A Uniqueness theorem for 5-dimensional Einstein-Maxwell black holes

TL;DR

This work extends a prior 5D vacuum uniqueness result to Einstein-Maxwell black holes under symmetry and regularity assumptions, showing that the exterior is determined by an interval structure augmented by magnetic charges, mass, and a single nonzero angular momentum (with $Q_{\rm E}=0$ and $J_1=0$). The authors employ a 2D reduced sigma-model on the orbit space with target space $\mathbb{H}$, comparing two solutions via geodesic-distance functionals $\sigma_i$ and a maximum principle to prove isometry when interval data, $m$, $J_2$, and $Q_{\rm M}[C_l]$ agree. Horizon topology is restricted to ${\cal H}\cong S^3$ or ${\cal H}\cong S^1\times S^2$ under the assumptions, and the simplest interval structure yields the Myers–Perry solution with vanishing Maxwell field. Overall, the paper provides a concrete, albeit restricted, uniqueness theorem for 5D Einstein-Maxwell black holes and clarifies how interval data encode global geometric and gauge information in higher dimensions.

Abstract

In a previous paper arXiv:0707.2775 [gr-qc] we showed that stationary asymptotically flat vacuum black hole solutions in 5 dimensions with two commuting axial Killing fields can be completely characterized by their mass, angular momentum, a set of real moduli, and a set of winding numbers. In this paper we generalize our analysis to include Maxwell fields.