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

TL;DR

The paper develops a perturbative framework for Einstein-Maxwell theory to study extremal rotating black holes with all equal angular momenta in odd dimensions. At next-to-leading order, the authors obtain analytic charge-induced corrections to thermodynamics around the extremal Myers–Perry solution; at NNLO, irrational near-horizon exponents emerge in D=7, and through careful numerical matching to asymptotically flat spacetime they demonstrate that these geometries describe genuine black holes with no-hair beyond mass, angular momentum, and charge. The work highlights subtle horizon structures in higher-dimensional gravity and confirms that global (asymptotic) requirements can fix horizon-scale irregularities, preserving physical black hole behavior in Einstein-Maxwell theory. The combination of analytic NLO results and targeted NNLO numerics in D=7 provides a concrete testbed for understanding extremal charged rotations in higher dimensions and the role of irrational near-horizon exponents.

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.

Figures (1)

• Figure 1: Here are the four $\delta_{q^4}$ metric functions, with the integration constants chosen so that the functions decay at large $r$.