Inside Anisotropic Black Hole with Vector Hair

TL;DR

This paper investigates the internal structure of anisotropic charged black holes with vector hair, revealing the absence of an inner horizon, oscillatory behaviors, and a complex Kasner epoch alternation near the singularity.

Contribution

It provides a general proof of no inner horizon in anisotropic black holes with vector hair and explores their detailed internal dynamics including oscillations and Kasner regimes.

Findings

No inner horizon exists in these black holes.

Vector hair induces oscillations in condensate and anisotropy.

The approach to the singularity involves endless Kasner epoch alternations.

Abstract

We study the internal structure of anisotropic black holes with charged vector hairs. Taking advantage of the scaling symmetries of the system, some radially conserved charges are found via the extension of the Noether theorem. Then, a general proof of no inner horizon of these black holes is presented and the geometry ends at a spacelike singularity. Before reaching the singularity, we find several intermediate regimes both analytically and numerically. In addition to the Einstein-Rosen bridge contracting towards the singularity, the instability triggered by the vector hair results in the oscillations of vector condensate and the anisotropy of spatial geometry. Moreover, the latter oscillates at twice the frequency of the condensate. Then, the geometry enters into Kasner epochs with spatial anisotropy. Due to the effects from vector condensate and U(1) gauge potential, there is generically a never-ending alternation of Kasner epochs towards the singularity. The character of evolution on approaching the singularity is found to be described by the Kasner epoch alternation with flipping of powers of the Belinskii-Khalatnikov-Lifshitz type.