Hairy black holes in AdS with Robin boundary conditions

Abstract

We study hairy black holes in Einstein-Maxwell-complex scalar theory in four-dimensional asymptotically global anti-de Sitter (AdS) spacetime when the Robin boundary conditions are imposed on the scalar field. This setup is dual to the double trace deformation of strongly interacting field theory on R × S2 by charged scalar operators. We identify the instability of the Reissner-Nordström-AdS (RNAdS) black holes under the Robin boundary conditions and construct backreacted geometries branching at the onset of the instability. Also considering associated horizonless geometries called boson stars, we obtain phase diagrams with fairly rich structure in the grand canonical ensemble depending on the boundary condition parameter or the deformation parameter, where phase transition occurs between thermal AdS, RNAdS, charged boson stars, and hairy black holes.

Convexity restoration from hairy black hole in Einstein-Maxwell-charged scalar system in AdS

“…In this paper, we have studied charged solitons and hairy black holes under the Dirichlet boundary condition at the AdS boundary. It is an interesting question to allow more general boundary conditions such as the Robin boundary condition to study the charged solitons and hairy black holes [16,40]. In the dual field theory perspective, it would correspond to double trace deformations [41,42].…”