Time-dependent matter instability and star singularity in $F(R)$ gravity

TL;DR

This paper studies the formation of curvature singularities during star collapse in $F(R)$ gravity and proposes modifications to eliminate these singularities, analyzing their formation timescales in different scenarios.

Contribution

It identifies the mechanism behind star collapse singularities in $F(R)$ gravity and demonstrates how adding specific terms can prevent these singularities.

Findings

Adding $R^eta$ terms can cure the singularity.

Singularity formation timescales differ between star collapse and cosmology.

In exponential gravity, singularity appears rapidly during star collapse.

Abstract

We investigate a curvature singularity appearing in the star collapse process in $F(R)$ gravity. In particular, we propose an understanding of the mechanism to produce the curvature singularity. Moreover, we explicitly demonstrate that $R^\alpha$ ($1 < \alpha \leq 2$) term addition could cure the curvature singularity and viable $F(R)$ gravity models could become free of such a singularity. Furthermore, we discuss the realization process of the curvature singularity and estimate the time scale of its appearance. For exponential gravity, it is shown that in case of the star collapse, the time scale is much shorter than the age of the universe, whereas in cosmological circumstances, it is as long as the cosmological time.