Analytical studies on 3D hairy rotating black hole interiors

TL;DR

This paper provides an analytical description of the complex interior structure of 3D hairy rotating black holes, revealing an infinite sequence of Kasner epochs leading to a curvature singularity.

Contribution

It introduces an explicit analytical model of the interior dynamics of 3D hairy rotating black holes, including Kasner epochs and transition mechanisms.

Findings

Interior exhibits an infinite sequence of Kasner epochs.

Late-time geometry develops into a curvature singularity.

Interior structure is more complex than 4D static black holes.

Abstract

We present an analytical study of the interior structure of hairy rotating black holes in three-dimensional Einstein gravity, minimally coupled to a complex scalar field with a super-exponential potential. The interior dynamics of these black holes are characterized by an infinite sequence of Kasner epochs, separated by inversion and transitions, each of which admits an analytical description. We derive an explicit analytical expression for this infinite sequence of epochs. At late interior times, the geometry evolves into a curvature singularity, despite the local resemblance of each Kasner epoch to a regular Milne universe on a circle. These results reveal an interior structure richer and more complex than that of its 4D static black hole counterparts.