Dissipative spherical collapse of charged anisotropic fluid in $$f(R)$$ f ( R ) gravity

H Rizwana Kausar,Ifra Noureen

doi:10.1140/epjc/s10052-014-2760-3

Abstract

This manuscript is devoted to the study of the combined effect of a viable $f(R)=R+{\alpha }{R^n}$ model and the electromagnetic field on the instability range of gravitational collapse. We assume the presence of a charged anisotropic fluid that dissipates energy via heat flow and discuss how the electromagnetic field, density inhomogeneity, shear, and phase transition of astrophysical bodies can be incorporated by a locally anisotropic background. The dynamical equations help to investigate the evolution of self-gravitating objects and lead to the conclusion that the adiabatic index depends upon the electromagnetic background, mass, and radius of the spherical objects.

Highlights

Gravitational collapse is a highly dissipative phenomenon
Due to a high dissipation, matter produces a large amount of charge in the collapse phenomenon and so one is well motivated to investigate the effects of the electromagnetic field on the gravitational collapse [15]
We adopt f (R) = R + α Rn to discuss the dynamical instability of gravitational collapse in the background of an electromagnetic field

Summary

Introduction

Gravitational collapse is a highly dissipative phenomenon. The effects of dissipation describe a wide range of situations. Positive values of the scalar curvature depicts standard cosmological corrections lead to de Sitter space [29], whereas negative values help to discuss the accelerating universe due to dark energy [30]. Models on the dynamical instability of gravitational collapse has been discussed in recent papers [31,32]. We adopt f (R) = R + α Rn to discuss the dynamical instability of gravitational collapse in the background of an electromagnetic field.

Evolution equations

A0 r A0

Newtonian regime

Asymptotic behavior

Summary and discussion