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

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.