A Penrose-Like Inequality with Charge

TL;DR

This paper proves a Penrose-like inequality for Einstein-Maxwell initial data, relating ADM energy to horizon area and charge, extending previous results to non-time-symmetric cases.

Contribution

It establishes a new inequality for charged spacetimes that generalizes previous Penrose inequalities to non-time-symmetric initial data.

Findings

ADM energy is bounded below by a function of horizon area and charge

Derived a proportionality constant depending on a linear elliptic equation

Presented a corrected version of a previous Penrose-like inequality

Abstract

We establish a Penrose-like inequality for general (not necessarily time-symmetric) initial data sets of the Einstein-Maxwell 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 sum of the square root of the area of the outermost future (or past) apparent horizon and the square of the total charge. The proportionality constants depend on the solution to a linear elliptic equation which incorporates the charge. In addition, a corrected version of the Penrose-like inequality in [13] is presented.