Evolutions from extremality

TL;DR

This paper studies how extremal black holes evolve under matter accretion, showing they typically become non-extremal and analyzing the properties of extremal dynamical horizons in various scenarios.

Contribution

It provides a general theory of extremal black hole evolution and explores specific cases involving null dust and scalar fields, highlighting horizon bifurcation and extremal dynamical horizons.

Findings

Extremal horizons bifurcate into non-extremal horizons under matter accretion.

Slow matter accretion can cause horizon growth to jump from zero to infinity.

Extremal dynamical horizons contain an inner isolated and an outer dynamical extremal horizon.

Abstract

We examine the evolution of extremal spherically symmetric black holes, developing both general theory as well as the specific cases of (charged) null dust and massless scalar field spacetimes. As matter accretes onto extremal marginally trapped tubes, they generically evolve to become non-extremal with the initial extremal horizon bifurcating into inner and outer non-extremal horizons. At the start of this process arbitrarily slow matter accretion can cause a geometrically invariant measure of horizon growth to jump from zero to infinity. We also consider dynamical horizons that are extremal throughout their evolution and see that such spacetimes contain two extremal black hole horizons: an inner isolated one and an outer dynamical one. We compare these extremal dynamical horizons with the dynamical extreme event horizon spacetimes of Murata, Reall and Tanahashi.