Effects of Electromagnetic Field on the Dynamical Instability of Expansionfree Gravitational Collapse

TL;DR

This study examines how electromagnetic fields influence the stability of spherically symmetric gravitational collapse, revealing that electromagnetic effects can reduce instability regions and are independent of the adiabatic index.

Contribution

It introduces a detailed analysis of electromagnetic effects on gravitational collapse stability using perturbation methods and matching conditions in a spherically symmetric context.

Findings

Electromagnetic field reduces the unstable region during collapse.

Instability depends on pressure anisotropy and energy density profile.

The adiabatic index does not influence the instability range.

Abstract

In this paper, we discuss the effects of electromagnetic field on the dynamical instability of a spherically symmetric expansionfree gravitational collapse. Darmois junction conditions are formulated by matching interior spherically symmetric spacetime to exterior Reissner-Nordstr$\ddot{o}$m spacetime. We investigate the role of different terms in the dynamical equation at Newtonian and post Newtonian regimes by using perturbation scheme. It is concluded that instability range depends upon pressure anisotropy, radial profile of energy density and electromagnetic field, but not on the adiabatic index $\Gamma$. In particular, the electromagnetic field reduces the unstable region.