Spherical vacuum and scalar collapse for the Starobinsky R^2 model

TL;DR

This study simulates spherical vacuum and scalar collapse in the Starobinsky R^2 model, revealing that strong fields lead to black hole formation with singularities, and semiclassical effects do not generally prevent singularities in f(R) gravity.

Contribution

It demonstrates that in the Starobinsky R^2 model, collapse can produce singularities despite quantum effects, highlighting the universality of singularity formation in f(R) gravity.

Findings

Black holes form with central singularities when fields are strong.

Gravity dominates potential near singularity, pushing Ricci scalar to infinity.

Semiclassical effects do not generally prevent singularities in f(R) gravity.

Abstract

Spherical vacuum and scalar collapse for the Starobinsky R^2 model is simulated. Obtained by considering the quantum-gravitational effects, this model would admit some cases of singularity-free cosmological spacetimes. It is found, however, that in vacuum and scalar collapse, when f' or the physical scalar field is strong enough, a black hole including a central singularity can be formed. In addition, near the central singularity, gravity dominates the repulsion from the potential, so that in some circumstances the Ricci scalar is pushed to infinity by gravity. Therefore, the semiclassical effects as included here do not avoid the singularity problem in general relativity. A strong physical scalar field can prevent the Ricci scalar from growing to infinity. Vacuum collapse for the RlnR model is explored, and it is observed that for this model the Ricci scalar can also go to infinity as the central singularity is approached. Therefore, this feature seems universal in vacuum and scalar collapse in f(R) gravity.