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arXiv:2606.10647

Hawking-Page phase transition for pure Lovelock black holes

Nitesh K. Dubey, Sanved Kolekar

gr-qchep-thquant-phSubmitted Jun 9, 2026• Announced Jun 10, 2026
v1 · Jun 9, 2026v2 · Oct 1, 2026
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Abstract

We investigate the thermodynamic properties of static, spherically symmetric Anti-de Sitter (AdS) black holes, focusing on the interplay between characteristic temperatures, as well as on the universality of Ruppeiner scalar curvature at the Hawking-Page (HP) phase transition. In particular, we study the relation between the minimum temperature and the HP phase transition temperature for static, spherically symmetric AdS black holes in pure Lovelock gravity. For the electromagnetically neutral case in Einstein gravity, the minimum temperature in $(d+1)$ dimensions coincides with the HP transition temperature in $d$ dimensions, while in higher pure Lovelock theories this relation is modified by a dimension- and order-dependent factor, reducing to the Einstein result in appropriate limits. For charged AdS black holes, in the grand canonical ensemble, in general relativity, the two temperatures differ by a simple dimension-dependent factor, whereas no universal relation persists in higher curvature pure Lovelock theories. We further analyze the normalized Ruppeiner scalar curvature at the HP transition and show that it is a universal constant depending only on the spacetime dimension for electromagnetically neutral black holes in pure Lovelock theories. The normalized scalar curvature remains a constant, under appropriate conditions, even for the charged static spherically symmetric black holes in the grand canonical ensemble for the Einstein theory case, whereas in general pure Lovelock theories it depends on thermodynamic parameters such as pressure and electrostatic potential, asymptotically approaching a constant in the large-pressure or simultaneous large-potential and large-pressure limits.

Journal reference
Phys. Rev. D 114, 084077 (2026)
DOI
10.1103/9lzt-qdw8
Comments
2 figures, 21 pages

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We investigate the charged q/2q/2q/2-body interacting Sachdev-Ye-Kitaev (SYK) model in the grand-canonical ensemble. By treating qqq as a large parameter, we are able to analytically study its phase diagram. By varying the chemical potential or temperature, we find that the system undergoes a phase transition between low and high entropies in the maximally chaotic regime. A similar transition in entropy is seen in charged anti--de Sitter (AdS) black holes transitioning between a large and small event horizon. Approaching zero temperature, we find a first-order chaotic-to-nonchaotic quantum phase transition, where the finite extensive entropy drops to zero. This again has a gravitational analog---the Hawking-Page transition between a large black hole and thermal radiation. An analytical study of the critical phenomena associated with the continuous phase transition provides us with mean-field van der Waals critical and effective exponents. We find that all analogous power laws are shared with several charged AdS black hole phase transitions. Together, these findings indicate a connection between the charged $q\ensuremath{\rightarrow}\ensuremath{\infty}$ SYK model and black holes.
The effect of the Hawking temperature on the entanglement and teleportation for the scalar field in a most general, static, and asymptotically flat black hole with spherical symmetry has been investigated. It has been shown that the same ``initial entanglement'' for the state parameter $\ensuremath{\alpha}$ and its ``normalized partners'' $\sqrt{1\ensuremath{-}{\ensuremath{\alpha}}^{2}}$ will be degraded by the Hawking effect with increasing Hawking temperature along two different trajectories except for the maximally entangled state. In the infinite Hawking temperature limit, corresponding to the case of the black hole evaporating completely, the state no longer has distillable entanglement for any $\ensuremath{\alpha}$. It is interesting to note that the mutual information in this limit is equal to just half of the ``initially mutual information.'' It has also been demonstrated that the fidelity of teleportation decreases as the Hawking temperature increases, which indicates the degradation of entanglement.
We demonstrate that the finite-temperature critical transverse-field Ising chain exhibits quantitative signatures of black-hole physics in its dual gravitational description within the AdS/CFT correspondence. Its finite-temperature dynamics and thermodynamics are consistently captured by a mixed thermal-AdS/BTZ black hole saddle, leading to three mutually compatible observations. First, antipodal excitation transport collapses onto a universal temperature-dependent curve determined by the relative AdS and BTZ contributions to the gravitational partition function, reflecting horizon absorption. Second, in the high-temperature regime, the retarded response exhibits exponential relaxation governed by the lowest quasi-normal mode of the dual black hole. Third, the temperature derivative of the von Neumann entropy develops a pronounced minimum at a temperature consistent with the Hawking-Page transition. These results identify critical quantum spin chains as minimal and experimentally accessible platforms for probing dynamical and thermodynamic aspects of quantum black holes in controllable many-body systems.
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We study the process of relaxation back to thermal equilibrium in (1+1)(1+1)(1+1)-dimensional conformal field theory at finite temperature. When the size of the system is much larger than the inverse temperature, perturbations decay exponentially with time. On the other hand, when the inverse temperature is large, the relaxation is oscillatory with the characteristic period set by the size of the system. We then analyze the intermediate regime in two specific models: namely, free fermions, and a strongly coupled large k conformal field theory which is dual to string theory on (2+1)(2+1)(2+1)-dimensional anti--de Sitter spacetime. In the latter case, there is a sharp transition between the two regimes in the $k=\ensuremath{\infty}$ limit, which is a manifestation of the gravitational Hawking-Page phase transition. In particular, we establish a direct connection between quasinormal and normal modes of the gravity system, and the decaying and oscillating behavior of the conformal field theory.
Using the AdS/CFT correspondence we derive a formula for the entanglement entropy of the anti-de Sitter black hole in two spacetime dimensions. The leading term in the large black hole mass expansion of our formula reproduces exactly the Bekenstein–Hawking entropy SBH, whereas the subleading term behaves as lnSBH. This subleading term has the universal form typical for the entanglement entropy of physical systems described by effective conformal fields theories (e.g. one-dimensional statistical models at the critical point). The well-known form of the entanglement entropy for a two-dimensional conformal field theory is obtained as analytic continuation of our result and is related with the entanglement entropy of a black hole with negative mass.