LAUSR

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 position corresponding to the event horizon in the original Schwarzschild space-time can develop a curvature singularity, which we call thunderbolt singularity. We also investigate a new class of theories in which all components of the Riemann tensor are bounded. We find that the thunderbolt singularity 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.