Positive mass theorems for asymptotically hyperbolic Riemannian manifolds with boundary

TL;DR

This paper establishes positive mass theorems for certain hyperbolic Riemannian manifolds with boundaries resembling black holes, extending the understanding of mass in these geometric contexts.

Contribution

It introduces new positive mass theorems applicable to asymptotically hyperbolic manifolds with boundary, including black-hole-type boundaries.

Findings

Positive mass theorems proven for asymptotically hyperbolic manifolds

Extension to locally hyperbolic cases with boundaries

Implications for geometric analysis of black-hole-type boundaries

Abstract

We prove positive mass theorems for asymptotically hyperbolic and asymptotically locally hyperbolic Riemannian manifolds with black-hole-type boundaries.