In this paper, we analyze the scalar field (quasi-)normal modes of recently derived rotating black holes within the framework of Einstein-Gauss-Bonnet theory at the Chern-Simons point in five dimensions. We also examine the mode spectrum of these probes on new static gravitational solitons. These solitons, featuring a regular center, are constructed from static black holes with gravitational hair via a double analytic continuation. By imposing ingoing boundary conditions at the horizons of rotating black holes, ensuring regularity at the soliton centers, and imposing Dirichlet boundary conditions at infinity, we obtain numerical spectra for the rotating black holes and solitons. For static black holes, we demonstrate analytically that the imaginary part of the mode frequencies is negative. Our analysis of the massless Klein-Gordon equation on five-dimensional geometries reveals an infinite family of gapped, massive three-dimensional Klein-Gordon fields, despite the presence of a non-compact extended direction. For the static solitons, the frequencies are real and non-equispaced, whereas in the rotating black holes, counter-rotating modes are absorbed more quickly, and the imaginary part of the co-rotating modes approaches zero as extremality is approached. Additionally, we show that both the rotating black holes and solitons can be equipped with non-trivial torsion, leading to a novel branch of solutions.

Chile

Lilianne Tapia

Monserrat Aguayo

Andrés Anabalón

Dumitru Astefanesei

Argentina

Nicolás Grandi

Fernando Izaurieta

Julio Oliva

Cristian Quinzacara

(Quasi-)normal modes of rotating black holes and new solitons in Einstein-Gauss-Bonnet

We present new, exact, rotating and accelerating solutions within the framework of five-dimensional Einstein-Gauss-Bonnet theory at the Chern-Simons point. The rotating solutions describe black holes characterized by a single rotation parameter, a mass parameter, and two extra integration constants that can be interpreted as hairs of a gravitational nature. It is noteworthy that the rotation cannot be removed by a large diffeomorphism. We also extend our procedure to dimension seven, providing a new rotating solution with two rotation parameters pertaining to cubic Lovelock theory with a unique vacuum.

Andres Anabalon

Brazil

Czechia

Adolfo Cisterna

Constanza Quijada

Rotating and accelerating AdS black holes in Einstein-Gauss-Bonnet gravity

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.

Spain

Romina Ballesteros

Paulina Cabrera

Gonzálo Casanova

Raúl Rojas

Existence of thermodynamically stable asymptotically flat black holes

We expand our earlier results [D. Astefanesei et al., Hairy black hole chemistry, J. High Energy Phys. 11 (2019) 043.] to investigate a general class of exact hairy black hole solutions in Einstein-Maxwell-dilaton gravity. The dilaton is endowed with a potential that originates from an electromagnetic Fayet-Iliopoulos term in <math><mi>N</mi><mo>=</mo><mn>2</mn></math> extended supergravity in four spacetime dimensions. We present the usual thermodynamics by using the counterterm method supplemented with boundary terms for a scalar field with mixed boundary conditions. We then extend our analysis by considering a dynamical cosmological constant and verify the isoperimetric inequality. We obtain a very rich phase diagram and criticality in both the canonical and grand canonical ensembles. Within string theory, the cosmological constant is related to the radius of the external sphere (of the compactification) and can be interpreted as a modulus. In this context, the existence of a critical value hints to the fact that the thermodynamic properties of black holes in lower dimensions depend on the size of the compactification.

Canada

Robert B. Mann

Extended phase space thermodynamics for hairy black holes

We consider an Einstein-scalar field model which is a consistent truncation of   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 8 D = 4 gauged supergravity, the scalar field possessing a potential which is unbounded from below and a tachyonic mass above the Breitenlohner-Freedman bound. We investigate the spherically symmetric asymptotically anti-de Sitter soliton and black hole solutions, with the aim of clarifying the asymptotics and the possible boundary conditions at infinity. The emerging picture is contrasted with that found for an Einstein-scalar field model with the same scalar mass and a quartic selfinteraction term. We also provide arguments for the existence of solitonic solutions which can be viewed as non-linear continuation of the (probe) scalar multipolar clouds, with emphasis on the dipole case. Apart from numerical results, exact solutions are found for solitons with a monopole and dipole scalar field, as perturbations around the AdS background.

China

Germany

Hyat Huang

Jutta Kunz

Portugal

Eugen Radu

Einstein-scalar field solutions in AdS spacetime: clouds, boundary conditions, and scalar multipoles

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.

David Choque

Jorge Maggiolo

Holography of AdS hairy black holes and Cardy-Verlinde formula

We consider how scalar fields affect the thermodynamic behavior of charged anti-de Sitter (AdS) black holes. We specifically investigate a class of (<math><mrow><mn>3</mn><mo>+</mo><mn>1</mn></mrow></math>)-dimensional exact hairy charged AdS black hole solutions to Einstein-Maxwell-scalar gravity, whose stable ground state and finite horizon area in the zero temperature limit make it of particular interest. We find that the reverse isoperimetric inequality is satisfied for this class and that there exists an intermediate range of the charge that admits reentrant phase behavior, the first example of this type of phase behavior in (<math><mrow><mn>3</mn><mo>+</mo><mn>1</mn></mrow></math>) dimensions in a consistent theory.

Reentrant phase transitions in Einstein-Maxwell-scalar black holes

In this paper we prove that the four-dimensional hyperbolic supersymmetric black holes can be unstable in the canonical ensemble. To this end, we work with an infinite class of   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 supergravity theories interpolating between all the single dilaton truncations of the SO(8) gauged   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 8 supergravity. Within these models, we study electrically charged solutions of two different kinds: supersymmetric hairy and extremal non-supersymmetric Reissner-Nordström black holes. We consider these solutions within the same canonical ensemble and show that, for suitable choices of the parameters defining the   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 model, the supersymmetric solution features a higher free energy than the non-supersymmetric one. In the absence of additional selection rules, this would imply an instability of the supersymmetric configuration, hinting towards a possible supersymmetry breaking mechanism.

Italy

Antonio Gallerati

Mario Trigiante

Instability of supersymmetric black holes via quantum phase transitions

In this article we study a family of four-dimensional,   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 supergravity theories that interpolates between all the single dilaton truncations of the SO(8) gauged   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 8 supergravity. In this infinitely many theories characterized by two real numbers — the interpolation parameter and the dyonic “angle” of the gauging — we construct non-extremal electrically or magnetically charged black hole solutions and their supersymmetric limits. All the supersymmetric black holes have non-singular horizons with spherical, hyperbolic or planar topology. Some of these supersymmetric and non-extremal black holes are new examples in the   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 8 theory that do not belong to the STU model. We compute the asymptotic charges, thermodynamics and boundary conditions of these black holes and show that all of them, except one, introduce a triple trace deformation in the dual theory.

New non-extremal and BPS hairy black holes in gauged   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 and   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 8 supergravity

We extend the analysis, initiated in [1], of the thermodynamic stability of four-dimensional asymptotically flat hairy black holes by considering a general class of exact solutions in Einstein-Maxwell-dilaton theory with a non-trivial dilaton potential. We find that, regardless of the values of the parameters of the theory, there always exists a sub-class of hairy black holes that are thermodynamically stable and have the extremal limit well defined. This generic feature that makes the equilibrium configurations locally stable should be related to the properties of the dilaton potential that is decaying towards the spatial infinity, but behaves as a box close to the horizon. We prove that these thermodynamically stable solutions are also dynamically stable under spherically symmetric perturbations.

Jose Blázquez-Salcedo

Netherlands

Francisco Gómez

Thermodynamically stable asymptotically flat hairy black holes with a dilaton potential: the general case