Dynamical and Thermodynamical Aspects of Interacting Kerr Black Holes

TL;DR

This paper analyzes the physical and thermodynamical properties of a double Kerr black hole system, exploring how their interactions affect angular velocity, ergo-region merging, horizon geometry, and stability in different ensembles.

Contribution

It provides new insights into the dynamics, horizon geometry, and thermodynamical stability of interacting Kerr black holes, including the behavior of ergoregions and phase transitions.

Findings

Angular velocity decreases as black holes approach each other.

Ergo-regions merge at a right angle for co-rotating black holes.

Thermodynamically stable for fast-spinning black holes in the canonical ensemble.

Abstract

We consider the asymptotically flat double-Kerr solution for two equal mass black holes with either the same or opposite angular momentum and with a massless strut between them. For fixed angular momentum and mass, the angular velocity of two co-rotating Kerr black holes decreases as they approach one another, from the Kerr value at infinite separation to the value of a single Kerr black hole with twice the mass and the angular momentum at the horizons merging limit. We show that the ratio J/M^2 for extremal co-rotating Kerr black holes varies from unity at infinite separation to two at the merging limit. These results are interpreted in terms of rotational dragging and compared with the case of counter-rotating Kerr black holes. We then analyse the merging of ergo-regions. In the co-rotating case the merger point occurs at an angle of \pi/2, in agreement with recent general arguments. In the counter-rotating case the ergo-regions never merge. We study the horizon geometry for both cases as a function of the distance and provide embedding diagrams. Finally, we study the thermodynamical evolution of the co-rotating double Kerr system, showing that, in the canonical ensemble, it is thermodynamically stable for fast spinning black holes. As for single Kerr black holes the stable and unstable phases are separated by a second order phase transition. We show that for large fixed angular momentum two Kerr black holes reach a minimum distance, before horizon merging has occurred, where the thermodynamical approximation breaks down. We also consider the micro-canonical ensemble to study the maximal energy that can be extracted from the double Kerr system as a function of the separation between the black holes.