'Cusp' solutions in Gauss-Bonnet gravity

TL;DR

This paper explores the existence of 'cusp' singularities in Einstein-dilaton-Gauss-Bonnet gravity, revealing special types of mild singularities that may be smoothed by quantum corrections, and analyzes their structure and implications.

Contribution

It introduces and characterizes 'cusp' solutions in Gauss-Bonnet gravity, a novel class of singularities with specific power-law behaviors.

Findings

Identification of 'cusp' singularities with 1/2 and 1/3 powers.

Space can be divided into cusps separated by classically impenetrable borders.

Solutions include configurations with flat asymptotics.

Abstract

Einstein-dilaton-Gauss-Bonnet gravity is investigated on existence of solutions with mild singularities, not shielded by the event horizons. These still may have sense since presumably such singularities will be smoothed by corrections to Einstein theory from quantum gravity/string theory. We show that gravity with the first-order correction, the Gauss--Bonnet term, gives rise to special types of singularities, which we call 'cusps', with 1/2-th and 1/3-th powers in series expansion. The full space then can be split onto several cusps with classically impenetrable borders, and/or flat asymptotic.