Black hole chemistry and holography in generalized quasi-topological gravity

Abstract

We investigate the thermodynamics of AdS black holes in Generalized Quasitopological Gravity with and without electric charge, concentrating on the version of the theory that is cubic in curvature. We study new aspects of Hawking-Page transitions that occur for these black holes. Working within the framework of black hole chemistry, we find a variety of familiar and new critical behaviour and phase transitions in four and higher dimensions for the charged black holes. We also consider some holographic aspects of our work, demonstrating how the ratio of viscosity to entropy is modified by inclusion of these cubic curvature terms.

On generalized quasi-topological cubic-quartic gravity: thermodynamics and holography

“…Since including quartic quasi-topological or Lovelock terms into the action does not alter the black hole entropy from its Einstein gravity value [34], only quartic GQG contributions are responsible for the occurrence of this pole. A previous study of cubic GQG found that similar behaviour for η/s took place [84].…”

“…In studying the behaviour at this point, we note that the equations of state need to be solved for these specific parameter values, instead of using (4.13) and (4.14), since the latter becomes invalid if the denominator of t c vanishes. If both couplings are non-zero, again the denominator of T c in (4.11) is quartic in v 2 , and a similar procedure can be employed to write a formula for α 4 in terms of β 3 and e. Doing so, we find that for any values of the parameters the only solution is α 4 = 0, however in cubic gravity critical temperature does not have a singularity in four dimensions [84]. In other words, this particular occurrence of this apparent thermodynamic singularity is obtained only in Einstein-quartic GQG (for which the cubic coupling vanishes).…”

“…Other possible critical points have one or both of γ 2 < 0 and S < 0. For vanishing charge we also have a region of at most two critical points for both k = 1 and just one critical point for k = −1; for vanishing α 4 there are still two physical critical points if k = +1, studied in detail in [84].…”

“…However for Lovelock and quasi-topological black holes accompanied with conformal scalar hair, isolated critical points have been observed in five and higher dimensions for massive black holes without coinciding with a thermodynamic singularity [50,51]. More recently, in GQG cubic gravity only, isolated critical points have been found in six dimensions with no scalar hair for spherical black holes [84]. In all of these cases there are initially only two critical points that converge to one isolated critical point.…”

“…[93]. We shall consider only the quartic term in the action; the cubic case was studied in [84]. We expect that when both couplings are nonzero a pattern similar to that of the fixed charge case for the number of critical points will emerge, though we shall not perform that analysis here.…”