The role of dimension and electric charge on a collapsing geometry in Einstein–Gauss–Bonnet gravity

Abstract

The analysis of the continual gravitational contraction of a spherically symmetric shell of charged radiation is extended to higher dimensions in Einstein–Gauss–Bonnet gravity. The spacetime metric, which is of Boulware–Deser type, is real only up to a maximumelectric charge and thus collapse terminates with the formation of a branch singularity. This branch singularity divides the higher dimensional spacetime into two regions, a real and physical one, and a complex region. This is not the case in neutral Einstein–Gauss–Bonnetgravityaswellasgeneralrelativity. The charged gravitational collapse process is also similar for all dimensions N ≥ 5 unlike in the neutral scenario where there is a marked difference between the N = 5 and N > 5 cases. In the case where N = 5uncharged collapse ceases with the formation of a weaker, conical singularity which remains naked for a time depending on the Gauss–Bonnet invariant, beforesuccumbingtoaneventhorizon.Thesimilarityofchargedcollapseforallhigher dimensionsisauniquefeatureinthetheory.Thesufficientconditionsfortheformation of anakedsingularity are studied for the higher dimensional charged Boulware–Deser spacetime. For particular choices of the mass and charge functions, naked branch singularities are guaranteed and indeed inevitable in higher dimensional Einstein Gauss–Bonnet gravity. The strength of the naked branch singularities is also tested andit is found that these singularities become stronger with increasing dimension, and no extension of spacetime through them is possible.