Multicritical phase transitions in Lovelock AdS black holes

Maxwell construction and multi-criticality in uncharged generalized quasi-topological black holes

“…A multi-critical point may not occur even if infinitely many couplings are turned on. This implies that the problem is not as simple as it is in Lovelock gravity where k = 1 and each density (2.7) similarly contributes to the thermodynamics [20]. We leave this question for future investigation.…”

“…A recent interesting discovery in black hole chemistry was that of multi-critical points. These were first seen in Einstein gravity coupled to non-linear electrodynamics [18], but were shortly afterward found to be present in multiply rotating Kerr-AdS black holes [19], and in Lovelock gravity [20]. In the latter case multi-critical behaviour can even occur for asymptotically flat black holes [21].…”

“…Previous methods for finding multiple phases and N-tuple critical points exploited the fact that, regarding temperature as a function of horizon radius, each extremum of T(r + ) corresponds to a cusp in the Gibbs free energy [18,20]. Hence N distinct phases require 2N − 2 distinct extrema.…”

“…In this paper, we demonstrate an alternative method for finding multi-critical points in black hole phase transitions. Previous methods exploited the fact that each extremum of the temperature (regarded as a function of horizon radius) corresponded to a cusp in the Gibbs free energy [18,20]. 2N − 2 distinct extrema were thus required to obtain N distinct phases, each with its own swallowtail in the Gibbs free energy diagram.…”

“…Previous studies have been carried out in limited contexts, with only a few low order couplings in dimensions not much larger than four [39][40][41][42][43][44]. Inspired by the multi-critical behaviour found for a broad range of black holes in different contexts [18][19][20][21], our interests lie both in demonstrating our method and in understanding multi-criticality in GQT gravity.…”