Singularities in Spherically Symmetric Solutions with Limited Curvature Invariants

TL;DR

This paper explores how limiting curvature invariants in spherically symmetric solutions impacts singularities, finding that some singularities persist while others can be avoided with new theories, but not all are removable.

Contribution

It introduces a new class of theories where all Riemann tensor components are bounded, analyzing their effectiveness in removing singularities in Schwarzschild-like solutions.

Findings

Limiting Gauss-Bonnet and Ricci scalar does not remove the singularity.

Bounded Riemann tensor components can avoid horizon curvature singularities.

Additional degrees of freedom still lead to other singularities.

Abstract

We investigate static, spherically symmetric solutions in gravitational theories which have limited curvature invariants, aiming to remove the singularity in the Schwarzschild space-time. We find that if we only limit the Gauss-Bonnet term and the Ricci scalar, then the singularity at the origin persists. Moreover we find that the event horizon can develop a curvature singularity. We also investigate a new class of theories in which all components of the Riemann tensor are bounded. We find that the divergence of the quadratic curvature invariants at the event horizon is avoidable in this theory. However, other kinds of singularities due to the dynamics of additional degrees of freedom cannot be removed, and the space-time remains singular.