Acena, A., Anabalon, A., & Astefanesei, D. (2013). Exact hairy black brane solutions in 5D antide Sitter space and holographic renormalization group flows. Phys. Rev. D, 87(12), 6 pp.
Abstract: We construct a general class of exact regular black hole solutions with toroidal horizon topology in fivedimensional antide Sitter gravity with a selfinteracting scalar field. With these boundary conditions and due to the nontrivial backreaction of the scalar field, the nohair theorems can be evaded so that an event horizon can be formed. The scalar field is regular everywhere outside the curvature singularity and it vanishes at the boundary where the potential is finite. We study the properties of these black holes in the context ofAdS/CFT duality and comment on the dual operators, which saturate the unitarity bound. We present exact expressions for the beta function and construct a cfunction that characterizes the renormalizationgroup flow.

Acena, A., Anabalon, A., Astefanesei, D., & Mann, R. (2014). Hairy planar black holes in higher dimensions. J. High Energy Phys., (1), 21 pp.
Abstract: We construct exact hairy planar black holes in Ddimensional AdS gravity. These solutions are regular except at the singularity and have stressenergy that satisfies the null energy condition. We present a detailed analysis of their thermodynamical properties and show that the first law is satisfied. We also discuss these solutions in the context of AdS/CFT duality and construct the associated cfunction.

Anabalon, A. (2012). Exact black holes and universality in the backreaction of nonlinear sigma models with a potential in (A)dS(4). J. High Energy Phys., (6), 18 pp.
Abstract: The aim of this paper is to construct accelerated, stationary and axisymmetric exact solutions of the Einstein theory with self interacting scalar fields in (A)dS4. To warm up, the backreaction of the (non)minimally coupled scalar field is solved, the scalar field equations are integrated and all the potentials compatible with the metric ansatz and Einstein gravity are found. With these results at hand the nonlinear sigma model is tackled. The scalar field Lagrangian is generic; neither the coupling to the curvature, neither the metric in the scalar manifold nor the potential, are fixed ab initio. The unique assumption in the analysis is the metric ansatz: it has the form of the most general Petrov type D vacuum solution of general relativity; it is a a cohomogeneity two Weyl rescaling of the Carter metric and therefore it has the typical PlebanskiDemianski form with two arbitrary functions of one variable and one arbitrary function of two variables. It is shown, by an straightforward manipulation of the field equations, that the metric is completely integrable without necessity of specifiying anything in the scalar Lagrangian. This results is that the backreaction of the scalar fields, within this class of metrics, is universal. The metric functions generically show an explicit dependence on a dynamical exponent that allows to smoothly connect this new family of solutions with the actual PlebanskiDemianski spacetime. The remaining field equations imply that the scalar fields follow geodesics in the scalar manifold with an affine parameter given by a nonlinear function of the spacetime coordinates and define the onshell form of the potential plus a functional equation that it has to satisfy. To further find the exact form of the potential the simplest case associated to a flat scalar manifold is taken. The most general potential compatible with the Einstein theory and the metric ansatz is constructed in this case and it is shown that it has less symmetry than the maximal compact subgroup of the coset construction. Finally, the most general family of (A) dS4 static hairy black holes is explicitly constructed and its properties are outlined.

Anabalon, A., & Astefanesei, D. (2013). On attractor mechanism of AdS(4) black holes. Phys. Lett. B, 727(45), 568–572.
Abstract: We construct a general family of exact nonextremal 4dimensional black holes in AdS gravity with U(1) gauge fields nonminimally coupled to a dilaton and a nontrivial dilaton potential. These black holes can have spherical, toroidal, and hyperbolic horizon topologies. We use the entropy function formalism to obtain the near horizon data in the extremal limit. Due to the nontrivial selfinteraction of the scalar field, the zero temperature black holes can have a finite horizon area even if only the electric field is turned on. (C) 2013 Elsevier B.V. All rights reserved.

Anabalon, A., & Astefanesei, D. (2014). Black holes in omegadeformed gauged N=8 supergravity. Phys. Lett. B, 732, 137–141.
Abstract: Motivated by the recently found 4dimensional omegadeformed gauged supergravity, we investigate the black hole solutions within the single scalar field consistent truncations of this theory. We construct black hole solutions that have spherical, toroidal, and hyperbolic horizon topologies. The scalar field is regular everywhere outside the curvature singularity and the stressenergy tensor satisfies the null energy condition. When the parameter CO does not vanish, there is a degeneracy in the spectrum of black hole solutions for boundary conditions that preserve the asymptotic Antide Sitter symmetries. These boundary conditions correspond to multitrace deformations in the dual field theory. (C) 2014 The Authors. Published by Elsevier B.V.

Anabalon, A., & Batista, C. (2016). A class of integrable metrics. Phys. Rev. D, 93(6), 13 pp.
Abstract: In four dimensions, the most general metric admitting two commuting Killing vectors and a ranktwo Killing tensor can be parametrized by ten arbitrary functions of a single variable. We show that picking a special vierbein, reducing the system to eight functions, implies the existence of two geodesic and sharefree, null congruences, generated by two principal null directions of the Weyl tensor. Thus, if the spacetime is an Einstein manifold, the GoldbergSachs theorem implies it is Petrov type D, and by explicit construction, is in the Carter class. Hence, our analysis provides a straightforward connection between the most general integrable structure and the Carter family of spacetimes.

Anabalon, A., & Cisterna, A. (2012). Asymptotically (anti) de Sitter black holes and wormholes with a selfinteracting scalar field in four dimensions. Phys. Rev. D, 85(8), 6 pp.
Abstract: The aim of this paper is to report on the existence of a wide variety of exact solutions, ranging from black holes to wormholes, when a conformally coupled scalar field with a selfinteracting potential containing a linear, a cubic and a quartic self interaction is taken as a source of the energymomentum tensor, in the Einstein theory with a cosmological constant. Among all the solutions there are two particularly interesting. On the one hand, the spherically symmetric black holes when the cosmological constant is positive; they are shown to be everywhere regular, namely, there is no singularity neither inside nor outside the event horizon. On the other hand, there are spherically symmetric and topological wormholes that connect two asymptotically (anti) de Sitter regions with a different value for the cosmological constant. The regular black holes and the wormholes are supported by everywhere regular scalar field configurations.

Anabalon, A., & Deruelle, N. (2013). Mechanical stability of asymptotically flat black holes with minimally coupled scalar hair. Phys. Rev. D, 88(6), 9 pp.
Abstract: We show that the asymptotically flat hairy black holes, solutions of the Einstein field equations minimally coupled to a scalar field, previously discovered by one of us, present mode instability against linear radial perturbations. It is also shown that the number of unstable modes is finite and their frequencies can be made arbitrarily small.

Anabalon, A., & Oliva, J. (2012). Exact hairy black holes and their modification to the universal law of gravitation. Phys. Rev. D, 86(10), 5 pp.
Abstract: In this paper two things are done. First, it is pointed out the existence of exact asymptotically flat, spherically symmetric black holes when a selfinteracting, minimally coupled scalar field is the source of the Einstein equations in four dimensions. The scalar field potential is recently found to be compatible with the hairy generalization of the PlebanskiDemianski solution of general relativity. This paper describes the spherically symmetric solutions that smoothly connect the Schwarzschild black hole with its hairy counterpart. The geometry and scalar field are everywhere regular except at the usual Schwarzschildlike singularity inside the black hole. The scalar field energy momentum tensor satisfies the nullenergy condition in the static region of spacetime. The first law holds when the parameters of the scalar field potential are fixed under thermodynamical variation. Second, it is shown that an extra, dimensionless parameter, present in the hairy solution, allows to modify the gravitational field of a spherically symmetric black hole in a remarkable way. When the dimensionless parameter is increased, the scalar field generates a flat gravitational potential that, however, asymptotically matches the Schwarzschild gravitational field. Finally, it is shown that a positive cosmological constant can render the scalar field potential convex if the parameters are within a specific rank.

Anabalon, A., Astefanesei, D., & Choque, D. (2015). On the thermodynamics of hairy black holes. Phys. Lett. B, 743, 154–159.
Abstract: We investigate the thermodynamics of a general class of exact 4dimensional asymptotically Antide Sitter hairy black hole solutions and show that, for a fixed temperature, there are small and large hairy black holes similar to the SchwarzschildAdS black hole. The large black holes have positive specific heat and so they can be in equilibrium with a thermal bath of radiation at the Hawking temperature. The relevant thermodynamic quantities are computed by using the Hamiltonian formalism and counterterm method. We explicitly show that there are first order phase transitions similar to the HawkingPage phase transition. (C) 2015 The Authors. Published by Elsevier B.V.

Anabalon, A., Astefanesei, D., & Choque, D. (2016). Hairy AdS solitons. Phys. Lett. B, 762, 80–85.
Abstract: We construct exact hairy AdS soliton solutions in Einsteindilaton gravity theory. We examine their thermodynamic properties and discuss the role of these solutions for the existence of first order phase transitions for hairy black holes. The negative energy density associated to hairy AdS solitons can be interpreted as the Casimir energy that is generated in the dual filed theory when the fermions are antiperiodic on the compact coordinate. (C) 2016 Published by Elsevier B.V.

Anabalon, A., Astefanesei, D., Choque, D., & Martinez, C. (2016). Trace anomaly and counterterms in designer gravity. J. High Energy Phys., (3), 29 pp.
Abstract: We construct concrete counterterms of the BalasubramanianKraus type for Einsteinscalar theories with designer gravity boundary conditions in AdS(4), so that the total action is fi nite onshell and satisfy a well de fi ned variational principle. We focus on scalar fi elds with the conformal mass m(2) = 2l(2) and show that the holographic mass matches the Hamiltonian mass for any boundary conditions. We compute the trace anomaly of the dual fi eld theory in the generic case, as well as when there exist logarithmic branches of nonlinear origin. As expected, the anomaly vanishes for the boundary conditions that are AdS invariant. When the anomaly does not vanish, the dual stress tensor describes a thermal gas with an equation of state related to the boundary conditions of the scalar fi eld. In the case of a vanishing anomaly, we recover the dual theory of a massless thermal gas. As an application of the formalism, we consider a general family of exact hairy black hole solutions that, for some particular values of the parameters in the moduli potential, contains solutions of fourdimensional gauged N = 8 supergravity and its omegadeformation. Using the AdS/CFT duality dictionary, they correspond to triple trace deformations of the dual fi eld theory.

Anabalon, A., Astefanesei, D., & Mann, R. (2013). Exact asymptotically flat charged hairy black holes with a dilaton potential. J. High Energy Phys., (10), 22 pp.
Abstract: We find broad classes of exact 4dimensional asymptotically flat black hole solutions in EinsteinMaxwell theories with a nonminimally coupled dilaton and its nontrivial potential. We consider a few interesting limits, in particular, a regular generalization of the dilatonic ReissnerNordstrom solution and, also, smooth deformations of supersymmetric black holes. Further examples are provided for more general dilaton potentials. We discuss the thermodynamical properties and show that the first law is satisfied. In the nonextremal case the entropy depends, as expected, on the asymptotic value of the dilaton. In the extremal limit, the entropy is determined purely in terms of charges and is independent of the asymptotic value of the dilaton. The attractor mechanism can be used as a criterion for the existence of the regular solutions. Since there is a 'competition' between the effective potential and dilaton potential, we also obtain regular extremal black hole solutions with just one U(1) gauge field turned on.

Anabalon, A., Astefanesei, D., & Mann, R. (2017). Holographic equation of state in fluid/gravity duality. Phys. Lett. B, 770, 272–277.
Abstract: We establish a precise relation between mixed boundary conditions for scalar fields in asymptotically anti de Sitter spacetimes and the equation of state of the dual fluid. We provide a detailed derivation of the relation in the case of five bulkdimensions for scalar fields saturating the BreitenlohnerFreedman bound. As a concrete example, we discuss the five dimensional scalartensor theories describing dark energy in four dimensions. (C) 2017 Published by Elsevier B.V.

Anabalon, A., Astefanesei, D., & Martinez, C. (2015). Mass of asymptotically antide Sitter hairy spacetimes. Phys. Rev. D, 91(4), 6 pp.
Abstract: In the standard asymptotic expansion of fourdimensional static asymptotically flat spacetimes, the coefficient of the first subleading term of the lapse function can be identified with the mass of the spacetime. Using the Hamiltonian formalism we show that, in asymptotically locally antide Sitter spacetimes endowed with a scalar field, the mass can read off in the same way only when the boundary conditions are compatible with the asymptotic realization of the antide Sitter symmetry. Since the mass is determined only by the spatial metric and the scalar field, the above effect appears by considering not only the constraints, but also the dynamic field equations, which relate the spatial metric with the lapse function. In particular, this result implies that some prescriptions for computing the mass of a hairy spacetime are not suitable when the scalar field breaks the asymptotic antide Sitter invariance.

Anabalon, A., Astefanesei, D., & Oliva, J. (2015). Hairy black hole stability in AdS, quantum mechanics on the halfline and holography. J. High Energy Phys., (10), 15 pp.
Abstract: We consider the linear stability of 4dimensional hairy black holes with mixed boundary conditions in Antide Sitter spacetinie. We focus on the mass of scalar fields around the maximally supersymmetric vacuum of the gauged N = 8 supergravity in four dimensions, m(2) = 2l(2). It is shown that the Schrodinger operator on the halfline, governing the S2, H2 or R2 invariant mode around the hairy black hole, allows for nontrivial selfadjoint extensions and each of them corresponds to a class of mixed boundary conditions in the gravitational theory. Discarding the selfadjoint extensions with a negative mode impose a restriction on these boundary conditions. The restriction is given in terms of an integral of the potential in the Schrodinger operator resembling the estimate of Simon for Schrodinger operators on the real line. In the context of AdS/CFT duality, our result has a natural interpretation in terms of the field theory dual effective potential.

Anabalon, A., Bicak, J., & Saavedra, J. (2014). Hairy black holes: Stability under oddparity perturbations and existence of slowly rotating solutions. Phys. Rev. D, 90(12), 6 pp.
Abstract: We show that, independently of the scalar field potential and of specific asymptotic properties of the spacetime (asymptotically flat, de Sitter or antide Sitter), any static, spherically symmetric or planar, black hole solution of the Einstein theory minimally coupled to a real scalar field with a general potential is mode stable under linear oddparity perturbations. To this end, we generalize the ReggeWheeler equation for a generic selfinteracting scalar field, and show that the potential of the relevant Schrodinger operator can be mapped, by the socalled Sdeformation, to a semipositively defined potential. With these results at hand we study the existence of slowly rotating configurations. The frame dragging effect is compared with the corresponding effect in the case of a Kerr black hole.

Anabalon, A., Canfora, F., Giacomini, A., & Oliva, J. (2011). Black holes with gravitational hair in higher dimensions. Phys. Rev. D, 84(8), 10 pp.
Abstract: A new class of vacuum black holes for the most general gravity theory leading to second order field equations in the metric in even dimensions is presented. These spacetimes are locally antide Sitter in the asymptotic region, and are characterized by a continuous parameter that does not enter in the conserve charges, nor it can be reabsorbed by a coordinate transformation: it is therefore a purely gravitational hair. The black holes are constructed as a warped product of a twodimensional spacetime, which resembles the rt plane of the BanadosTeitelboimZanelli black hole, times a warp factor multiplying the metric of a D – 2dimensional Euclidean base manifold, which is restricted by a scalar equation. It is shown that all the Noether charges vanish. Furthermore, this is consistent with the Euclidean action approach: even though the black hole has a finite temperature, both the entropy and the mass vanish. Interesting examples of base manifolds are given in eight dimensions which are products of Thurston geometries, giving then a nontrivial topology to the black hole horizon. The possibility of introducing a torsional hair for these solutions is also discussed.

Anabalon, A., Canfora, F., Giacomini, A., & Oliva, J. (2011). Gribov ambiguity in asymptotically AdS threedimensional gravity. Phys. Rev. D, 83(6), 7 pp.
Abstract: In this paper the zero modes of the de Donder gauge FaddeevPopov operator for threedimensional gravity with negative cosmological constant are analyzed. It is found that the AdS(3) vacuum produces (infinitely many) normalizable smooth zero modes of the FaddeevPopov operator. On the other hand, it is found that the BanadosTeitelboimZanelli black hole (including the zero mass black hole) does not generate zero modes. This differs from the usual Gribov problem in QCD where, close to the maximally symmetric vacuum, the FaddeevPopov determinant is positive definite while "far enough'' from the vacuum it can vanish. This suggests that the zero mass BanadosTeitelboimZanelli black hole could be a suitable ground state of threedimensional gravity with negative cosmological constant. Because of the kinematic origin of this result, it also applies for other covariant gravity theories in three dimensions with AdS(3) as maximally symmetric solution, such as new massive gravity and topologically massive gravity. The relevance of these results for supersymmetry breaking is pointed out.

Anabalon, A., Canfora, F., Giacomini, A., & Oliva, J. (2012). Black holes with primary hair in gauged N=8 supergravity. J. High Energy Phys., (6), 12 pp.
Abstract: In this paper, we analyze the static solutions for the U(1)(4) consistent truncation of the maximally supersymmetric gauged supergravity in four dimensions. Using a new parametrization of the known solutions it is shown that for fixed charges there exist three Possible black hole configurations according to the pattern of symmetry breaking of the (scalars sector of the) Lagrangian. Namely a black hole without scalar fields, a black hole with a primary hair and a black hole with a secondary hair respectively. This is the first, exact, example of a black hole with a primary scalar hair, where both the black hole and the scalar fields are regular on and outside the horizon. The configurations with secondary and primary hair can be interpreted as a spontaneous symmetry breaking of discrete permutation and reflection symmetries of the action. It is shown that there exist a triple point in the thermodynamic phase space where the three solution coexist. The corresponding phase transitions are discussed and the free energies are written explicitly as function of the thermodynamic coordinates in the uncharged case. In the charged case the free energies of the primary hair and the hairless black hole are also given as functions of the thermodynamic coordinates.
