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We revisit the study of the phase structure of higher spin black holes carried out in arXiv$:1210.0284$ using the canonical formalism. In particular we study the low as well as high temperature regimes. We show that the Hawking-Page transition takes place in the low temperature regime. The thermodynamically favoured phase changes from conical surplus to black holes and then again to conical surplus as we increase temperature. We then show that in the high temperature regime the diagonal embedding gives the appropriate description. We also give a map between the parameters of the theory near the IR and UV fixed points. This makes the good solutions near one end map to the bad solutions near the other end and vice versa.
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We propose a set of boundary terms for higher spin theories in AdS$_3$ that lead to a well-defined variational principle compatible with Dirichlet boundary conditions for the metric and higher spin fields. These boundary terms are valid for higher spin theories in the Fefferman-Graham gauge and they allow us to compute the canonical free energy of higher spin black holes directly from the Euclidean, covariant, on-shell action. Using these results we reproduce the thermodynamics of the higher spin black hole of Ammon, Gutperle, Kraus, and Perlmutter and comment on the corresponding theory of induced $cal{W}$-gravity at the boundary.
We give analytical arguments and demonstrate numerically the existence of black hole solutions of the $4D$ Effective Superstring Action in the presence of Gauss-Bonnet quadratic curvature terms. The solutions possess non-trivial dilaton hair. The hair, however, is of ``secondary type, in the sense that the dilaton charge is expressed in terms of the black hole mass. Our solutions are not covered by the assumptions of existing proofs of the ``no-hair theorem. We also find some alternative solutions with singular metric behaviour, but finite energy. The absence of naked singularities in this system is pointed out.
In arbitrary dimension, we consider a theory described by the most general quadratic curvature corrections of Einstein gravity together with a self-interacting nonminimally coupled scalar field. This theory is shown to admit five different families of Lifshitz black holes dressed with a nontrivial scalar field. The entropy of these configurations is microscopically computed by means of a higher-dimensional anisotropic Cardy-like formula where the role of the ground state is played by the soliton obtained through a double analytic continuation. This involves to calculate the correct expressions for the masses of the higher-dimensional Lifshitz black hole as well as their corresponding soliton. The robustness of this Cardy-like formula is checked by showing that the microscopic entropy is in perfect agreement with the gravitational Wald entropy. Consequently, the calculated global charges are compatible with the first law of thermodynamics. We also verify that all the configurations satisfy an anisotropic higher-dimensional version of the Smarr formula.
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.
General relativity predicts that the Kerr black hole develops qualitatively new and surprising features in the limit of maximal spin. Most strikingly, the region of spacetime near the event horizon stretches into an infinitely long throat and displays an emergent conformal symmetry. Understanding dynamics in this NHEK (Near-Horizon Extreme Kerr) geometry is necessary for connecting theory to upcoming astronomical observations of high-spin black holes. We review essential properties of NHEK and its relationship to the rapidly rotating Kerr black hole. We then completely solve the geodesic equation in the NHEK region and describe how the resulting trajectories transform under the action of its enhanced symmetries. In the process, we derive explicit expressions for the angular integrals appearing in the Kerr geodesic equation and obtain a useful formula, valid at arbitrary spin, for a particles polar angle in terms of its radial motion. These results will aid in the analytic computation of astrophysical observables relevant to ongoing and future experiments.
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