Super-Extremal Spinning Black Holes via Accretion

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, the bound needs to be reformulated in terms of local measurements of $M$ and $J$ directly associated with the black hole. The isolated and dynamical horizons framework provides such natural quasi-local characterization of $M$ and $J$, making possible in axi-symmetry to reformulate the extremality limit as $J \le 2\,M^2$, with $M$ the irreducible mass computed from the apparent horizon area and $J$ obtained using approximate rotational Killing vectors on the apparent horizon. This 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.