Gravitational Collapse of an Inhomogeneous Fluid in Rastall Theory

TL;DR

This paper explores non-singular gravitational collapse in Rastall gravity with an inhomogeneous, anisotropic fluid, demonstrating scenarios where collapse leads to a bounce without forming trapped surfaces or singularities.

Contribution

It constructs exact non-singular collapse solutions in Rastall gravity with a specific equation of state, avoiding trapped surface formation and singularities.

Findings

Collapse solutions exhibit a bounce instead of singularity.

Trapped surfaces can be avoided during collapse.

Weak energy condition is satisfied in the solutions.

Abstract

We study spherically symmetric gravitational collapse of an inhomogeneous fluid with anisotropic energy momentum tensor (EMT) in Rastall gravity. Considering a linear equation of state (EoS) for the fluid profiles, i.e., $p_r=w_r\rho$ and $p_\theta=w_\theta\rho$, we try to build and investigate non-singular collapse scenarios for which, the spacetime singularity that appears in the homogeneous case~\cite{ahz2019}, is absent. We therefore set the Rastall parameter in such a way that the effective radial pressure vanishes. This helps us to obtain a class of exact nonsingular solutions in which the matter shells undergo a {collapse} process in a contracting regime, reach a bounce point, and then enter an expanding phase. We further investigate formation of trapped surfaces during the dynamical evolution of the collapsing body. {It is found} that for the obtained solutions, {the} trapped surface formation can be avoided and consequently, the bounce event is not covered by the apparent horizon. Validity of weak energy condition (WEC) is also examined for the obtained solutions.