scholarly journals BAROTROPIC THIN SHELLS WITH LINEAR EOS AS MODELS OF STARS AND CIRCUMSTELLAR SHELLS IN GENERAL RELATIVITY

1999 ◽  
Vol 08 (04) ◽  
pp. 549-555 ◽  
Author(s):  
KONSTANTIN G. ZLOSHCHASTIEV
Keyword(s):  
General Relativity ◽  
Equation Of State ◽  
Equations Of Motion ◽  
Thin Shells ◽  
Spherically Symmetric ◽  
Equilibrium Configurations ◽  
Barotropic Fluids ◽  
Circumstellar Shells ◽  
Relativistic Models ◽  
The Stability

The spherically symmetric thin shells of the barotropic fluids with the linear equation of state are considered within the frameworks of general relativity. We study several aspects of the shells as completely relativistic models of stars, first of all the neutron stars and white dwarfs, and circumstellar shells. The exact equations of motion of the shells are obtained. Also we calculate the parameters of the equilibrium configurations, including the radii of static shells. Finally, we study the stability of the equilibrium shells against radial perturbations.

scholarly journals SINGULAR SHELLS OF QUARK-GLUON MATTER

1999 ◽  
Vol 08 (03) ◽  
pp. 363-371 ◽  
Author(s):  
KONSTANTIN G. ZLOSHCHASTIEV
Keyword(s):  
General Relativity ◽  
Equation Of State ◽  
Equations Of Motion ◽  
Thin Shells ◽  
Spherically Symmetric ◽  
Two Dimensional ◽  
Bag Model ◽  
Equilibrium Configurations

The spherically symmetric thin shells of the macroscopically stable quark-gluon matter are considered within the frameworks of the bag model and theory of discontinuities in general relativity. The equation of state for the two-dimensional matter is suggested, and its features are discussed. The exact equations of motion of such shells are obtained. Distinguishing the two cases, circumstellar and microscopical shells, we calculate the parameters of equilibrium configurations, including the conditions of decay (deconfinement).

scholarly journals Stability of spherically symmetric timelike thin-shells in general relativity with a variable equation-of-state

2017 ◽  
Vol 26 (14) ◽  
pp. 1750158 ◽  
Author(s):  
S. Habib Mazharimousavi ◽  
M. Halilsoy ◽  
S. N. Hamad Amen
Keyword(s):  
General Relativity ◽  
Equation Of State ◽  
Energy Density ◽  
Surface Energy ◽  
Thin Shell ◽  
Minkowski Spacetime ◽  
Thin Shells ◽  
Spherically Symmetric ◽  
Surface Energy Density ◽  
Variable Equation

We study spherically symmetric timelike thin-shells in [Formula: see text]-dimensional bulk spacetime with a variable equation-of-state for the fluid presented on the shell. In such a fluid, the angular pressure [Formula: see text] is a function of both surface energy density [Formula: see text] and the radius [Formula: see text] of the thin-shell. Explicit cases of the thin shells connecting two nonidentical cloud of strings spacetimes and a flat Minkowski spacetime to the Schwarzschild metric are investigated.

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.

scholarly journals The theory of spherically symmetric thin shells in conformal gravity

2018 ◽  
Vol 27 (06) ◽  
pp. 1841012 ◽  
Author(s):  
Victor Berezin ◽  
Vyacheslav Dokuchaev ◽  
Yury Eroshenko
Keyword(s):  
General Relativity ◽  
Weyl Tensor ◽  
Delta Function ◽  
Einstein Gravity ◽  
Riemann Tensor ◽  
Momentum Tensor ◽  
Thin Shells ◽  
Spherically Symmetric ◽  
Gravitational Fields ◽  
Gravitational Theories

The spherically symmetric thin shells are the nearest generalizations of the point-like particles. Moreover, they serve as the simple sources of the gravitational fields both in General Relativity and much more complex quadratic gravity theories. We are interested in the special and physically important case when all the quadratic in curvature tensor (Riemann tensor) and its contractions (Ricci tensor and scalar curvature) terms are present in the form of the square of Weyl tensor. By definition, the energy–momentum tensor of the thin shell is proportional to Diracs delta-function. We constructed the theory of the spherically symmetric thin shells for three types of gravitational theories with the shell: (1) General Relativity; (2) Pure conformal (Weyl) gravity where the gravitational part of the total Lagrangian is just the square of the Weyl tensor; (3) Weyl–Einstein gravity. The results are compared with these in General Relativity (Israel equations). We considered in detail the shells immersed in the vacuum. Some peculiar properties of such shells are found. In particular, for the traceless ([Formula: see text] massless) shell, it is shown that their dynamics cannot be derived from the matching conditions and, thus, is completely arbitrary. On the contrary, in the case of the Weyl–Einstein gravity, the trajectory of the same type of shell is completely restored even without knowledge of the outside solution.

Stability of generalized polytropic models

2019 ◽  
Vol 16 (04) ◽  
pp. 1950056
Author(s):  
I. Nazir ◽  
M. Azam
Keyword(s):  
Equation Of State ◽  
Local Density ◽  
Hydrostatic Equilibrium ◽  
Physical Parameters ◽  
Spherically Symmetric ◽  
Anisotropic Matter ◽  
Polytropic Equation ◽  
Density Perturbations ◽  
Radial Forces ◽  
The Stability

In this paper, we have investigated the stability of a spherically symmetric object with charged anisotropic matter by using the concept of cracking. The cracking is a very intuitive technique to check the stability which is based on the analysis of the radial forces that appear on the system due to perturbations taking it out of its equilibrium state. For this, we have applied and studied the effect of local density perturbations to the hydrostatic equilibrium equation and on all the physical parameters with generalized polytropic equation of state. It is found that some of the generalized polytropic models exhibit cracking.

scholarly journals Evolution of thin shells in D-dimensional general relativity

2019 ◽  
Vol 28 (04) ◽  
pp. 1950069 ◽  
Author(s):  
Marcos A. Ramirez ◽  
Daniel Aparicio
Keyword(s):  
Energy Condition ◽  
Cosmic Censorship ◽  
Einstein Equations ◽  
Thin Shells ◽  
Dominant Energy Condition ◽  
Spherically Symmetric ◽  
Barotropic Fluids ◽  
Large Shell ◽  
Asymptotic Dynamics ◽  
Electrovacuum Solution

In this paper, we consider singular timelike spherical hypersurfaces embedded in a [Formula: see text]-dimensional spherically symmetric bulk spacetime which is an electrovacuum solution of Einstein equations with cosmological constant. We analyze the different possibilities regarding the orientation of the gradient of the standard [Formula: see text] coordinate in relation to the shell. Then we study the dynamics according to Einstein equations for arbitrary matter satisfying the dominant energy condition. In particular, we thoroughly analyze the asymptotic dynamics for both the small and large-shell-radius limits. We also study the main qualitative aspects of the dynamics of shells made of linear barotropic fluids that satisfy the dominant energy condition. Finally, we prove weak cosmic censorship for this class of solutions.

Stable wormhole models in general relativity under conformal symmetry

2021 ◽  
Vol 18 (03) ◽  
pp. 2150041
Author(s):  
Asifa Ashraf ◽  
Zhiyue Zhang
Keyword(s):  
General Relativity ◽  
Symmetric Space ◽  
Conformal Symmetry ◽  
Energy Condition ◽  
Null Energy Condition ◽  
Anisotropic Fluid ◽  
Spherically Symmetric ◽  
Shape Functions ◽  
The Stability ◽  
Tov Equation

In this study, we shall explore conformal symmetry to examine the wormhole models by considering traceless fluid. In this regard, we shall take anisotropic fluid with spherically symmetric space-time. Further, we shall calculate the properties of shape-functions, which are necessary for the existence of wormhole geometry. The presence of exotic matter is confirmed in all the cases through the violation of the Null Energy Condition. Furthermore, we have discussed the stability of wormhole solutions through the Tolman–Oppenheimer–Volkoff (TOV) equation. It is observed that our acquired solutions are stable under the particular values of involved parameters in different cases in conformal symmetry.

scholarly journals Thermodynamical and dynamical stability of a self-gravitating uncharged thin shell

2020 ◽  
Vol 80 (8) ◽  
Author(s):  
Santiago Esteban Perez Bergliaffa ◽  
Marcelo Chiapparini ◽  
Luz Marina Reyes
Keyword(s):  
Equation Of State ◽  
Energy Density ◽  
Thin Shell ◽  
Dynamical Stability ◽  
Thin Shells ◽  
Maximum Mass ◽  
Equilibrium Configurations

Abstract The dynamical stability of massive thin shells with a given equation of state (EOS) (both for the barotropic and non-barotropic case) is here compared with the results coming from thermodynamical stability. Our results show that the restrictions in the para-meter space of equilibrium configurations of the shell following from thermodynamical stability are much more stringent that those obtained from dynamical stability. As a byproduct, we furnish evidence that the link between the maximum mass along a sequence of equilibrium configurations and the onset of dynamical stability is valid for EOS relating the pressure P, the energy density $$\sigma $$σ of the matter on the shell, and its radius R, namely $$P=P(R, \sigma )$$P=P(R,σ).

scholarly journals DE SITTER STABILITY IN QUADRATIC GRAVITY

2007 ◽  
Vol 16 (06) ◽  
pp. 1075-1085 ◽  
Author(s):  
A. V. TOPORENSKY ◽  
P. V. TRETYAKOV
Keyword(s):  
General Relativity ◽  
Simple Form ◽  
Equations Of Motion ◽  
Cosmological Solution ◽  
Stability Conditions ◽  
De Sitter ◽  
Bianchi I ◽  
Quadratic Gravity ◽  
The Stability ◽  
Hilbert Action

Quadratic curvature corrections to the Einstein–Hilbert action lead in general to higher-order equations of motion, which can induce instability of some unperturbed solutions of General Relativity. We study the conditions for the stability of the de Sitter cosmological solution. We argue that the simple form of this condition known for the FRW background in (3+1) dimensions changes seriously if at least one of these two assumptions is violated. In the present paper, the stability conditions for the de Sitter solution are found for the multidimensional FRW background and for Bianchi I metrics in (3 + 1) dimensions.

scholarly journals Stability Against Radial Perturbations of Slowly Rotating Neutron Stars

1981 ◽  
Vol 93 ◽  
pp. 327-327
Author(s):  
Kenzo Arai ◽  
Keisuke Kaminishi
Keyword(s):  
General Relativity ◽  
Equation Of State ◽  
Angular Velocity ◽  
Neutron Stars ◽  
Radial Displacement ◽  
Cold Neutron ◽  
Symmetric Body ◽  
Slow Rotation ◽  
Spherically Symmetric ◽  
Dynamical Equations

The dynamical equations governing pulsation in rotating neutron stars are derived in the framework of general relativity. Stellar models are constructed by using a realistic equation of state for cold neutron matter. Small radial displacement and slow rotation are treated as perturbations on spherically symmetric body. In these models the maximum masses are 1.761 M⊙ at the central density 3.461 × 1015 g cm−3 for a sequence of nonrotating configurations and 2.165 M⊙ for rotating models with the critical angular velocity (GM/R3)½.

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