Uniqueness Theorem for Black Hole Space-Times with Multiple Disconnected Horizons

TL;DR

This paper proves the uniqueness of certain five-dimensional black hole solutions with multiple disconnected horizons, incorporating local charges and fluxes, and introduces a systematic boundary condition framework based on rod structure analysis.

Contribution

It introduces a new uniqueness theorem for multi-horizon black holes in five-dimensional supergravity, including local charges and fluxes, and develops a systematic boundary condition method.

Findings

Proves uniqueness of multi-horizon black hole solutions.

Incorporates local charges and fluxes into the uniqueness framework.

Provides a systematic approach to boundary conditions based on rod structure.

Abstract

We show uniqueness of stationary and asymptotically flat black hole space-times with multiple disconnected horizons and with two rotational Killing vector fields in the context of five-dimensional minimal supergravity (Einstein-Maxwell-Chern-Simons gravity). The novelty in this work is the introduction in the uniqueness theorem of intrinsic local charges measured near each horizon as well as the measurement of local fluxes besides the asymptotic charges that characterize a particular solution. A systematic method of defining the boundary conditions on the fields that specify a black hole space-time is given based on the study of its rod structure (domain structure). Also, an analysis of known solutions with disconnected horizons is carried out as an example of an application of this theorem.