Charged rotating black holes at large D

TL;DR

This paper uses the large D expansion method to derive effective equations for charged rotating black holes in higher dimensions, revealing their nonlinear dynamics and instabilities, including connections between ultraspinning and charge-related instabilities.

Contribution

It introduces a large D effective theory for charged rotating black holes and analyzes their stability, providing analytic formulas for quasinormal modes and linking different types of instabilities.

Findings

Charged rotating black holes exhibit instabilities.

Ultraspinning instability connects to charge-related instability.

Analytic quasinormal mode frequencies are derived.

Abstract

We study odd dimensional charged equally rotating black holes in the Einstein-Maxwell theory with/without a cosmological constant by using the large D expansion method, where D is a spacetime dimension. Solving the Einstein-Maxwell equations in the 1/D expansion we obtain the large D effective equations for charged equally rotating black holes. The effective equations describe the nonlinear dynamics of charged equally rotating black holes. Especially the perturbation analysis of the effective equations gives analytic formula for quasinormal mode frequencies, and we can show charged equally rotating black holes have instabilities. As one interesting feature of instabilities, we observe that the ultraspinning instability of neutral equally rotating black holes in de Sitter is connected with the instability of de Sitter Reissner-Nordstrom black hole in a rotation-charge plane of the solution parameter space. So these instabilities have same origin as dynamical properties of charged rotating black holes. We also give perturbation analysis by a small charge for even dimensional equally rotating black holes.