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

Understand

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.