Internal structure of hairy rotating black holes in three dimensions

TL;DR

This paper constructs and analyzes hairy rotating black hole solutions in three-dimensional Einstein gravity coupled to a scalar field, revealing their internal structure and evolution into Kasner universes under various boundary conditions.

Contribution

It introduces new hairy rotating black hole solutions in 3D gravity with scalar fields and studies their internal dynamics and evolution, including Kasner transitions.

Findings

No inner horizon for stationary black holes with real scalar sources.

Black holes with complex sources exhibit oscillations and Kasner inversions inside.

Metric fields show simple relations between horizon and Kasner epoch values.

Abstract

We construct hairy rotating black hole solutions in three dimensional Einstein gravity coupled to a complex scalar field. When we turn on a real and uniform source on the dual CFT, the black hole is stationary with two Killing vectors and we show that there is no inner horizon for the black hole and the system evolves smoothly into a Kasner universe. When we turn on a complex and periodic driving source on the dual CFT with a phase velocity equal to the angular velocity of the black hole, we have a time-dependent black hole with only one Killing vector. We show that inside the black hole, after a rapid collapse of the Einstein-Rosen bridge, oscillations of the scalar field follow. Then the system evolves into the Kasner epoch with possible Kasner inversion, which occurs in most of the parameter regimes. In both cases, one of the metric fields obeys a simple relation between its value at the horizon and in the Kasner epoch.