A criterion for the stability of a charged sphere in general relativity

1974 ◽  
Vol 5 (4) ◽  
pp. 387-397 ◽  
Author(s):  
Miroru Omote ◽  
Haruo Sato
Keyword(s):  
General Relativity ◽  
Charged Sphere ◽  
The Stability

scholarly journals CAN f(R) GRAVITY MIMIC GENERAL RELATIVITY?

2012 ◽  
Vol 10 ◽  
pp. 63-68 ◽  
Author(s):  
JE-AN GU
Keyword(s):  
General Relativity ◽  
Differential Equations ◽  
Early Time ◽  
Einstein Equations ◽  
Modified Theories Of Gravity ◽  
Cosmological Perturbations ◽  
Long Run ◽  
Theories Of Gravity ◽  
The Stability ◽  
Higher Order Differential Equations

We discuss the stability of the general-relativity (GR) limit in modified theories of gravity, particularly the f(R) theory. The problem of approximating the higher-order differential equations in modified gravity with the Einstein equations (2nd-order differential equations) in GR is elaborated. We demonstrate this problem with a heuristic example involving a simple ordinary differential equation. With this example we further present the iteration method that may serve as a better approximation for solving the equation, meanwhile providing a criterion for assessing the validity of the approximation. We then discuss our previous numerical analyses of the early-time evolution of the cosmological perturbations in f(R) gravity, following the similar ideas demonstrated by the heuristic example. The results of the analyses indicated the possible instability of the GR limit that might make the GR approximation inaccurate in describing the evolution of the cosmological perturbations in the long run.

scholarly journals Dark matter from non-relativistic embedding gravity

2021 ◽  
pp. 2150101
Author(s):  
S. A. Paston
Keyword(s):  
General Relativity ◽  
Dark Matter ◽  
Explicit Form ◽  
Equations Of Motion ◽  
Additional Contribution ◽  
Relativistic Limit ◽  
The Core ◽  
The Stability ◽  
Dimensional Surface

We study the possibility to explain the mystery of the dark matter (DM) through the transition from General Relativity to embedding gravity. This modification of gravity, which was proposed by Regge and Teitelboim, is based on a simple string-inspired geometrical principle: our spacetime is considered here as a four-dimensional surface in a flat bulk. We show that among the solutions of embedding gravity, there is a class of solutions equivalent to solutions of GR with an additional contribution of non-relativistic embedding matter, which can serve as cold DM. We prove the stability of such type of solutions and obtain an explicit form of the equations of motion of embedding matter in the non-relativistic limit. According to them, embedding matter turns out to have a certain self-interaction, which could be useful in the context of solving the core-cusp problem that appears in the [Formula: see text]CDM model.

A stable charged sphere in general relativity

1967 ◽  
Vol 48 (4) ◽  
pp. 975-981 ◽  
Author(s):  
N. K. Sharma
Keyword(s):  
General Relativity ◽  
Charged Sphere

scholarly journals Cosmological bounce in Horndeski theory and beyond

2018 ◽  
Vol 191 ◽  
pp. 07013 ◽  
Author(s):  
R. Kolevatov ◽  
S. Mironov ◽  
V. Rubakov ◽  
N. Sukhov ◽  
V. Volkova
Keyword(s):  
General Relativity ◽  
Scalar Field ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Cosmological Solutions ◽  
The Stability ◽  
The Way

We discuss the stability of the classical bouncing solutions in the general Horndeski theory and beyond Horndeski theory. We restate the no-go theorem, showing that in the general Horndeski theory there are no spatially flat non-singular cosmological solutions which are stable during entire evolution. We show the way to evade the no-go in beyond Horndeski theory and give two specific examples of bouncing solutions, whose asymptotic past and future or both are described by General Relativity (GR) with a conventional massless scalar field. Both solutions are free of any pathologies at all times.

Exact solution of a static charged sphere in general relativity

1969 ◽  
Vol 47 (21) ◽  
pp. 2401-2404 ◽  
Author(s):  
S. J. Wilson
Keyword(s):  
Exact Solution ◽  
General Relativity ◽  
Gravitational Constant ◽  
The Self ◽  
Spherically Symmetric ◽  
Charged Sphere ◽  
Field Equations ◽  
First Order ◽  
Self Energy ◽  
Spherically Symmetric Distribution

An exact solution of the field equations of general relativity is obtained for a static, spherically symmetric distribution of charge and mass which can be matched with the Reissner–Nordström metric at the boundary. The self-energy contributions to the total gravitational mass are computed retaining only the first order terms in the gravitational constant.

A solution for a charged sphere in general relativity

1979 ◽  
Vol 11 (5) ◽  
pp. 333-336 ◽  
Author(s):  
A. L. Mehra ◽  
M. L. Bohra
Keyword(s):  
General Relativity ◽  
Charged Sphere
Sign in / Sign up

Export Citation Format

Share Document