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

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.

10 pages, 6 figures. Major change

References in corpus (9)

• Future of the universe in modified gravitational theories: Approaching to the finite-time future singularity
• The future evolution and finite-time singularities in $F(R)$-gravity unifying the inflation and cosmic acceleration
• Non-singular exponential gravity: a simple theory for early- and late-time accelerated expansion
• A Singularity Problem with f(R) Dark Energy
• Collapsing spherical stars in f(R) gravity
• Classifying and avoiding singularities in the alternative gravity dark energy models
• Time-dependent matter instability and star singularity in $F(R)$ gravity
• Robust approach to f(R) gravity
• Note on Nariai and Tomita's and Starobinsky's cosmological solutions in the R^2 modified gravity

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• Gravitational collapse of massless scalar field in $f(R)$ gravity
• Rotating Killing horizons in generic $F(R)$ gravity theories
• Gravitational Collapse without Singularity Formation in Brans-Dicke Theory