Bekenstein Bounds, Penrose Inequalities, and Black Hole Formation

TL;DR

This paper derives geometric inequalities related to energy, size, angular momentum, and charge, supporting Bekenstein's entropy bounds and establishing new criteria for black hole formation.

Contribution

It proves versions of Bekenstein's bound for axisymmetric bodies and a Penrose-like inequality involving energy, horizon area, angular momentum, and charge.

Findings

Validated Bekenstein's entropy bounds for specific bodies.

Established a Penrose-like inequality with energy bounds.

Proposed new criteria for black hole formation based on angular momentum and charge.

Abstract

A universal geometric inequality for bodies relating energy, size, angular momentum, and charge is naturally implied by Bekenstein's entropy bounds. We establish versions of this inequality for axisymmetric bodies satisfying appropriate energy conditions, thus lending credence to the most general form of Bekenstein's bound. Similar techniques are then used to prove a Penrose-like inequality in which the ADM energy is bounded from below in terms of horizon area, angular momentum, and charge. Lastly, new criteria for the formation of black holes is presented involving concentration of angular momentum, charge, and nonelectromagnetic matter energy.