Superfluid Black Holes

Abstract

We present what we believe is the first example of a "λ-line" phase transition in black hole thermodynamics. This is a line of (continuous) second order phase transitions which in the case of liquid 4 He marks the onset of superfluidity. The phase transition occurs for a class of asymptotically AdS hairy black holes in Lovelock gravity where a real scalar field is conformally coupled to gravity. We discuss the origin of this phase transition and outline the circumstances under which it (or generalizations of it) could occur. The study of black hole thermodynamics provides valuable insight into quantum properties of the gravitational field. The thermodynamics of anti de Sitter black holes has been of great interest since the pioneering work of Hawking and Page which demonstrated the existence of a thermal radiation/large AdS black hole phase transition [1]. Furthermore, these spacetimes admit a gauge duality description via a dual thermal field theory.Recently there has been interest in treating the cosmological constant as a thermodynamic variable [2] which plays the role of pressure in the first law [3][4][5]. Within this context, the black hole mass takes on the interpretation of enthalpy and a number of connections with ordinary thermodynamics emerge. It was shown that the thermodynamic behaviour of a charged AdS black hole is analogous to the van der Waals liquid/gas system, with the role of the liquid/gas transition played by a small/large black hole phase transition [6]. Subsequent work has revealed examples of triple points [7], (multiple) reentrant phase transitions [8,9], isolated critical points [10, 11] and a host of other behaviour for black holes (see [12] and references therein for a review).Here we present the first example of a line of second order (continuous) black hole phase transitions which strongly resemble those which occur in condensed matter systems, e.g. the onset of superfluidity in liquid helium [13]. The phase transition occurs in a broad class of asymptotically AdS hairy black holes in Lovelock gravity. Lovelock gravity [14] is a geometric higher curvature theory of gravity and is the natural generalization of Einstein gravity to higher dimensions, giving rise to second order field equations for the metric. It provides an excellent testbed for examining the effects of higher curvature corrections which appear in, for example, the low energy effective action of string theory [15]. Recently, it has been shown [16] that a scalar field can be conformally coupled to the Lovelock terms and the resulting theory gives rise to analytic hairy black hole solutions [17] evading no-go results which had been reported previously [18]. These solutions have already been shown to possess interesting thermodynamic properties [19][20][21] (such as reentrant phase transitions), and are of inherent interest due to the role scalar hair plays in holography, e.g. in descriptions of holographic superconductors and superfluids [22,23].The model we consider consists of Lovelock gravity, a Maxwell field, and a ...

Generalized quasitopological gravity

“…Second, it should be possible to study black hole solutions which are asymptotic to AdS and study their extended thermodynamics [40]. Coupling the theory to Maxwell or scalar fields [41] could lead to further examples of new, novel phase transitions such as the recently discovered superfluid-like transition [42]. It should also be possible to cast the theory in terms of horizon thermodynamics [43], at least for a certain class of matter actions, e.g.…”

Lovelock black holes surrounded by quintessence

“…In this analysis the case of no quintessence ω = 0 reduces to the Boulware and Deser [27][28][29] Gauss-Bonnet black hole solution, and for quintessence parameter ω = 1/2 with an appropriate choice of the integration constant it is mathematically similar to the charged Gauss-Bonnet black hole case due to Wiltshire [30]. The spherically symmetric vacuum solutions to Lovelock gravity have been found independently in [39,43]; also, recent work includes a class of Lovelock black holes with conformal scalar hair [40][41][42]. It is the purpose of this paper to model the possible effect of surrounding quintessence matter on the spherically symmetric black hole solution in Lovelock gravity.…”

“…For the limit D = 4 it becomes a standard area law. The phase transition occurs in a asymptotically AdS hairy Lovelock black holes [41]. Next we discuss the stability of black holes by computing heat capacity and the effect of surrounding quintessence matter.…”

“…The Lovelock black holes obeys extended first law and Smarr formula provided variations of the Lovelock couplings [49] and shall not be considered here. Since a black hole behaves as a thermodynamic system, the associated quantities should obey the first law which due to background quintessence modifies [14]: (42) and for constant q, it is the same as dM = T dS. Hence the entropy is given by…”

Black holes in quasi-topological gravity and conformal couplings

“…In particular, this implies that black holes with arbitrarily low temperature exist in AdS 5 . The theory also allows for the existence of phase transitions [24,34,35] involving hairy black holes. As mentioned in the introduction, this provides an interesting setup to study AdS/CFT.…”