Transformations of Asymptotically AdS Hyperbolic Initial Data and Associated Geometric Inequalities

TL;DR

This paper develops transformations that convert asymptotically AdS hyperbolic initial data into asymptotically flat data, enabling the derivation of geometric inequalities relating mass, angular momentum, charge, and horizon area.

Contribution

It introduces a method to transfer geometric inequalities from asymptotically flat to asymptotically AdS hyperbolic settings using specific transformations.

Findings

Derived new geometric inequalities in AdS hyperbolic context.

Established conditions under which inequalities hold.

Connected inequalities to solutions of elliptic equations.

Abstract

We construct transformations which take asymptotically AdS hyperbolic initial data into asymptotically flat initial data, and which preserve relevant physical quantities. This is used to derive geometric inequalities in the asymptotically AdS hyperbolic setting from counterparts in the asymptotically flat realm, whenever a geometrically motivated system of elliptic equations admits a solution. The inequalities treated here relate mass, angular momentum, charge, and horizon area.