Odd-dimensional Extremal Rotating Black Holes with All Equal Angular Momenta and Small Electric Charges

TL;DR

This paper constructs and analyzes small electric charge perturbations of extremal odd-dimensional rotating black holes with equal angular momenta, revealing new analytic solutions and singular horizon behaviors.

Contribution

It provides the first analytic charge corrections to thermodynamics of extremal rotating black holes in odd dimensions and demonstrates the existence of singular horizon geometries.

Findings

Exact solutions at next-to-leading order for small charge perturbations.

Charge corrections to thermodynamic quantities derived analytically.

Existence of singular horizon behavior confirmed through numerical integration.

Abstract

We consider Einstein-Maxwell gravity in diverse dimensions and construct the small charge perturbation to the extremal rotating black holes with all equal angular momenta in odd $D=2n+1$ dimensions. Exact solutions exist at the next-to-leading order (NLO), and they are analytic, allowing us to obtain the charge corrections to thermodynamic quantities at this order. Irrational exponents in the near-horizon power-series expansion emerge at the next-to-next-to-leading order (NNLO). We show, by numerical computation, that these horizon geometries can indeed be integrated out to asymptotic Minkowski spacetime, thereby proving the existence of the unusual singular horizon behavior of the extremal charged rotating black holes.