Hairy Black Holes in a Box

TL;DR

This paper systematically studies charged black holes and scalar fields in a finite box, revealing phase structures similar to holographic superconductors and highlighting subtleties in defining quasi-local charges.

Contribution

It extends previous flat space studies by including scalar fields, demonstrating stable hairy black holes and boson stars, and draws parallels with holographic superconductor phases.

Findings

Existence of stable hairy black holes in a box.

Presence of boson star solutions.

Phase diagram resembles holographic superconductor models.

Abstract

We do a systematic study of the phases of gravity coupled to an electromagnetic field and charged scalar in flat space, with box boundary conditions. The scalar-less box has previously been investigated by Braden, Brown, Whiting and York (and others) before AdS/CFT and we elaborate and extend their results in a language more familiar from holography. The phase diagram of the system is analogous to that of AdS black holes, but we emphasize the differences and explain their origin. Once the scalar is added, we show that the system admits both boson stars as well as hairy black holes as solutions, providing yet another way to evade flat space no-hair theorems. Furthermore both these solutions can exist as stable phases in regions of the phase diagram. The final picture of the phases that emerges is strikingly similar to that found recently for holographic superconductors in global AdS, arXiv: 1602.07211. Our construction lays bare certain previously unnoticed subtleties associated to the definition quasi-local charges for gravitating scalar fields in finite regions.