Super-Extremal Spinning Black Holes via Accretion

TL;DR

This paper demonstrates that black holes can temporarily exceed the classical extremality limit through accretion of negative energy density matter, using a new numerical evolution method within the isolated horizon framework.

Contribution

It introduces a novel matter-without-matter numerical method and applies it to show super-extremal black holes in dynamical scenarios.

Findings

Black holes can temporarily violate the extremality inequality.

A new numerical method for evolving matter without explicit matter fields.

Confirmation that extremality bounds can be exceeded in dynamical processes.

Abstract

A Kerr black hole with mass $M$ and angular momentum $J$ satisfies the extremality inequality $|J| \le M^2$. In the presence of matter and/or gravitational radiation, this bound needs to be reformulated in terms of local measurements of the mass and the angular momentum directly associated with the black hole. The isolated and dynamical horizon framework provides such quasi-local characterization of black hole mass and angular momentum. With this framework, it is possible in axisymmetry to reformulate the extremality limit as $|J| \le 2\,M_H^2$, with $M_H$ the irreducible mass of the black hole computed from its apparent horizon area and $J$ obtained using approximate rotational Killing vectors on the apparent horizon. The $|J| \le 2\,M_H^2$ condition is also equivalent to requiring a non-negative black hole surface gravity. We present numerical experiments of an accreting black hole that temporarily violates this extremality inequality. The initial configuration consists of a single, rotating black hole surrounded by a thick, shell cloud of negative energy density. For these numerical experiments, we introduce a new matter-without-matter evolution method.