arXiv subjects

Mokhtar Hassaine

Publications and source records attributed to Mokhtar Hassaine.

At least 55 records · Page 3Linked to original sources

arXiv2017

Black holes and solitons in an extended Proca theory

We study a massive vector tensor theory that acquires mass via a standard Proca term but also via a higher order term containing an explicit coupling to curvature. We find static solutions that are asymptotically flat, adS or Lifshitz black holes. Since the higher order term regularizes the effect of the Proca mass term, generically solutions are asymptotically regular for arbitrary couplings. This is true in particular for asymptotically flat black holes. For a particular coupling we find particle like solitons that have a regular and non trivial geometry everywhere. In all adS solutions the Proca mass term plays the role of an effective cosmological constant distinctly different from the bare cosmological constant.

gr-qc↗

arXiv2017

Quintic quasi-topological gravity

We construct a quintic quasi-topological gravity in five dimensions, i.e. a theory with a Lagrangian containing $\mathcal{R}^5$ terms and whose field equations are of second order on spherically (hyperbolic or planar) symmetric spacetimes. These theories have recently received attention since when formulated on asymptotically AdS spacetimes might provide for gravity duals of a broad class of CFTs. For simplicity we focus on five dimensions. We show that this theory fulfils a Birkhoff's Theorem as it is the case in Lovelock gravity and therefore, for generic values of the couplings, there is no s-wave propagating mode. We prove that the spherically symmetric solution is determined by a quintic algebraic polynomial equation which resembles Wheeler's polynomial of Lovelock gravity. For the black hole solutions we compute the temperature, mass and entropy and show that the first law of black holes thermodynamics is fulfilled. Besides of being of fourth order in general, we show that the field equations, when linearized around AdS are of second order, and therefore the theory does not propagate ghosts around this background. Besides the class of theories originally introduced in arXiv:1003.4773 [gr-qc], the general geometric structure of these Lagrangians remains an open problem.

hep-th↗

arXiv2016

Static and rotating solutions for Vector-Galileon theories

We consider a particular truncation of the generalized Proca field theory in four dimensions for which we construct a static and axisymmetric rotating black hole "stealth solutions", namely solutions with (Anti) de Sitter or Kerr metric but non-trivial vector field. The static configuration is promoted to a backreacting black hole with asymptotic (Anti) de Sitter behavior by turning on a nonlinear electrodynamic source given as a fixed power of the Maxwell invariant. Finally we extend our solutions to arbitrary dimensions.

gr-qc↗

arXiv2015

Cardy formula for charged black holes with anisotropic scaling

We first observe that for Lifshitz black holes whose only charge is the mass, the resulting Smarr relation is a direct consequence of the Lifshitz Cardy formula. From this observation, we propose to extend the Cardy formula to the case of electrically charged Lifshitz black holes satisfying as well a Smarr relation. The expression of our formula depends on the dynamical exponent, the energy and the charge of the ground state which is played by a magnetically charged soliton obtained through a double Wick rotation. The expression also involves a factor multiplying the chemical potentials which varies in function of the electromagnetic theory considered. This factor is precisely the one that appears in the Smarr formula for charged Lifshitz black holes. We test the validity of this Cardy formula in different situations where electrically Lifshitz charged black holes satisfying a Smarr relation are known. We then extend these results to electrically charged black holes with hyperscaling violation. Finally, an example in the charged AdS case is also provided.

hep-th↗

arXiv2015

Towards the Cardy formula for hyperscaling violation black holes

The aim of this paper is to propose a generalized Cardy formula in the case of three-dimensional hyperscaling violation black holes. We first note that for the hyperscaling violation metrics, the scaling of the entropy in term of the temperature (defined as the effective spatial dimensionality divided by the dynamical exponent) depends explicitly on the gravity theory. Starting from this observation, we first explore the case of quadratic curvature gravity theory for which we derive four classes of asymptotically hyperscaling violation black holes. For each solution, we compute their masses as well as those of their soliton counterparts obtained through a double Wick rotation. Assuming that the partition function has a certain invariance involving the effective spatial dimensionality, a generalized Cardy formula is derived. This latter is shown to correctly reproduce the entropy where the ground state is identified with the soliton. Comparing our formula with the one derived in the standard Einstein gravity case with source, we stress the role played by the effective spatial dimensionality. From this observation, we speculate the general form of the Cardy formula in the case of hyperscaling violation metric for an arbitrary value of the effective spatial dimensionality. Finally, we test the viability of this formula in the case of cubic gravity theory.

hep-th↗

arXiv2015

Thermodynamics of charged Lifshitz black holes with quadratic corrections

In arbitrary dimension, we consider the Einstein-Maxwell Lagrangian supplemented by the more general quadratic-curvature corrections. For this model, we derive four classes of charged Lifshitz black hole solutions for which the metric function is shown to depend on a unique integration constant. The masses of these solutions are computed using the quasilocal formalism based on the relation established between the off-shell ADT and Noether potentials. Among these four solutions, three of them are interpreted as extremal in the sense that their mass vanishes identically. For the last family of solutions, the quasilocal mass and the electric charge both are shown to depend on the integration constant. Finally, we verify that the first law of thermodynamics holds for each solution and a Smarr formula is also established for the four solutions.

hep-th↗

arXiv2015

Charged Galileon black holes

We consider an Abelian gauge field coupled to a particular truncation of Horndeski theory. The Galileon field has translation symmetry and couples non minimally both to the metric and the gauge field. When the gauge-scalar coupling is zero the gauge field reduces to a standard Maxwell field. By taking into account the symmetries of the action, we construct charged black hole solutions. Allowing the scalar field to softly break symmetries of spacetime we construct black holes where the scalar field is regular on the black hole event horizon. Some of these solutions can be interpreted as the equivalent of Reissner-Nordstrom black holes of scalar tensor theories with a non trivial scalar field. A self tuning black hole solution found previously is extended to the presence of dyonic charge without affecting whatsoever the self tuning of a large positive cosmological constant. Finally, for a general shift invariant scalar tensor theory we demonstrate that the scalar field Ansatz and method we employ are mathematically compatible with the field equations. This opens up the possibility for novel searches of hairy black holes in a far more general setting of Horndeski theory.

gr-qc↗

arXiv2015

New black holes of vacuum Einstein equations with hyperscaling violation and Nil geometry horizons

In this paper, we present a new solution of the vacuum Einstein equations in five dimensions which is a static black hole with hyperscaling violation and with a three-dimensional horizon modeled by one the eight Thurston geometries, namely the Nil geometry. This homogeneous geometry is non-trivial in the sense that it is neither of constant curvature nor a product of constant curvature manifolds. Using the Hamiltonian formalism, we identify the mass and entropy of the black hole solution. Curiously enough, in spite of the fact that the entropy turns to be negative, the mass is positive and the first law of thermodynamics holds. We also discuss the extension in higher dimension.

hep-th↗

arXiv2014

Thermodynamics of a BTZ black hole solution with an Horndeski source

In three dimensions, we consider a particular truncation of the Horndeski action that reduces to the Einstein-Hilbert Lagrangian with a cosmological constant $Λ$ and a scalar field whose dynamics is governed by its usual kinetic term together with a nonminimal kinetic coupling. Requiring the radial component of the conserved current to vanish, the solution turns out to be the BTZ black hole geometry with a radial scalar field well-defined at the horizon. This means in particular that the stress tensor associated to the matter source behaves on-shell as an effective cosmological constant term. We construct an Euclidean action whose field equations are consistent with the original ones and such that the constraint on the radial component of the conserved current also appears as a field equation. With the help of this Euclidean action, we derive the mass and the entropy of the solution, and found that they are proportional to the thermodynamical quantities of the BTZ solution by an overall factor that depends on the cosmological constant. The reality condition and the positivity of the mass impose the cosmological constant to be bounded from above as $Λ\leq-\frac{1}{l^2}$ where the limiting case $Λ=-\frac{1}{l^2}$ reduces to the BTZ solution with a vanishing scalar field. Exploiting a scaling symmetry of the reduced action, we also obtain the usual three-dimensional Smarr formula. In the last section, we extend all these results in higher dimensions where the metric turns out to be the Schwarzschild-AdS spacetime with planar horizon.

hep-th↗

arXiv2014

Lifshitz black holes with a time-dependent scalar field in Horndeski theory

In arbitrary dimensions, we consider a particular Horndeski action given by the Einstein-Hilbert Lagrangian with a cosmological constant term, while the source part is described by a real scalar field with its usual kinetic term together with a nonminimal kinetic coupling. In order to evade the no-hair theorem, we look for solutions where the radial component of the conserved current vanishes identically. Under this hypothesis, we prove that this model can not accommodate Lifshitz solutions with a radial scalar field. This problem is finally circumvented by turning on the time dependence of the scalar field, and we obtain a Lifshitz black hole solution with a fixed value of the dynamical exponent z=1/3. The same metric is also shown to satisfy the field equations arising only from the variation of the matter source.

hep-th↗

arXiv2014

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.

hep-th↗

arXiv2013

Thermodynamics of Lovelock black holes with a nonminimal scalar field

We source the Lovelock gravity theories indexed by an integer k and fixed by requiring a unique anti-de Sitter vacuum with a self-interacting nonminimal scalar field in arbitrary dimension d. For each inequivalent Lovelock gravity theory indexed by the integer k, we establish the existence of a two-parametric self-interacting potential that permits to derive a class of black hole solutions with planar horizon for any arbitrary value of the nonminimal coupling parameter. In the thermodynamical analysis of the solution, we show that, once regularized the Euclidean action, the mass contribution coming form the gravity side exactly cancels, order by order, the one arising from the matter part yielding to a vanishing mass. This result is in accordance with the fact that the entropy of the solution, being proportional to the lapse function evaluated at the horizon, also vanishes. Consequently, the integration constant appearing in the solution is interpreted as a sort of hair which turns out to vanish at high temperature.

hep-th↗

arXiv2013

Rotating AdS black hole stealth solution in D=3

We show that the rotating asymptotically anti de Sitter black hole solution of new massive gravity in three dimensions can support a static stealth configuration given by a conformally coupled scalar field. By static stealth configuration, we mean a nontrivial time independent scalar field whose energy-momentum tensor vanishes identically on the rotating black hole metric solution of new massive gravity. The existence of this configuration is rendered possible because of the presence of a gravitational hair in the black hole metric that prevents the scalar field to be trivial. In the extremal case, the stealth scalar field diverges at the horizon as it occurs for the conformal scalar field of the Bocharova-Bronnikov-Melnikov-Bekenstein solution in four dimensions.

hep-th↗

arXiv2013

Planar AdS black holes in Lovelock gravity with a nonminimal scalar field

In arbitrary dimension D, we consider a self-interacting scalar field nonminimally coupled with a gravity theory given by a particular Lovelock action indexed by an integer k. To be more precise, the coefficients appearing in the Lovelock expansion are fixed by requiring the theory to have a unique AdS vacuum with a fixed value of the cosmological constant. This yields to k=1,2,...,[(D-1)/2] inequivalent possible gravity theories; here the case k=1 corresponds to the standard Einstein-Hilbert Lagrangian. For each par (D,k), we derive two classes of AdS black hole solutions with planar event horizon topology for particular values of the nonminimal coupling parameter. The first family of solutions depends on a unique constant and is valid only for k>1. In fact, its GR counterpart k=1 reduces to the pure AdS metric with a vanishing scalar field. The second family of solutions involves two independent constants and corresponds to a stealth black hole configuration; that is a nontrivial scalar field together with a black hole metric such that both side of the Einstein equations (gravity and matter parts) vanishes identically. In this case, the standard GR case k=1 reduces to the Schwarzschild-AdS-Tangherlini black hole metric with a trivial scalar field. In both cases, the existence of these solutions is strongly inherent of the presence of the higher order curvature terms k>1 of the Lovelock gravity. We also establish that these solutions emerge from a stealth configuration defined on the pure AdS metric through a Kerr-Schild transformation. Finally, in the last part, we include multiple exact (D-1)-forms homogenously distributed and coupled to the scalar field. For a specific coupling, we obtain black hole solutions for arbitrary value of the nonminimal coupling parameter generalizing those obtained in the pure scalar field case.

hep-th↗

arXiv2013

Topological black holes for Einstein-Gauss-Bonnet gravity with a nonminimal scalar field

We consider the Einstein-Gauss-Bonnet gravity with a negative cosmological constant together with a source given by a scalar field nonminimally coupled in arbitrary dimension D. For a certain election of the cosmological and Gauss-Bonnet coupling constants, we derive two classes of AdS black hole solutions whose horizon is planar. The first family of black holes obtained for a particular value of the nonminimal coupling parameter only depends on a constant M, and the scalar field vanishes as M=0. The second class of solutions corresponds to a two-parametric (with constants M and A) black hole stealth configuration, that is a nontrivial scalar field with a black hole metric such that both side (gravity and matter parts) of the Einstein equations vanishes. In this case, in the vanishing M, the solution reduces to a stealth scalar field on the pure AdS metric. We note that the existence of these two classes of solutions is inherent of the particular choice of the coupling constants and, they can not be promoted to spherical or hyperboloid black hole solutions in a standard fashion. In the last part, we add to the original action some exacts (D-1)-forms coupled to the scalar field. The direct benefit of introducing such extra fields is to obtain black hole solutions with planar horizon for arbitrary value of the nonminimal coupling parameter.

hep-th↗

arXiv2012

Critical gravity waves

Critical Gravity in D dimensions is discussed from the point of view of its exact solutions. The special features that certain type of solutions of higher-curvature gravity develop when one approaches the critical point of the parameter space are reviewed. In particular, a non-linear realization of the logarithmic modes of linearized Critical Gravity is seen to emerge as a peculiarity of the sector of anti-de Sitter wave solutions. Logarithmic solutions are shown to occur at a second point of the parameter space, at which the effective mass of the anti-de Sitter waves equals the Breitenlohner-Freedman bound. Other type of solutions with anisotropic scale invariance are also discussed and the special features they develop at the critical point are studied as well. This note is the written version of the talk delivered by one of the authors at the 13th Marcel Grossmann Meeting on general relativity, held in Stockholm, Sweden, in July 2012. The proceeding contribution is based on authors' previous works.

gr-qc↗

arXiv2010

Magnetic black holes with higher-order curvature and gauge corrections in even dimensions

We obtain magnetic black-hole solutions in arbitrary $n(\ge 4)$ even dimensions for an action given by the Einstein-Gauss-Bonnet-Maxwell-$Λ$ pieces with the $F^4$ gauge-correction terms. This action arises in the low energy limit of heterotic string theory with constant dilaton and vanishing higher form fields. The spacetime is assumed to be a warped product ${\ma M}^{2} \times {\ma K}^{n-2}$, where ${\ma K}^{n-2}$ is a $(n-2)$-dimensional Einstein space satisfying a condition on its Weyl tensor, originally considered by Dotti and Gleiser. Under a few reasonable assumptions, we establish the generalized Jebsen-Birkhoff theorem for the magnetic solution in the case where the orbit of the warp factor on ${\ma K}^{n-2}$ is non-null. We prove that such magnetic solutions do not exist in odd dimensions. In contrast, in even dimensions, we obtain an explicit solution in the case where ${\ma K}^{n-2}$ is a product manifold of $(n-2)/2$ two-dimensional maximally symmetric spaces with the same constant warp factors. In this latter case, we show that the global structure of the spacetime sharply depends on the existence of the gauge-correction terms as well as the number of spacetime dimensions.

hep-th↗

arXiv2009

Thermodynamics of charged black holes with a nonlinear electrodynamics source

We study the thermodynamical properties of electrically charged black hole solutions of a nonlinear electrodynamics theory defined by a power p of the Maxwell invariant, which is coupled to Einstein gravity in four and higher spacetime dimensions. Depending on the range of the parameter p, these solutions present different asymptotic behaviors. We compute the Euclidean action with the appropriate boundary term in the grand canonical ensemble. The thermodynamical quantities are identified and in particular, the mass and the charge are shown to be finite for all classes of solutions. Interestingly, a generalized Smarr formula is derived and it is shown that this latter encodes perfectly the different asymptotic behaviors of the black hole solutions. The local stability is analyzed by computing the heat capacity and the electrical permittivity and we find that a set of small black holes are locally stable. In contrast to the standard Reissner-Nordstrom solution, there is a first-order phase transition between a class of these non-linear charged black holes and the Minkowski spacetime.

hep-th↗