New type of phase transition in gravitational theories

Abstract

We set forth a new type of phase transition that might take place in gravitational theories whenever higher-curvature corrections are considered. It can be regarded as a sophisticated version of the Hawking-Page transition, mediated by the nucleation of a bubble in anti-de Sitter (AdS) space. The bubble hosts a black hole in its interior, and separates two spacetime regions with different effective cosmological constants. We compute the free energy of this configuration and compare it with that of thermal AdS. The result suggests that a phase transition actually occurs above certain critical temperature, ultimately changing the value of the cosmological constant. We discuss the consistency of the thermodynamic picture and its possible relevance in the context of AdS/CFT.

On AdS to dS transitions in higher-curvature gravity

“…This entails a quite interesting scenario in which thermal AdS can decay into a black hole dS geometry. At least two novel features occur, in comparison to the AdS to AdS phase transitions studied earlier in [26,27]. The thermalon does not exist above a threshold temperature T that is a function of λ.…”

“…This triggered the discussion about a suitable holographic interpretation of these gravitational phase transitions. Even though it is still unclear to us, we pointed out in [26,27] that the whole process resembles that of quantum quenches in strongly coupled field theory (see, for instance, [28]). …”

“…To that end we will consider the simplest non-trivial gravity possessing all the necessary ingredients, namely, the Lanczos-Gauss-Bonnet (LGB) theory with a positive bare cosmological constant. 1 The case involving a bare negative cosmological constant has been already analyzed in [26], where no AdS to dS transition was found: bubble configurations exist but they are all nonstatic; see [27]. In the canonical ensemble, whether or not the transition takes place can be decided by evaluating and comparing the Euclidean action among the various smooth classical configurations satisfying the appropriate boundary conditions.…”

“…Notice that the bare cosmological constant is positive, Λ = (d − 1)(d − 2)/2L 2 > 0, and we have a single dimensionless coupling, λ, while dimension-full parameters are the Newton constant and the characteristic length, L. We take λ > 0 which is the natural sign inherited, for instance, from string theory embeddings of (2.1). The additional boundary term, I ∂ , is necessary in order to have a well defined variational principle (see [26] for further details). It plays a fundamental role in the phase transitions discussed in this letter, as we will explain below.…”

“…We showed in [26] that phase transitions among different vacua are possible and indeed generic [27]. In analogy to the Hawking-Page process, above a critical temperature T c some of the Lovelock higher-curvature vacua shall decay by nucleating a bubble that hosts a black hole.…”