Size, angular momentum and mass for objects

TL;DR

This paper establishes a geometric inequality relating the ADM mass, angular momentum, and size of axially symmetric objects using inverse mean curvature flow, supported by numerical tests.

Contribution

It introduces a new inequality connecting mass, angular momentum, and size for axially symmetric objects, utilizing the Geroch quasi-local energy and inverse mean curvature flow.

Findings

Derived a geometric inequality involving ADM mass, angular momentum, and size.

Validated the inequality through numerical examples.

Demonstrated the robustness of the hypotheses and results.

Abstract

We obtain a geometrical inequality involving the ADM mass, the angular momentum and the size of an ordinary, axially symmetric object. We use the monotonicity of the Geroch quasi-local energy on 2-surfaces along the inverse mean curvature flow. We also compute numerical examples to test the robustness of our hypotheses and results