Horizon/Matter Systems near the Extreme State

TL;DR

This paper investigates the properties of static and rotating black holes in the extreme limit where surface gravity vanishes but local temperature remains nonzero, revealing the structure of the limiting metric and conditions for thermal equilibrium.

Contribution

It extends the understanding of extreme black hole limits to both static and rotating cases, showing how the limiting metric depends on horizon-induced geometry and stress-energy tensor behavior.

Findings

Limiting metric determined by horizon geometry and a coordinate function.

In the extreme limit, static and rotating horizons are in thermal equilibrium.

The analysis applies to merging black hole and cosmological horizons.

Abstract

It is shown that in the extreme limit with a zero surface gravity but nonzero local temperature the limiting metric of a generic static black hole is determined by a metric induced on a horizon and one function of two coordinates, stress-energy tensor of a source picking up its values from a horizon. The limiting procedure is extended to rotating black holes. If the extreme limit is due to merging a black hole horizon and cosmological one both horizons are always in thermal equilibrium in this limit. This is proved for a generic case of static or axially-symmetrical rotating spacetimes.