Conformally coupled scalar black holes admit a flat horizon due to axionic charge

TL;DR

This paper introduces new static, charged black hole solutions with flat horizons in four-dimensional anti-de Sitter space, stabilized by axionic charges, and explores their thermodynamics and phase transitions relevant to holographic superconductors.

Contribution

It presents the first planar black hole solutions with conformally coupled scalar hair supported by axionic charges, extending known curved horizon solutions to flat horizons.

Findings

Existence of two solution branches: undressed and hairy black holes.

Identification of a critical temperature for a second order phase transition.

Analysis of thermodynamic properties and phase structure of the solutions.

Abstract

Static, charged black holes in the presence of a negative cosmological constant and with a planar horizon are found in four dimensions. The solutions have scalar secondary hair. We claim that these constitute the planar version of the Martinez-Troncoso-Zanelli black holes, only known up to now for a curved event horizon in four dimensions. Their planar version is rendered possible due to the presence of two, equal and homogeneously distributed, axionic charges dressing the flat horizon. The solutions are presented in the conformal and minimal frame and their basic properties and thermodynamics analysed. Entertaining recent applications to holographic superconductors, we expose two branches of solutions: the undressed axionic Reissner-Nordstrom-AdS black hole, and the novel black hole carrying secondary hair. We show that there is a critical temperature at which the (bald) axionic Reissner-Nordstrom-AdS black hole undergoes a second order phase transition to the hairy black hole spontaneously acquiring scalar hair.