A Penrose-Like Inequality for General Initial Data Sets

TL;DR

This paper proves a Penrose-like inequality for general initial data in Einstein's equations, relating ADM energy to the area of apparent horizons, extending previous results beyond time-symmetric cases.

Contribution

It introduces a new inequality for non-time-symmetric initial data satisfying the dominant energy condition, linking ADM energy to apparent horizon area.

Findings

Establishes a lower bound for ADM energy based on horizon area.

Extends Penrose inequality to more general initial data sets.

Provides a mathematical foundation for energy-horizon relations in general relativity.

Abstract

We establish a Penrose-Like Inequality for general (not necessarily time symmetric) initial data sets of the Einstein equations which satisfy the dominant energy condition. More precisely, it is shown that the ADM energy is bounded below by an expression which is proportional to the square root of the area of the outermost future (or past) apparent horizon.