Dynamical instability of collapsing radiating fluid
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UCLEI, PARTICLES, FIELDS, GRAVITATION, AND ASTROPHYSICS
Dynamical Instability of Collapsing Radiating Fluid1 M. Sharifa and M. Azama,b a
Department of Mathematics, University of the Punjab, Lahore54590, Pakistan Division of Science and Technology, University of Education, Lahore54590, Pakistan email: [email protected], [email protected]
b
Received December 3, 2012
Abstract—We take the collapsing radiative fluid to investigate the dynamical instability with cylindrical sym metry. We match the interior and exterior cylindrical geometries. Dynamical instability is explored at radia tive and nonradiative perturbations. We conclude that the dynamical instability of the collapsing cylinder depends on the critical value ϒ < 1 for both radiative and nonradiative perturbations. DOI: 10.1134/S1063776113060125 1
1. INTRODUCTION The subject of dynamical instability of selfgravi tating objects has attracted many astrophysicists due to explosions and evolution of these objects. The evolu tion of different selfgravitating objects during gravita tional collapse for different ranges of instability is an important feature of dynamical instability. The static stellar model would be interesting if it remains stable under fluctuations. In this scenario, Chandrasekhar [1] found the instability range ϒ < 4/3 for the spheri cally symmetric spacetime with isotropic fluid. After that, many people investigated the effects of physical properties of the fluid in the onset of dynamical insta bility with spherical symmetry. In [2], it was found that dissipation at Newtonian (N) limit reduces the stability of the sphere and boosts at postNewtonian (pN) limit. The conclusion in [3] was that the effects of radiation appears similar to dis sipation in the N and pN limits. The same authors [4] examined the instability of a spherically symmetric spacetime with shear viscosity and found that it decreases the instability of the fluid. The dynamical instability of a collapsing radiating star would be increased due to the presence of anisotropic pressure and shear viscosity [5]. Cylindrically symmetric spacetimes are idealized models in general relativity. The study of gravitational collapse of these astrophysical objects is an important problem. Some recent work [6–10] indicate great interest in cylindrical gravitational collapse with dif ferent fluids with and without an electromagnetic field. Recently, Sharif and his collaborators [11] inves tigated the dynamical instability for spherically and cylindrically symmetric spacetimes in general relativ ity and f(R) gravity in the N and pN regimes, respec tively. They have shown that the electromagnetic field, pressure anisotropy, dissipation, and f(R) models have
great relevance in the range of instability. The same authors [12] have also explored this problem for the thinshell wormholes in nonlinear electrodynamics. In this paper, we explore the dynamical instability of a collapsing radiating cylinder in the N and pN approximations. The paper is organized as follows. In Sect
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