Formation of Singularity and Apparent Horizon for Dissipative Collapse in $f(R,T)$ Theory of Gravity

TL;DR

This study investigates the formation of singularities and apparent horizons during dissipative gravitational collapse within $f(R,T)$ gravity, deriving conditions under which singularities are concealed by horizons.

Contribution

It introduces a model of dissipative collapse in $f(R,T)$ gravity with specific junction conditions and analyzes the conditions for singularity and horizon formation.

Findings

Derived matching conditions for interior and exterior regions.

Determined the timing of singularity and horizon formation.

Identified constraints ensuring singularities are hidden behind horizons.

Abstract

In this paper, we consider the spherically symmetric gravitational collapse of isotropic matter undergoing dissipation in the form of heat flux, with a generalized Vaidya exterior, in the context of $f(R, T)$ gravity. Choosing $f(R, T)=R+2\lambda T$, and applying the $f(R, T)$ junction conditions on the field equations for the interior and exterior regions, we have obtained matching conditions of the matter-Lagrangian and its derivatives across the boundary. The time of formation of singularity and the time of formation of apparent horizon have been determined and constraints on the integration constants are examined for which the final singularity is hidden behind the horizon.