Extremality conditions for isolated and dynamical horizons

TL;DR

This paper extends extremality conditions from Kerr black holes to isolated and dynamical horizons, introducing a parameter to measure how close a horizon is to extremality, applicable in numerical simulations.

Contribution

It introduces generalized extremality conditions for isolated and dynamical horizons, not limited to stationary or symmetric cases, and proposes a calculable parameter for extremality in simulations.

Findings

Defined extremality restrictions for non-stationary horizons

Introduced a parameter e to quantify proximity to extremality

Discussed physical implications and potential applications

Abstract

A maximally rotating Kerr black hole is said to be extremal. In this paper we introduce the corresponding restrictions for isolated and dynamical horizons. These reduce to the standard notions for Kerr but in general do not require the horizon to be either stationary or rotationally symmetric. We consider physical implications and applications of these results. In particular we introduce a parameter e which characterizes how close a horizon is to extremality and should be calculable in numerical simulations.