On the fate of singularities and horizons in higher derivative gravity

TL;DR

This paper investigates static spherically symmetric solutions in high derivative gravity theories, finding most are nonsingular near the origin but cannot eliminate Schwarzschild singularities without additional horizons, leading to a potential replacement of horizons with smooth transitions.

Contribution

It analyzes solutions in gravity theories with up to 10 derivatives, revealing limitations in removing singularities and proposing a new horizon replacement mechanism.

Findings

Most solutions are nonsingular near the origin.

Schwarzschild singularity cannot be smoothed without extra horizons.

Proposes a rapid nonsingular transition replacing the horizon.

Abstract

We study static spherically symmetric solutions of high derivative gravity theories, with 4, 6, 8 and even 10 derivatives. Except for isolated points in the space of theories with more than 4 derivatives, only solutions that are nonsingular near the origin are found. But these solutions cannot smooth out the Schwarzschild singularity without the appearance of a second horizon. This conundrum, and the possibility of singularities at finite r, leads us to study numerical solutions of theories truncated at four derivatives. Rather than two horizons we are led to the suggestion that the original horizon is replaced by a rapid nonsingular transition from weak to strong gravity. We also consider this possibility for the de Sitter horizon.