Vaidya-like exterior solution and formation of singularity in $f(R, T)$ theory of gravity

TL;DR

This paper investigates gravitational collapse in $f(R,T)$ gravity, deriving a Vaidya-like exterior solution, analyzing singularity formation, and showing the singularity remains hidden behind the horizon.

Contribution

It introduces a Vaidya-like exterior solution in $f(R,T)$ gravity and studies collapse dynamics and singularity formation within this framework.

Findings

Exterior Vaidya-like metric derived for $f(R,T)$ gravity

Singularity forms after apparent horizon, remaining hidden

Collapse dynamics consistent with cosmic censorship

Abstract

In this paper, we study the gravitational collapse of a fluid ball undergoing dissipation in the form of heat flux, in the framework of $f(R,T)$ gravity. To apply the junction conditions in order to match the interior and the exterior spacetimes and analyze the dynamics of collapse, it is necessary to know the exterior metric for the radiating fireball, which is not yet available in the context of $f(R,T)$ gravity. Therefore, at the outset, we have determined the exterior Vaidya-like radiating metric in $f(R,T)$ gravity. Subsequently, we solved the $f(R,T)$ field equations and used the $f(R,T)$ junction conditions to match the exterior with the interior spacetime. The time of formation of the singularity and the time of formation of the apparent horizon have been determined. It is concluded that the final singularity is hidden behind the horizon.