Penrose-like inequality with angular momentum for minimal surfaces

TL;DR

This paper proves a strengthened Penrose inequality incorporating angular momentum for minimal surfaces in axially symmetric, asymptotically flat spacetimes, linking mass, surface area, and angular momentum.

Contribution

It establishes a new inequality relating ADM mass, minimal surface area, and angular momentum using inverse mean curvature flow techniques.

Findings

Derived a lower bound for ADM mass involving angular momentum.

Extended Penrose inequality to include angular momentum for minimal surfaces.

Utilized Geroch energy monotonicity along inverse mean curvature flow.

Abstract

In axially symmetric spacetimes the Penrose inequality can be strengthened to include angular momentum. We prove a version of this inequality for minimal surfaces, more precisely, a lower bound for the ADM mass in terms of the area of a minimal surface, the angular momentum and a particular measure of the surface size. We consider axially symmetric and asymptotically flat initial data, and use the monotonicity of the Geroch quasi-local energy on 2-surfaces along the inverse mean curvature flow.