The Positive Mass Theorem with Angular Momentum and Charge for Manifolds with Boundary

TL;DR

This paper proves a lower bound on the mass of certain 3-manifolds with boundary, incorporating angular momentum and charge, without assuming simple connectivity or completeness, advancing understanding in mathematical relativity.

Contribution

It establishes a new mass lower bound for asymptotically flat manifolds with boundary, considering angular momentum and charge, without restrictive topological assumptions.

Findings

Mass lower bound incorporating angular momentum and charge

No need for simple connectivity or completeness assumptions

Supports the cosmic censorship conjecture in mathematical relativity

Abstract

Motivated by the cosmic censorship conjecture in mathematical relativity, we establish the precise mass lower bound for an asymptotically flat Riemannian 3-manifold with nonnegative scalar curvature and minimal surface boundary, in terms of angular momentum and charge. In particular this result does not require the restrictive assumptions of simple connectivity and completeness, which are undesirable from both a mathematical and physical perspective.