Non-Singular Collapse Scenario From Matter-Curvature Coupling

TL;DR

This paper investigates non-singular gravitational collapse in a modified gravity theory where matter-curvature coupling varies, leading to bounce scenarios that avoid singularities and may mimic quantum effects.

Contribution

It introduces a dynamic matter-curvature coupling in Rastall theory, showing how it can produce non-singular bounce collapse scenarios replacing classical singularities.

Findings

Collapse can halt at a finite scale, avoiding singularity.

Existence of a minimum initial radius for horizon formation.

Matter-curvature interaction mimics quantum correction effects.

Abstract

In the present work we study spherically symmetric gravitational collapse of a homogeneous perfect fluid in the context of Generalized Rastall Theory (GRT). In this modified version of the original {Rastall Gravity (RG)}, the coupling parameter which is a representative of matter-curvature interaction is no longer a constant parameter. Such a dynamic coupling may play the role of dark energy which is responsible for the present accelerating expansion of the Universe. Assuming then a linear equation of state (EoS) for the fluid profiles, we seek for physically reasonable collapse scenarios in which the spacetime singularity that occurs in general relativity (GR) is replaced by a non-singular bounce. We therefore find that depending on model parameters, the collapse process which starts from regular initial data, will halt at a minimum value for the scale function and then turns into an expansion at a finite time. We further find that there exists a minimum value for the initial radius of collapsing object so that for radii smaller than this minimum radius, formation of apparent horizon can be avoided and hence the bounce can be visible to the observers within the Universe. We also compare our results to quantum corrected collapse scenarios and find that the mutual interaction between matter and geometry can play the role of quantum corrections to energy density.