Black hole hair in higher dimensions

TL;DR

This paper investigates matter properties around static, spherically symmetric black holes in higher-dimensional spacetimes, revealing unique conditions and limits that depend on the spacetime dimension, with D=4 being particularly special.

Contribution

It identifies specific equations of state for matter in equilibrium with black holes in D dimensions and uncovers dimension-dependent limits, highlighting the special role of four-dimensional spacetime.

Findings

Black hole matter equilibrium requires a specific equation of state independent of D

Black holes in D=2+2kn are surrounded by cosmic strings

Linear dilaton fields can only surround black holes in 4D

Abstract

We study the property of matter in equilibrium with a static, spherically symmetric black hole in D-dimensional spacetime. It requires this kind of matter has an equation of state (\omega\equiv p_r/\rho=-1/(1+2kn), k,n\in \mathbb{N}), which seems to be independent of D. However, when we associate this with specific models, some interesting limits on space could be found: (i)(D=2+2kn) while the black hole is surrounded by cosmic strings; (ii)the black hole can be surrounded by linear dilaton field only in 4-dimensional spacetime. In both cases, D=4 is special.