Singularity Avoidance in Gravitational Collapse of an Inhomogeneous Fluid in Rastall Gravity

TL;DR

This paper explores conditions under which inhomogeneous gravitational collapse in Rastall gravity avoids singularities, resulting in nonsingular models where collapsing matter rebounds, respecting physical energy conditions.

Contribution

It introduces exact nonsingular collapse solutions in Rastall gravity with specific pressure conditions, extending the understanding of gravitational collapse without singularities.

Findings

Nonsingular collapse solutions where matter rebounds after reaching a minimum radius.

Solutions respect the weak energy condition, ensuring physical plausibility.

Collapse models avoiding singularities in Rastall gravity with specific equations of state.

Abstract

Various types of inhomogeneous collapse models in general relativity (GR) lead to the formation of spacetime singularities either visible or hidden by a spacetime horizon. Our aim in the present work is to search for nonsingular models in Rastall gravity that arise as the final outcomes of spherically symmetric gravitational collapse of an inhomogeneous matter cloud. We firstly assume linear equations of state (EoS) for radial and tangential pressure profiles, i.e., $p_r=w_r\rho$ and $p_\theta=w_\theta\rho$, then we set the Rastall parameter in such a way that the effective pressure in radial direction vanishes and examine the conditions under which the spacetime singularity can be avoided. We find exact nonsingular collapse solutions for which the collapsing cloud reaches a minimum physical radius at a finite amount of time and then rebounds to an expanding phase where the matter shells start moving away from each other. The solutions we obtain respect the weak energy condition (WEC), which is important for the physical validity of the model.