Universality of P − V criticality in horizon thermodynamics

Abstract

We study P −V criticality of black holes in Lovelock gravities in the context of horizon thermodynamics. The corresponding first law of horizon thermodynamics emerges as one of the Einstein-Lovelock equations and assumes the universal (independent of matter content) form δE = T δS − P δV , where P is identified with the total pressure of all matter in the spacetime (including a cosmological constant Λ if present). We compare this approach to recent advances in extended phase space thermodynamics of asymptotically AdS black holes where the 'standard' first law of black hole thermodynamics is extended to include a pressure-volume term, where the pressure is entirely due to the (variable) cosmological constant. We show that both approaches are quite different in interpretation. Provided there is sufficient non-linearity in the gravitational sector, we find that horizon thermodynamics admits the same interesting black hole phase behaviour seen in the extended case, such as a Hawking-Page transition, Van der Waals like behaviour, and the presence of a triple point. We also formulate the Smarr formula in horizon thermodynamics and discuss the interpretation of the quantity E appearing in the horizon first law.

Criticality and surface tension in rotating horizon thermodynamics

“…(Only a limited number of solutions to Einstein-matter equations can be written in the form we consider.) This is in strong contrast to the spherically symmetric case, in which metric ansatz is general (within the symmetry requirements) and the horizon first law is completely universal, dependent only on the type of gravitational theory but not its matter content [13].…”

“…in terms of the entropy S. The horizon angular velocity Ω = − g tϕ g ϕϕ r+ = a r 2 + + a 2 (13) can likewise be identified, as can the black hole temperature…”

“…Contrary to (2), the extended first law (4) is typically of maximal cohomogeneity. The two approaches were, for spherically symmetric spacetimes, compared in [12,13], where universality of the P − V criticality of the horizon equation of state (1) was also demonstrated. Surprisingly, despite its relative success for black holes with spherical symmetry, horizon thermodynamics has not really been fully extended to rotating black hole spacetimes.…”

The last lost charge and phase transition in Schwarzschild AdS minimally coupled to a cloud of strings

“…The extended phase space refers to a phase space in which the first law of black holes is corrected by a V dP term and the cosmological constant is regarded as thermodynamical pressure of the black hole and its conjugate variable is a volume covered by the event horizon of the black hole [7][8]. Thermodynamical behaviors of a wide range of AdS black holes are studied in details in several works [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. In a different and interesting work, Tian [28][29] introduces the spatial curvature of Reissner-Nordstrom as a topological charge that naturally arises in holography.…”

Horizon thermodynamics from Einstein's equation of state

“…Following [18], let us include the contribution of the cosmological constant (if present) to the matter part, replacing the definitions in (7) by…”