A lower bound for the mass of axisymmetric connected black hole data sets

TL;DR

This paper extends the positivity of mass proof for axisymmetric black hole data to include black hole boundaries, establishing a lower bound based on the Schwarzschild metric.

Contribution

It generalizes the Brill-type proof to initial data sets with black hole boundaries, providing a new lower bound for the mass of such configurations.

Findings

Established a positive lower bound for black hole data mass

Extended positivity proof to include black hole boundaries

Connected mass bounds to Schwarzschild reference metric

Abstract

We present a generalisation of the Brill-type proof of positivity of mass for axisymmetric initial data to initial data sets with black hole boundaries. The argument leads to a strictly positive lower bound for the mass of simply connected, connected axisymmetric black hole data sets in terms of the mass of a reference Schwarzschild metric.