Abstract
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 Martínez-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-Nordström-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-Nordström-AdS black hole undergoes a second order phase transition to the hairy black hole spontaneously acquiring scalar hair.
Highlights
JHEP09(2012)008 additional non-trivial phases of bald black holes
Static, charged black holes in the presence of a negative cosmological constant and with a planar horizon are found in four dimensions
We show that there is a critical temperature at which the axionic Reissner-Nordstrom-AdS black hole undergoes a second order phase transition to the hairy black hole spontaneously acquiring scalar hair
Summary
Aφ αφ i=1 where G is Newton’s constant. The non-trivial coupling of the Einstein and scalar sectors, given by φ2. 1, 2), originating from two Kalb-Ramond potentials B(i) such that H(i) = dB(i) Note that they are non-minimally coupled to the scalar field φ. An important property of the field equations stemming from the conformal coupling is the following: taking the trace of the metric equations (2.5), and replacing it in the equation of motion for the scalar field (2.6) gives, φ. This is the equation of motion which emanates from the theory (2.1) in the absence of these axionic fields. We can try to find a solution related to a hairy solution of the non-axionic theory
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