Lower Bounds for the Area of Black Holes in Terms of Mass, Charge, and Angular Momentum

TL;DR

This paper proves a lower bound for the area of a single black hole based on mass, charge, and angular momentum within Einstein-Maxwell theory, with conditions for equality and extensions to multiple black holes.

Contribution

It establishes the lower bound for black hole area in axisymmetric maximal initial data, extending Penrose's inequality and analyzing special cases and multiple black hole scenarios.

Findings

Lower bound for black hole area in Einstein-Maxwell theory established.

Equality holds only for extreme Kerr-Newman black holes.

Refinements provided for cases with zero charge or angular momentum.

Abstract

The most general formulation of Penrose's inequality yields a lower bound for ADM mass in terms of the area, charge, and angular momentum of black holes. This inequality is in turn equivalent to an upper and lower bound for the area in terms of the remaining quantities. In this note, we establish the lower bound for a single black hole in the setting of axisymmetric maximal initial data sets for the Einstein-Maxwell equations, when the non-electromagnetic matter fields are not charged and satisfy the dominant energy condition. It is shown that the inequality is saturated if and only if the initial data arise from the extreme Kerr-Newman spacetime. Further refinements are given when either charge or angular momentum vanish. Lastly, we discuss the validity of the lower bound in the presence of multiple black holes.