The mass gap in five dimensional Einstein–Gauss–Bonnet black holes: a geometrical explanation

Abstract

It is well known that, unlike in higher dimensional general relativity (GR), we cannot have a black hole with an arbitrarily small mass in five dimensional Einstein–Gauss–Bonnet gravity. When we study the dynamical black hole formation via the radiation collapse in the radiating Boulware–Deser spacetime in five dimensions, the central zero mass singularity is weak, conical and naked, and the horizon forms only when a finite amount of matter, that depends on the coupling constant of the Gauss–Bonnet term, falls into the central singularity. To understand this phenomenon transparently and geometrically, we study the radiating Boulware–Deser spacetime in five dimensions using a 1+1+3 spacetime decomposition, for the first time. We find that the geometric and thermodynamic quantities can be expressed in terms of the gravitational mass and the Gauss–Bonnet (GB) parameter and separate each of them into their Gauss–Bonnet and matter parts. Drawing comparisons with five dimensional GR at every step, we explicitly show how the mass gap arises for a general mass function M(v) and what functions for M(v) make certain geometrical quantities well defined at the central singularity. We show in the case of self-similar radiation collapse in the modified theory, the central singularity is not a sink for timelike geodesics and is extendable. This clearly demonstrates how the GB invariant affects the nature of the final state of a continual collapse in this modified theory.