Raúl Rojas

We propose a new way to relate the black hole thermodynamics and geometry by generalizing the Euclidean formalism to include ‘virtual geometries’, which do not necessarily satisfy Einstein equations. This provides a physically well motivated route to study black hole criticality and obtain the Landau–Ginzburg potential. We compute the ‘virtual thermodynamic potential’ and show that it satisfies a modified quantum statistical relation that is compatible with the first law of black hole thermodynamics supplemented with an extra term, interpreted as virtual work in previous literature. The novelty is that, within our formalism, we can explicitly compute this term as the first derivative of the virtual thermodynamic potential with respect to the horizon radius that is considered as the order parameter. Imposing the physical condition that the first derivative vanishes is at the basis of the matching between the first law of black hole thermodynamics and (one of the) Einstein equations evaluated at the horizon. Interestingly, imposing the physical conditions that the second and third derivatives vanish, we can concretely study the criticality and existence of swallow tails. As a specific example, we apply this formalism to an exact 4- 4 − dimensional asymptotically flat hairy black hole, namely the generalized Kaluza-Klein (KK) black hole when the dilaton potential is included, and show that it is thermodynamically stable and has a non-trivial critical behaviour corresponding to an inverted swallowtail.

We study the interplay between higher-curvature terms and the backreaction of quantum fluctuations in three-dimensional massive gravity in asymptotically (anti–)de Sitter space. We focus on the theory at the special point of the parameter space where the two maximally symmetric vacua coincide. In the case of positive cosmological constant, this corresponds to the partially massless point, at which the classical theory admits de Sitter black holes and exhibits an extra conformal symmetry at linear level. We explicitly find the quantum corrected black hole geometry in the semiclassical approximation and show that it induces a relaxation of the standard asymptotic conditions. Nonetheless, the new asymptotic behavior is still preserved by an infinite-dimensional algebra, which, in addition to Virasoro, contains logarithmic supertranslations. Finally, we show that all the results we obtain for the quadratic massive gravity theory can be extended to theories including cubic and quartic terms in the curvature. Published by the American Physical Society 2024

We use the quasilocal formalism of Brown and York, supplemented with counterterms, to investigate the thermodynamics of asymptotically flat black holes. We consider two families of exact regular black hole solutions, which are thermodynamically stable. The first one consists of four-dimensional static charged hairy black holes in extended supergravity. The second family consists of five-dimensional static charged black holes in Gauss-Bonnet (GB) gravity. Despite the fact that their characteristics are completely different, we found a striking similarity between their thermodynamic behavior. Published by the American Physical Society 2024

We discuss some aspects related to holography of anti–de Sitter (AdS) dyonic hairy black holes, which break the conformal symmetry of the boundary. We use counterterms for the scalar field that satisfies mixed boundary conditions to compute the Euclidean action and dual stress tensor. We apply these results to show that the Cardy-Verlinde formula is not satisfied. However, when the magnetic (or electric) charge vanishes, the conformal symmetry is preserved and the entropy of the black hole can be put in the Cardy-Verlinde form. In our analysis, there is no need of adding extra finite counterterms and, in this particular case, we explicitly show that our results match the ones obtained from using the superpotential as a counterterm.

We investigate the thermodynamics of dyonic hairy black holes in flat spacetime when the asymptotic value of the scalar field is not fixed. We use the quasilocal formalism of Brown and York and corresponding boundary terms that make the variational principle well defined to prove that the scalar charges do not contribute to the first law of thermodynamics. We also provide a unified picture of obtaining exact solutions by comparing two different methods and discuss in detail the ansatz used in each coordinate system and the relation between them.

We investigate the thermodynamics of dyonic hairy black holes in flat spacetime when the asymptotic value of the scalar field is not fixed. We use the quasilocal formalism of Brown and York and corresponding boundary terms that make the variational principle well defined to prove that the scalar charges do not contribute to the first law of thermodynamics. We also provide a unified picture of obtaining exact solutions by comparing two different methods and discuss in detail the ansatz used in each coordinate system and the relation between them.