We argue that a convenient way to analyze instabilities of black holes in AdS space is via Bragg-Williams construction of a free energy function. Starting with a pedagogical review of this construction in condensed matter systems and also its implementation to Hawking-Page transition, we study instabilities associated with hairy black holes and also with the $R$-charged black holes. For the hairy black holes, an analysis of thermal quench is presented.
We study the behavior of black hole singularities across the Hawking-Page phase transitions, uncovering the possible connection between the physics inside and outside the horizon. We focus on the case of spacelike singularities in Einstein-scalar theory which are of the Kasner form. We find that the Kasner exponents are continuous and non-differentiable during the second order phase transitions, while discontinuous in the first order phase transitions. We give some arguments on the universality of this behavior. We also discuss possible observables in the dual field theory which encode the Kasner exponents.
We consider a generic first-order phase transition at finite temperature and investigate to what extent a population of primordial black holes, of variable masses, can affect the rate of bubble nucleation. Using a thin-wall approximation, we construct the Euclidean configurations that describe transition at finite temperature. After the transition, the remnant black hole mass is dictated dynamically by the equations of motion. The transition exponent is computed and displays an explicit dependence on temperature. We find the configuration with the lowest Euclidean action to be static and $O(3)$ symmetric; therefore, the transition takes place via thermal excitation. The transition exponent exhibits a strong dependence on the seed mass black hole, $M_+$, being almost directly proportional. A new nucleation condition in the presence of black holes is derived and the nucleation temperature is compared to the familiar flat-space result, i.e. $S_3/T$. For an electroweak-like phase transition it is possible to enhance the nucleation rate if $M_+ lesssim 10^{15} M_{rm P}$. Finally, we outline the possible transition scenarios and the consequences for the power spectrum of stochastic gravitational waves produced due to the first-order phase transition.
We study scalar field configurations around Kerr black holes with a time-independent energy-momentum tensor. These stationary `scalar clouds, confined near the black hole (BH) by their own mass or a mirror at fixed radius, exist at the threshold for energy extraction via superradiance. Motivated by the electromagnetic Blandford-Znajek (BZ) mechanism, we explore whether scalar clouds could serve as a proxy for the force-free magnetosphere in the BZ process. We find that a stationary energy-extracting scalar cloud solution exists when the reflecting mirror is replaced by a semi-permeable surface which allows the cloud to radiate some energy to infinity while maintaining self-sustained superradiance. The radial energy flux displays the same behaviour for rapidly rotating holes as magnetohydrodynamic simulations predict for the BZ mechanism.
Primordial black holes (PBHs) produced in the early Universe have attracted wide interest for their ability to constitute dark matter and explain the compact binary coalescence. We propose a new mechanism of PBH production during first-order phase transitions (PTs) and find that PBHs are naturally produced during PTs model-independently. Because of the randomness of the quantum tunneling, there always exists some probability that the vacuum decay is postponed in a whole Hubble volume. Since the vacuum energy density remains constant while radiation is quickly redshifted in the expanding Universe, the postponed vacuum decay then results in overdense regions, which finally collapse into PBHs as indicated by numerical simulations. Utilizing this result one can obtain mutual predictions and constraints between PBHs and GWs from PTs. The predicted mass function of PBHs is nearly monochromatic. We investigate two typical cases and find that 1) PBHs from a PT constitute all dark matter and GWs peak at $1$Hz, 2) PBHs from a PT can explain the coalescence events observed by LIGO-Virgo collaboration, and meanwhile GWs can explain the common-spectrum process detected by NANOGrav collaboration.
Recently, it has been found that, with the Renyi statistics, the asymptotically flat Schwarzschild black hole can be in thermal equilibrium with infinite heat reservior at a fixed temperature when its event horizon radius is larger than the characteristic length scale $L_lambda=1/sqrt{pi lambda}$, where $lambda$ is the nonextensivity parameter. In the Renyi extended phase space with the $PdV$ work term, an off-shell free energy in the canonical ensemble with the thermodynamic volume as an order parameter is considered to identify a first-order Hawking-Page (HP) phase transition as a solid/liquid phase transition. It has the latent heat of fusion from solid (corresponding to thermal radiation) to liquid (corresponding to black hole) in the form of $sim 1/sqrt{lambda}$; this is evident of the absence of the HP phase transition in the case of asymptotically flat Schwarzschild black hole from the GB statistics ($lambda=0$). Moreover, we investigate the generalized second law of black hole thermodynamics (GSL) in Renyi statistics by considering the black hole as a working substance in heat engine. Interestingly, an efficiency $eta$ of the black hole in a Carnot cycle takes the form $eta_c=1-T_text{C}/T_text{H}$. This confirms the validity of the GSL in the Renyi extended phase space.