Smooth extremal horizons are the exception, not the rule

TL;DR

Most charged, rotating black holes in five-dimensional Einstein-Maxwell theory have singular extremal horizons, with smooth horizons being rare exceptions, especially outside special cases like supergravity.

Contribution

This paper demonstrates that generic extremal black holes in five-dimensional Einstein-Maxwell and Einstein-Maxwell-Chern-Simons theories have singular horizons, highlighting the rarity of smooth extremal horizons.

Findings

Only zero charge or zero angular momentum solutions have smooth extremal horizons.

Most extremal black holes in these theories have singular horizons.

Smooth extremal horizons are exceptions, not the norm.

Abstract

We show that the general charged, rotating black hole in five-dimensional Einstein-Maxwell theory has a singular extremal limit. Only the known analytic solutions with exactly zero charge or zero angular momenta have smooth extremal horizons. We also consider general black holes in five-dimensional Einstein-Maxwell-Chern-Simons theory, and show that they also have singular extremal limits except for one special value of the coefficient of the Chern-Simons term (the one fixed by supergravity). Combining this with earlier results showing that extremal black holes have singular horizons in four-dimensional general relativity with small higher derivative corrections, and in anti-de Sitter space with perturbed boundary conditions, one sees that smooth extremal horizons are indeed the exception and not the rule.