Phases of global AdS black holes

Abstract

Abstract:We study the phases of gravity coupled to a charged scalar and gauge field in an asymptotically Anti-de Sitter spacetime (AdS 4 ) in the grand canonical ensemble. For the conformally coupled scalar, an intricate phase diagram is charted out between the four relevant solutions: global AdS, boson star, Reissner-Nordstrom black hole and the hairy black hole. The nature of the phase diagram undergoes qualitative changes as the charge of the scalar is changed, which we discuss. We also discuss the new features that arise in the extremal limit.

Hairy black holes in a box

“…This also introduces difficulty in defining quasi-local charges directly, as we will discuss. But the free energy is well-defined and computable and gives rise to a phase diagram that matches with our qualitative expectations from global AdS [12] as well as reduces to the hairless case when the scalar is turned off. We will conclude with some comments and possible future directions for work.…”

“…The phase diagram that we uncover bears striking resemblance to that of the EinsteinMaxwell-scalar system in global AdS studied in [12] (see also [13][14][15][16][17]). This is re-assuring because our expectation is that AdS should really be viewed as a box.…”

“…This is re-assuring because our expectation is that AdS should really be viewed as a box. We work with the specific case of the massless scalar for concreteness, and our comparison will be with the conformally coupled scalar studied in [12].…”

“…In the case of global AdS, as we look at larger values of µ along the Hawking-Page transition curve, the horizon continues to shrink, and intersects the T = 0 axis at µ = 1 (see eg., [12]). However, in the case of the RN black hole in the box, the black hole gets bigger and bigger as we go up in µ, and gets closer to extremality as the black hole becomes almost the size of the box itself, as can be seen from the following relation…”

“…Since the boundary metric of all the systems are rescaled to be of the same form as the boundary metric of empty box, the temperatures of all the systems can be consistently compared. Using the equations of motions, we can rewrite the action (for details of a similar calculation see appendix of [12])…”