Thermodynamically stable phases of asymptotically flat Lovelock black holes

Abstract

We present the first examples of phase transitions in asymptotically flat black hole solutions. We analyze the thermodynamic properties of black holes in order N ‒ 3 Lovelock gravity, with zero cosmological constant. We find a new type of “reversed” swallowtail which can support stable temperature regions for an otherwise unstable neutral black hole, and demonstrate multiple such stable phases can exist and coexist at multi-critical points. We also find that for charged black holes, ordinary swallowtails can exists on the stable Gibbs free energy branch, allowing for multiple first order phase transitions as seen for AdS black holes. A triple point for N = 5 and a quadruple point for N = 7 are presented explicitly. We investigate changes in the Gibbs free energy as the lowest order non-fixed Lovelock constant is varied and draw comparisons to pressure changes for AdS black hole systems.

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

“…First, the application of the Maxwell construction turns the problem into algebra which enables our method to produce critical points with arbitrarily high precision such that very tiny phase structures can be discovered easily. More importantly, the method is more efficient in the sense that it does not need any fine-tuning procedure such as those previously employed [18][19][20][21] where N-tuple points were obtained by manipulating thermodynamic variables so that a common point of inflection occurred between multiple maxima and minima of the temperature as a function of r + . However, due to the additional physical constraint γ 2 > 0 induced from the non-algebraic nature of equation of motions in genuine GQTGs, finding a physical multicritical point with a large N is still time-consuming.…”

“…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]. An Nth order multi-critical point occurs when N distinct phases merge at a single value of pressure and temperature, generalizing the notion of a triple point (with N = 3).…”

“…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.…”