Spherical collapse for the Starobinsky R^2 model

Abstract

Spherical scalar collapse for the Starobinsky R^2 model is simulated to explore the black hole and singularity formation scenarios. This model was obtained by considering quantum-gravitational effects and would admit some cases of singularity-free cosmological spacetimes. It is found, however, that in gravitational collapse situations, when the matter field is strong enough, a black hole including a central singularity can be formed. The nature of this singularity is examined, and it is seen that near the central singularity gravity dominates the repulsion from the R^2 term, so that in some circumstances the Ricci scalar R is pushed to infinity by gravity. Therefore, the semi-classical effects as included here do not avoid the singularity problem in general relativity.