Family Of Black Hole Solutions Research Articles

Deforming charged black holes with dipolar differential rotation boundary

Motivated by the recent studies of the novel asymptotically global hbox {AdS}_4 black hole with deformed horizon, we consider the action of Einstein–Maxwell gravity in AdS spacetime and construct the charged deforming AdS black holes with differential boundary. In contrast to deforming black hole without charge, there exists at least one value of horizon for an arbitrary temperature. The extremum of temperature is determined by charge q and divides the range of temperature into several parts. Moreover, we use an isometric embedding in the three-dimensional space to investigate the horizon geometry. The entropy and quasinormal modes of deforming charged AdS black hole are also studied in this paper. Due to the existence of charge q, the phase diagram of entropy is more complicated. We consider two cases of solutions: (1) fixing the chemical potential mu ; (2) changing the value of mu according to the values of horizon radius and charge. In the first case, it is interesting to find there exist two families of black hole solutions with different horizon radii for a fixed temperature, but these two black holes have same horizon geometry and entropy. The second case ensures that deforming charged AdS black hole solutions can reduce to standard RN–AdS black holes.

Quadratic gravity and conformally coupled scalar fields

We construct black hole solutions in four-dimensional quadratic gravity, supported by a scalar field conformally coupled to quadratic terms in the curvature. The conformal matter Lagrangian is constructed with powers of traces of a conformally covariant tensor, which is defined in terms of the metric and a scalar field, and has the symmetries of the Riemann tensor. We find exact, neutral and charged, topological black hole solutions of this theory when the Weyl squared term is absent from the action functional. Including terms beyond quadratic order on the conformally covariant tensor, allows to have asymptotically de Sitter solutions, with a potential that is bounded from below. For generic values of the couplings we also show that static black hole solutions must have a constant Ricci scalar, and provide an analysis of the possible asymptotic behavior of both, the metric as well as the scalar field in the asymptotically AdS case, when the solutions match those of general relativity in vacuum at infinity. In this frame, the spacetime fulfils standard asymptotically AdS boundary conditions, and in spite of the non-standard couplings between the curvature and the scalar field, there is a family of black hole solutions in AdS that can be interpreted as localized objects. We also provide further comments on the extension of these results to higher dimensions.

Generalized uncertainty principle and black holes in higher dimensional self-complete gravity

In this paper we consider generalized uncertainty principle (GUP) effects in higher dimensional black hole spacetimes via a nonlocal gravity approach. We study three possible modifications of momentum space measure emerging from GUP, including the original Kempf-Mangano-Mann (KMM) proposal. By following the KMM model we derive a family of black hole spacetimes. The case of five spacetime dimensions is a special one. We found an exact black hole solution with a Barriola-Vilenkin monopole at the origin. This object turns out to be the end point of the black hole evaporation. Interestingly for smaller masses, we found a “naked monopole” rather than a generic naked singularity. We also show that the Carr-Lake-Casadio-Scardigli proposal leads to mild modifications of spacetime metrics with respect to the Schwarzschild-Tangherlini solution. Finally, by demanding the same degree of convergence in the ultraviolet regime for any spacetime dimension, we derive a family of black hole solutions that fulfill the gravity self-completeness paradigm. The evaporation of such black holes is characterized by a fluctuating luminosity, which we dub a lighthouse effect.

Deforming black holes in AdS

We investigate how changes in the boundary metric affect the shape of AdS black holes. Most of our work is analytic and based on the AdS C-metric. Both asymptotically hyperbolic and compact black holes are studied. It has recently been shown that the AdS C-metric contains configurations of highly deformed black holes, and we show that these deformations are usually the result of similar deformations of the boundary metric. However, quite surprisingly, we also find cases where the horizon is insensitive to certain large changes in the boundary geometry. This motivates the search for a new family of black hole solutions with the same boundary geometry in which the horizon does respond to the changes in the boundary. We numerically construct these solutions and we (numerically) explore how the horizon response to boundary deformations depends on temperature.

On the time dependence of holographic complexity in a dynamical Einstein-dilaton model

We study the holographic “complexity = action” (CA) and “complexity = volume” (CV) proposals in Einstein-dilaton gravity in all spacetime dimensions. We analytically construct an infinite family of black hole solutions and use CA and CV proposals to investigate the time evolution of the complexity. Using the CA proposal, we find dimensional dependent violation of the Lloyd bound in early as well as in late times. Moreover, depending on the parameters of the theory, the bound violation relative to the conformal field theory result can be tailored in the early times as well. In contrast to the CA proposal, the CV proposal in our model yields results similar to those obtained in the literature.

D=10 dyonic black holes in string inspired models

We consider string inspired models in $D=10$ spacetime dimensions, which include couplings with 1- and 3-form fields as well as $R^4$ higher curvature corrections to the gravitational action. For such models, we explicitly construct a family of black hole solutions with both electric and magnetic charges, and with different horizon topologies. The solutions exhibit some features similar to those of self-gravitating monopoles in Einstein-Yang-Mills theory, which we discuss. When higher-curvature corrections are switched off, our solutions reduce to charged $p$-brane solutions previously studied in the literature. Novel qualitative features appear due to the $R^4$ terms, though. Such is the case of the emergence of branch singularities for charged solutions that, nonetheless, can be shielded by the event horizon.

Black holes in a cubic Galileon universe

We find and study the properties of black hole solutions for a subclass of Horndeski theory including the cubic Galileon term. The theory under study has shift symmetry but not reflection symmetry for the scalar field. The Galileon is assumed to have linear time dependence characterized by a velocity parameter. We give analytic 3-dimensional solutions that are akin to the BTZ solutions but with a non-trivial scalar field that modifies the effective cosmological constant. We then study the 4-dimensional asymptotically flat and de Sitter solutions. The latter present three different branches according to their effective cosmological constant. For two of these branches, we find families of black hole solutions, parametrized by the velocity of the scalar field. These spherically symmetric solutions, obtained numerically, are different from GR solutions close to the black hole event horizon, while they have the same de-Sitter asymptotic behavior. The velocity parameter represents black hole primary hair.

Maxwell perturbations on Kerr–anti–de Sitter black holes: Quasinormal modes, superradiant instabilities, and vector clouds

Scalar and gravitational perturbations on Kerr-anti-de Sitter (Kerr-AdS) black holes have been addressed in the literature and have been shown to exhibit a rich phenomenology. In this paper we complete the analysis of bosonic fields on this background by studying Maxwell perturbations, focusing on superradiant instabilities and vector clouds. For this purpose, we solve the Teukolsky equations numerically, imposing the boundary conditions we have proposed in\cite{Wang:2015goa} for the radial Teukolsky equation. As found therein, two Robin boundary conditions can be imposed for Maxwell fields on Kerr-AdS black holes, one of which produces a new set of quasinormal modes even for Schwarzschild-AdS black holes. Here, we show these different boundary conditions produce two different sets of superradiant modes. Interestingly the "new modes" may be unstable in a larger parameter space. We then study stationary Maxwell clouds, that exist at the threshold of the superradiant instability, with the two Robin boundary conditions. These clouds, obtained at the linear level, indicate the existence of a new family of black hole solutions at the nonlinear level, within the Einstein-Maxwell-AdS system, branching off from the Kerr-Newman-AdS family. As a comparison with the Maxwell clouds, scalar clouds on Kerr-AdS black holes are also studied, and it is shown there are Kerr-AdS black holes that are stable against scalar, but not vector modes, with the same "quantum numbers".

Black holes and Thunderbolt singularities with Lifshitz scaling terms

We study a static, spherically symmetric and asymptotic flat spacetime, assuming the hypersurface orthogonal Einstein-aether theory with an ultraviolet modification motivated by the Horava-Lifshitz theory, which is composed of the $z=2$ Lifshitz scaling terms such as scalar combinations of a three-Ricci curvature and the acceleration of the aether field. For the case with the quartic term of the acceleration of the aether field, we obtain a two-parameter family of black hole solutions, which possess a regular universal horizon. While, if three-Ricci curvature squared term is joined in ultraviolet modification, we find a solution with a thunderbolt singularity such that the universal horizon turns to be a spacelike singularity.

Lumpy AdS5× S5 black holes and black belts

Sufficiently small Schwarzschild black holes in global AdS5×S5 are Gregory-Laflamme unstable. We construct new families of black hole solutions that bifurcate from the onset of this instability and break the full SO(6) symmetry group of the S5 down to SO(5). These new “lumpy” solutions are labelled by the harmonics ℓ. We find evidence that the ℓ = 1 branch never dominates the microcanonical/canonical ensembles and connects through a topology-changing merger to a localised black hole solution with S8 topology. We argue that these S8 black holes should become the dominant phase in the microcanonical ensemble for small enough energies, and that the transition to Schwarzschild black holes is first order. Furthermore, we find two branches of solutions with ℓ = 2. We expect one of these branches to connect to a solution containing two localised black holes, while the other branch connects to a black hole solution with horizon topology S4 × S4 which we call a “black belt”.

Black holes in new massive gravity dressed by a (non)minimally coupled scalar field

We consider a self-interacting, massive scalar field (non)minimally coupled to new massive gravity in three dimensions. For this model, we first derive a family of black hole solutions depending on a unique integration constant and parameterized in terms of the nonminimal coupling parameter. Imposing the absence of naked singularities restricts the parameters in such a way that the field vanishes at infinity and fixes the metric to be asymptotically AdS. Within this family of solutions it is possible to find a black hole supported by a minimally coupled scalar field and therefore the existence of these solutions is not inherent to the presence of the nonminimal coupling. The Wald formula for the entropy, being proportional to the lapse function evaluated at the horizon, yields a zero entropy in spite of the fact that the solution has a non zero temperature. As a consequence, the unique integration constant may be interpreted as a sort of gravitational hair. As in the source free case, we show that the same field equations admit as well asymptotically Lifshitz black hole solutions in a different region of the space of parameters. These Lifshitz solutions are divided in three families for which all the parameters entering in the action may be expressed in term of the dynamical exponent.

Regular black holes: Electrically charged solutions, Reissner-Nordström outside a de Sitter core

To have the correct picture of a black hole as a whole, it is of crucial importance to understand its interior. The singularities that lurk inside the horizon of the usual Kerr-Newman family of black hole solutions signal an endpoint to the physical laws and, as such, should be substituted in one way or another. A proposal that has been around for sometime is to replace the singular region of the spacetime by a region containing some form of matter or false vacuum configuration that can also cohabit with the black hole interior. Black holes without singularities are called regular black holes. In the present work, regular black hole solutions are found within general relativity coupled to Maxwell's electromagnetism and charged matter. We show that there are objects which correspond to regular charged black holes, whose interior region is de Sitter, whose exterior region is Reissner-Nordstr\"om, and the boundary between both regions is made of an electrically charged spherically symmetric coat. There are several types of solutions: regular nonextremal black holes with a null matter boundary, regular nonextremal black holes with a timelike matter boundary, regular extremal black holes with a timelike matter boundary, and regular overcharged stars with a timelike matter boundary. The main physical and geometrical properties of such charged regular solutions are analyzed.

Maximal analytic extensions of the Emparan-Reall black ring

The Emparan-Reall black rings are a two-parameter family of black hole solutions of the vacuum Einstein's equation in dimension 4+1, the word ring refers to the event horizon, which has topology 2 × 1 × . We construct an analytic extension, whose global structure is similar to the Kruskal-Szekeres extension of the Schwarzschild space-time, and show that it is maximal, globally hyperbolic, and unique within a natural class of extensions.

Maximal analytic extensions of the Emparan-Reall black ring

The Emparan-Reall black rings are a two-parameter family of black hole solutions of the vacuum Einstein's equation in dimension 4+1, the word "ring" refers to the event horizon, which has topology \U0001d4ae2 × \U0001d4ae1 × ℛ. We construct an analytic extension, whose global structure is similar to the Kruskal-Szekeres extension of the Schwarzschild space-time, and show that it is maximal, globally hyperbolic, and unique within a natural class of extensions.

An instability of higher-dimensional rotating black holes

We present the first example of a linearized gravitational instability of an asymptotically at vacuum black hole. We study perturbations of a Myers-Perry black hole with equal angular momenta in an odd number of dimensions. We find no evidence of any instability in five or seven dimensions, but in nine dimensions, for sufficiently rapid rotation, we find perturbations that grow exponentially in time. The onset of instability is associated with the appearance of time-independent perturbations which generically break all but one of the rotational symmetries. This is interpreted as evidence for the existence of a new 70-parameter family of black hole solutions with only a single rotational symmetry. We also present results for the Gregory-Laflamme instability of rotating black strings, demonstrating that rotation makes black strings more unstable.

Analytic Lifshitz black holes in higher dimensions

We generalize the four-dimensional R^2-corrected z=3/2 Lifshitz black hole to a two-parameter family of black hole solutions for any dynamical exponent z and for any dimension D. For a particular relation between the parameters, we find the first example of an extremal Lifshitz black hole. An asymptotically Lifshitz black hole with a logarithmic decay is also exhibited for a specific critical exponent depending on the dimension. We extend this analysis to the more general quadratic curvature corrections for which we present three new families of higher-dimensional D>=5 analytic Lifshitz black holes for generic z. One of these higher-dimensional families contains as critical limits the z=3 three-dimensional Lifshitz black hole and a new z=6 four-dimensional black hole. The variety of analytic solutions presented here encourages to explore these gravity models within the context of non-relativistic holographic correspondence.

Supersymmetric coloured/hairy black holes

We discuss all possible spherically symmetric black hole type solutions to an N=2 supergravity model with SO(3) gauging. The solutions consist of a one parameter family of black hole solutions evading the no-hair theorem and an isolated solution that is a supersymmetric analogue of a coloured black hole.

Conformal black hole solutions of axidilaton gravity inDdimensions

Static, spherically symmetric solutions of axi-dilaton gravity in $D$ dimensions is given in the Brans-Dicke frame for arbitrary values of the Brans-Dicke constant $\omega$ and an axion-dilaton coupling parameter $k$. The mass and the dilaton and axion charges are determined and a BPS bound is derived. There exists a one parameter family of black hole solutions in the scale invariant limit.

New classes of black hole spacetimes in 2+1 gravity

The electrogravity transformation is applied to the three-dimensional Einstein field equations to obtain new multi-parameter families of black hole solutions. The Bañados–Teitelboim–Zanelli black hole is shown to be a special case of one of these families. The causal structure, associated matter, as well as the mechanical and thermodynamical properties of some of the solutions are discussed.

Initial data and the end state of spherically symmetric gravitational collapse

Generalizing earlier results on the initial data and the final fate of dust collapse, we study here the relevance of the initial state of a spherically symmetric matter cloud towards determining its end state in the course of a continuing gravitational collapse. It is shown that given an arbitrary regular distribution of matter at the initial epoch, there always exists an evolution from this initial data which would result either in a black hole or a naked singularity, depending on the allowed choice of free functions available in the solution. It follows that given any initial density and pressure profiles for the cloud, there is a non-zero measure set of configurations leading either to black holes or naked singularities, subject to the usual energy conditions ensuring the positivity of energy density. We also characterize here wide new families of black hole solutions resulting from spherically symmetric collapse without requiring the cosmic censorship assumption.