Inequality between size and angular momentum for bodies

TL;DR

This paper presents a universal inequality linking the size and angular momentum of bodies, supported by physical arguments and proven for rotating, axially symmetric, constant density bodies within Einstein's framework.

Contribution

It introduces a new inequality relating size and angular momentum, with a rigorous proof for specific relativistic bodies, advancing understanding of physical bounds in general relativity.

Findings

Proves the inequality for rotating axially symmetric bodies

Supports the inequality with heuristic physical arguments

Discusses the physical relevance of the inequality

Abstract

A universal inequality that bounds the angular momentum of a body by the square of its size is presented and heuristic physical arguments are given to support it. We prove a version of this inequality, as consequence of Einstein equations, for the case of rotating axially symmetric, constant density, bodies. Finally, the physical relevance of this result is discussed.