Gravitational Collapse and Singularity Removal in Rastall Theory

Ehsan Dorrani,Hooman Moradpour

doi:10.1155/2021/6638827

Abstract

In the present work, we study spherically symmetric gravitational collapse of a homogeneous fluid in the framework of Rastall gravity. Considering a nonlinear equation of state (EoS) for the fluid profiles, we search for a class of nonsingular collapse solutions and the possibility of singularity removal. We find that depending on the model parameters, the collapse scenario halts at a minimum value of the scale factor at which a bounce occurs. The collapse process then enters an expanding phase in the postbounce regime, and consequently the formation of a spacetime singularity is prevented. We also find that, in comparison to the singular case where the apparent horizon forms to cover the singularity, the formation of apparent horizon can be delayed allowing thus the bounce to be causally connected to the external universe. The nonsingular solutions we obtain satisfy the weak energy condition (WEC) which is crucial for physical validity of the model.

Highlights

The process of gravitational collapse of a massive object and its final outcome is one of the central questions in relativistic astrophysics and gravitation theory
In the framework of general relativity (GR), the Hawking and Penrose singularity theorems predict that under physically reasonable conditions, a continual collapse process leads to the formation of a spacetime singularity, that is, a spacetime event where densities and spacetime curvatures grow limitlessly and diverge [1]
Much attempts have been directed towards exploring different aspects of the gravitational collapse process and the studies along this line of research indicate that the spacetime singularity that forms as the collapse end product could be dressed by a spacetime event horizon or visible by the observers in the universe [2]

Summary

Introduction

The process of gravitational collapse of a massive object and its final outcome is one of the central questions in relativistic astrophysics and gravitation theory. During the past decades, many examples of naked singularity formation as possible counterexamples to the cosmic censorship conjecture have been reported in the literature, among which we can quote gravitational collapse of dust, perfect fluids, and radiation shells [8, 9] Such a study has been extended to gravitational collapse in the presence of a cosmological constant term [10], higher dimensional collapse models [11,12,13,14], higher-order gravity theories [15], scalar field collapse [16,17,18,19,20], and self-similar collapse [21,22,23] (see [2] for a recent review).

Field Equations of Rastall Gravity

Solutions to the Field Equations

Concluding Remarks