Squashed black holes at large $D$

TL;DR

This paper develops an analytical large D effective theory to construct static, squashed black hole solutions in Kaluza-Klein spacetimes, revealing new insights into their geometry and extremal limits.

Contribution

It introduces a novel large D approach to solve for non-extremal and extremal squashed black holes with compactified dimensions, including their asymptotic and near-horizon geometries.

Findings

Successfully constructed static solutions with/without charge

Derived a first-order flow equation for the background

Confirmed extremal limit matches known results

Abstract

Using the large $D$ effective theory approach, we construct a static solution of non-extremal and squashed black holes with/without an electric charge, which describes a spherical black hole in a Kaluza-Klein spacetime with a compactified dimension. The asymptotic background with a compactified dimension and near-horizon geometry are analytically solved by the $1/D$ expansion. Particularly, our work demonstrates that the large $D$ limit can be applied to solve the non-trivial background with a compactified direction, which leads to a first-order flow equation. Moreover, we show that the extremal limit consistently reproduces the known extremal result.