Super-Extremal Spinning Black Holes via Accretion

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 $|J|\le 2M_H^2$, 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 $|J|\le 2M_H^2$ 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.

11 pages, 10 figures

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• Geometrical inequalities bounding angular momentum and charges in General Relativity
• Template Mode Hierarchies for Binary Black Hole Mergers
• Decoding the final state in binary black hole mergers
• Bowen-York Type Initial Data for Binaries with Neutron Stars
• Dynamics of scalar hair with self-interactions around a Schwarzchild black hole