The Positive Mass Theorem for Multiple Rotating Charged Black Holes

TL;DR

This paper extends the positive mass theorem to multiple rotating charged black holes, providing a lower bound on ADM mass based on angular momenta and charges, generalizing previous inequalities.

Contribution

It generalizes the mass-angular momentum-charge inequality to multiple black holes and weakens the assumptions needed for the proof.

Findings

Established a lower bound for ADM mass in multi-black hole configurations.

Generalized previous inequalities to axisymmetric initial data with multiple black holes.

Proved a rigidity statement under weaker hypotheses.

Abstract

In this paper a lower bound for the ADM mass is given in terms of the angular momenta and charges of black holes present in axisymmetric initial data sets for the Einstein-Maxwell equations. This generalizes the mass-angular momentum-charge inequality obtained by Chrusciel and Costa to the case of multiple black holes. We also weaken the hypotheses used in the proof of this result for single black holes, and establish the associated rigidity statement.