Asymptotically Hyperbolic Einstein Constraint Equations with Apparent Horizon Boundary and the Penrose Inequality for Perturbations of Schwarzschild-AdS

TL;DR

This paper establishes the existence of asymptotically hyperbolic Einstein initial data with apparent horizon boundaries and verifies the Penrose inequality for specific perturbations of Schwarzschild-AdS black holes.

Contribution

It proves the existence of solutions to Einstein constraints with horizon boundaries and confirms the Penrose inequality for perturbed Schwarzschild-AdS data.

Findings

Existence of hyperbolic Einstein solutions with apparent horizons.

Verification of the Penrose inequality in perturbative Schwarzschild-AdS cases.

Application of the conformal method to boundary value problems.

Abstract

We prove the existence of asymptotically hyperbolic solutions to the vacuum Einstein constraint equations with a marginally outer trapped boundary of positive mean curvature, using the constant mean curvature conformal method. As an application of this result, we verify the Penrose inequality for certain perturbations of Schwarzschild Anti-de Sitter black hole initial data.