. is closely related to the Hamiltonian derivative of the Gaussian curvature, so that the general results obtained may be applied to the field equations of General Relativity Theory, with n=a=4. is then the total energy density; and formally every static distribution of matter has a " reciprocal distribution" associated with it. In particular, the equation of state of a distribution of fluid reciprocal to a distribution of fluid possessing a given equation of state may be obtained directly from the latter, i.e. without the solution of the field equations being known.

scholarly journals Charged and Non-Charged Black Hole Solutions in Mimetic Gravitational Theory

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 559 ◽  
Author(s):  
Gamal Nashed
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Black Hole ◽  
Gravitational Theory ◽  
Relativity Theory ◽  
Charged Black Hole ◽  
Field Equations ◽  
General Relativity Theory ◽  
Mimetic Theory ◽  
Black Hole Solutions

In this study, we derive, in the framework of mimetic theory, charged and non-charged black hole solutions for spherically symmetric as well as flat horizon spacetimes. The asymptotic behavior of those black holes behave as flat or (A)dS spacetimes and coincide with the solutions derived before in general relativity theory. Using the field equations of non-linear electrodynamics mimetic theory we derive new black hole solutions with monopole and quadrupole terms. The quadruple term of those black holes is related by a constant so that its vanishing makes the solutions coincide with the linear Maxwell black holes. We study the singularities of those solutions and show that they possess stronger singularity than the ones known in general relativity. Among many things, we study the horizons as well as the heat capacity to see if the black holes derived in this study have thermodynamical stability or not.

Sign in / Sign up

Export Citation Format

Share Document