Reduction Arguments for Geometric Inequalities Associated With Asymptotically Hyperboloidal Slices

TL;DR

This paper demonstrates how to reduce geometric inequalities involving mass, charge, and angular momentum in asymptotically hyperboloidal slices to known cases in asymptotically flat settings, under certain elliptic equation solutions.

Contribution

It introduces a reduction method for geometric inequalities in asymptotically hyperboloidal slices based on solving specific elliptic equations, extending known flat case results.

Findings

Reduction of hyperboloidal inequalities to flat case

Conditions for elliptic system solutions

Extension of geometric inequality applicability

Abstract

We consider several geometric inequalities in general relativity involving mass, area, charge, and angular momentum for asymptotically hyperboloidal initial data. We show how to reduce each one to the known maximal (or time symmetric) case in the asymptotically flat setting, whenever a geometrically motivated system of elliptic equations admits a solution.