Dynamical instability and the expansion-free condition

Abstract

We study the dynamical instability of a spherically symmetric anisotropic fluid which collapses adiabatically under the condition of vanishing expansion scalar. The Newtonian and post Newtonian regimes are considered in detail. It is shown that within those two approximations the adiabatic index $\Gamma_1$, measuring the fluid stiffness, does not play any role. Instead, the range of instability is determined by the anisotropy of the fluid pressures and the radial profile of the energy density, independently of its stiffness, in a way which is fully consistent with results previously obtained from the study on the Tolman mass.Comment: 12 pages Revtex. Some changes in the text to match the version accepted in Gen. Rel. Gra

Radiating star with a time-dependent Karmarkar condition

“…The Santos junction conditions have been generalised to include shear [5,6], the cosmological constant as well as the electromagnetic field [7,8]. Since 1985 there has been a concerted effort in generating exact models of dissipative collapse with Herrera and co-workers establishing many of the fundamental results in terms of stability, energy conditions and thermodynamics of these models [9][10][11][12][13][14]. Maartens et al investigated the temperature and luminosity profiles of these models by employing casual thermodynamics [15][16][17].…”

Role of $$f(R,T,R_{\mu \nu }T^{\mu \nu })$$ f ( R , T , R μ ν T μ ν ) model on the stability of cylindrical stellar model

“…It was demonstrated by Chandrasekhar [17] and Herrera et al [18] that all the terms coming in the stability conditions should be positive definite. Therefore, to attain the instability regions of the cylindrical stellar system, we consider each term in the respective collapse equation to be positive.…”

“…Initially, the celestial system is considered to be in hydrostatic equilibrium, but as time passes, it is subject to oscillatory motion. All the metric functions and fluid parameters can be perturbed [18],…”

“…Chandrasekhar [17] studied the dynamical instability of an oscillating spherically symmetric model by using a perfect fluid and found the instability limits in terms of the adiabatic index. Herrera et al [18] analyzed the dynamical instability of dense stars with zero expansion scalar in a spherically symmetric configuration and found instability limits that are independent of adiabatic index. Cembranos et al [19] studied gravitational collapse in f (R) gravity and found this phenomenon to possibly work as a key tool to constrain modified gravity models that describe late time cosmological acceleration.…”

Effects of electromagnetic field on the dynamical instability of expansionfree gravitational collapse

“…Horvat et al [24] explored that instability of anisotropic star occurs at higher surface compactness when the anisotropy of the pressure is present. Herrera et al [25] discussed the dynamical instability of expansionfree fluid at Newtonian and post Newtonian order and found that the range of instability is determined by the anisotropic pressure and radial profile of the energy density. In a recent paper [26], this problem has been explored in f (R) gravity.…”