arXiv subjects

Mokhtar Hassaine

Publications and source records attributed to Mokhtar Hassaine.

At least 37 records · Page 2Linked to original sources

arXiv2023

Uniqueness of the Jackiw non-Noetherian conformal scalar field

Jackiw was undoubtedly the first to exhibit an example of a scalar field action which is not conformally invariant whereas its equation of motion is. This feature has recently been dubbed as a non-Noetherian conformal scalar field. The paradigmatic example of Jackiw was the generalization to curved spacetime of the two-dimensional Liouville action. Here, we prove that, up to second order, this is the unique example of a non-Noetherian conformal scalar field in two dimensions. We establish this result using an old and somewhat forgotten theorem which is none other than the solution to the inverse problem of the calculus of variations.

hep-th↗

arXiv2023

Non-Noetherian conformal scalar fields

Recently, an extension of the standard four-dimensional scalar conformal action, yielding a second-order field equation that remains conformally invariant, was proposed. In spite of this, the corresponding action is not invariant under conformal transformations and this motivates us to define the notion of non-Noetherian conformal scalar field. In this article, we go further by determining the most general action in four dimensions that gives rise to a non-Noetherian conformal scalar field satisfying a second-order equation. This task is achieved by using the solution to the inverse problem of the calculus of variations. Surprisingly enough, the standard equation is shown to be extended by a non-Noetherian conformal piece involving a nonminimal coupling with a very particular combination of squared curvature terms, which is none other than the one defining the so-called Critical Gravity. We also prove that the most general second-order Euler-Lagrange equation for a conformal scalar field involves additional Noetherian conformal nonminimal couplings defined by an arbitrary function of the Weyl tensor. The recently proposed non-Noetherian conformal extension is recovered as a particular example of this function.

hep-th↗

arXiv2023

Selecting Horndeski theories without apparent symmetries and their black hole solutions

Starting from a generalised Kaluza-Klein action including arbitrary Horndeski potentials, we establish integrability and compatibility conditions that solve the generic field equations for spherical symmetry. The resulting theories can be identified as general Horndeski theories having no apparent symmetries in four dimensions or as effective string theory actions with an IR logarithmic running for the dilaton, higher order corrections and generalised Liouville type potentials. For such actions, we then find black holes with secondary hair parameterized by two coupling constants essentially characterising the theories at hand. One is related to an action which is conformally coupled in five dimensions while the second is related to a Kaluza-Klein reduction of Lovelock theory. We show that the full action can also be interpreted as a sum of conformally coupled actions in differing dimensions. Known solutions are mapped within the general chart of the found theories and novel general black holes are discussed, focusing on their important properties and some of their observational constraints.

gr-qc↗

arXiv2023

Conformally coupled scalar in Lovelock theory

In arbitrary higher dimension, we consider the combination of Lovelock gravity alongside a scalar-tensor action built out of higher order operators and Euler densities. The latter action is constructed in such a way as to ensure conformal invariance for the scalar field. For the combined version of these theories, we show the existence of black hole solutions interpreted as stealth configurations within Lovelock gravity theory. The scalar field solutions are endowed with an integration constant that may be identified as a scalar charge. In particular, we show that these stealth solutions can be extended to include a time-dependent scalar field despite the underlying theory being non shift-symmetric. Finally, we present a procedure to obtain a non-conformally invariant action in even dimensions from the considered theory. For the target theory, the scalar field is not conformally coupled to gravity although the scalar field equation itself is conformally invariant. By means of this procedure, the black hole stealth configurations are converted into non-stealth black hole solutions, as discovered recently in four dimensions.

gr-qc↗

arXiv2022

Conformally coupled theories and their deformed compact objects: from black holes, radiating spacetimes to eternal wormholes

We study a higher order conformally coupled scalar tensor theory endowed with a covariant geometric constraint relating the scalar curvature with the Gauss-Bonnet scalar. It is a particular Horndeski theory including a canonical kinetic term but without shift or parity symmetry for the scalar. The theory also stems from a Kaluza-Klein reduction of a well defined higher dimensional metric theory. Properties of an asymptotically flat spherically symmetric black hole are analyzed, and new slowly rotating and radiating extensions are found. Through disformal transformations of the static configurations, gravitating monopole-like solutions and eternal wormholes are presented. The latter are shown to extract from spacetime possible naked singularities, yielding completely regular and asymptotically flat spacetimes.

gr-qc↗

arXiv2021

Regular black holes and gravitational particle-like solutions in generic DHOST theories

We construct regular, asymptotically flat black holes of higher order scalar tensor (DHOST) theories, which are obtained by making use of a generalized Kerr-Schild solution generating method. The solutions depend on a mass integration constant, admit a smooth core of chosen regularity, and generically have an inner and outer event horizon. In particular, below a certain mass threshold, we find massive, horizonless, particle-like solutions. We scan through possible observational signatures ranging from weak to strong gravity and study the thermodynamics of our regular solutions, comparing them, when possible, to General Relativity black holes and their thermodynamic laws.

hep-th↗

arXiv2021

Rotating stealth black holes with a cohomogeneity-1 metric

In five dimensions we consider a general shift symmetric and parity preserving scalar tensor action that contains up to second order covariant derivatives of the scalar field. A rotating stealth black hole solution is constructed where the metric is given by the Myers-Perry spacetime with equal momenta and the scalar field is identified with the Hamilton-Jacobi potential. This nontrivial scalar field has an extra hair associated with the rest mass of the test particle, and the solution does not require any fine tuning of the coupling functions of the theory. Interestingly enough, we show that the disformal transformation, generated by this scalar field, and with a constant degree of disformality, leaves invariant (up to diffeomorphisms) the Myers-Perry metric with equal momenta. This means that the hair of the scalar field, along with the constant disformality parameter, can be consistently absorbed into further redefinitions of the mass and of the single angular parameter of the disformed metric. These results are extended in higher odd dimensions with a Myers-Perry metric for which all the momenta are equal. The key of the invariance under disformal transformation of the metric is mainly the cohomogeneity-1 character of the Myers-Perry metric with equal momenta. Starting from this observation, we consider a general class of cohomogeneity-1 metrics in arbitrary dimension, and we list the conditions ensuring that this class of metrics remain invariant (up to diffeomorphisms) under a disformal transformation with a constant degree of disformality and with a scalar field with constant kinetic term. The extension to the Kerr-(A)dS case is also considered where it is shown that rotating stealth solutions may exist provided some fine tuning of the coupling functions of the scalar tensor theory.

hep-th↗

arXiv2021

Disforming the Kerr metric

Starting from a recently constructed stealth Kerr solution of higher order scalar tensor theory involving scalar hair, we analytically construct disformal versions of the Kerr spacetime with a constant degree of disformality and a regular scalar field. While the disformed metric has only a ring singularity and asymptotically is quite similar to Kerr, it is found to be neither Ricci flat nor circular. Non-circularity has far reaching consequences on the structure of the solution. As we approach the rotating compact object from asymptotic infinity we find a static limit ergosurface similar to the Kerr spacetime with an enclosed ergoregion. However, the stationary limit of infalling observers is found to be a timelike hypersurface. A candidate event horizon is found in the interior of this stationary limit surface. It is a null hypersurface generated by a null congruence of light rays which are no longer Killing vectors. Under a mild regularity assumption, we find that the candidate surface is indeed an event horizon and the disformed Kerr metric is therefore a black hole quite distinct from the Kerr solution.

gr-qc↗

arXiv2020

Regular black holes via the Kerr-Schild construction in DHOST theories

We extend the standard Kerr-Schild solution generating method to higher order scalar tensor theories that are shift-invariant for the scalar field. Certain degeneracy conditions, crucial for the absence of Ostrogradski ghosts, are found to be required for the validity of the Kerr-Schild ansatz while on the other hand, theories with no parity symmetry are excluded from the solution generating method. The extended Kerr-Schild symmetry turns out to be a very useful tool to easily construct black hole solutions from simple seed configurations. In particular, the generating method developed is adapted to construct generic black holes but also regular black hole solutions within Degenerate Higher Order Scalar Tensor (DHOST) theories. As a particular example we show how to construct explicitly the Hayward metric as a solution to a specific DHOST theory.

hep-th↗

arXiv2020

Spinning black holes for generalized scalar tensor theories in three dimensions

We consider a general class of scalar tensor theories in three dimensions whose action contains up to second-order derivatives of the scalar field with coupling functions that only depend on the standard kinetic term of the scalar field, thus ensuring the invariance under the constant shift of the scalar field. For this model, we show that the field equations for a stationary metric ansatz together with a purely radial scalar field can be fully integrated. The kinetic term of the scalar field solution is shown to satisfy an algebraic relation depending only on the coupling functions, and hence is constant while the metric solution is nothing but the BTZ metric with an effective cosmological constant fixed in terms of the coupling functions. As a direct consequence the thermodynamics of the solution is shown to be identical to the BTZ one with an effective cosmological constant, despite the presence of a scalar field. Finally, the expression of the semi-classical entropy of this solution is also confirmed through a generalized Cardy-like formula involving the mass of the scalar soliton obtained from the black hole by means of a double Wick rotation.

hep-th↗

arXiv2019

Microscopic derivation of the Schwarzschild black hole entropy

The main part of this work is to present a formula allowing a microscopic derivation of the Schwarzschild black hole entropy in arbitrary dimension. More generally, this Cardy-like formula applies for static black holes whose gravitational entropy scales as a power of the temperature, and is also effective for negative heat capacity solutions. The formula involves the scaling power, the black hole mass and the energy of a gravitational soliton identified as the ground state of the theory. The robustness of this formula is verified in the most famous example of solution with negative heat capacity, namely the Schwarzschild black hole. The mass of the Schwarzschild regular soliton is computed using the counterterm method for asymptotically flat spacetimes. Corrections of the black hole entropy of the order of logarithm of the area are shown to arise for dimensions strictly greater than four. Finally, we will see that a slight modification of the Cardy-like formula involving the angular generator, perfectly reproduces the four-dimensional Kerr entropy.

hep-th↗

arXiv2019

Microscopic entropy of higher-dimensional nonminimally dressed Lifshitz black holes

In arbitrary dimension, we consider a theory described by the most general quadratic curvature corrections of Einstein gravity together with a self-interacting nonminimally coupled scalar field. This theory is shown to admit five different families of Lifshitz black holes dressed with a nontrivial scalar field. The entropy of these configurations is microscopically computed by means of a higher-dimensional anisotropic Cardy-like formula where the role of the ground state is played by the soliton obtained through a double analytic continuation. This involves to calculate the correct expressions for the masses of the higher-dimensional Lifshitz black hole as well as their corresponding soliton. The robustness of this Cardy-like formula is checked by showing that the microscopic entropy is in perfect agreement with the gravitational Wald entropy. Consequently, the calculated global charges are compatible with the first law of thermodynamics. We also verify that all the configurations satisfy an anisotropic higher-dimensional version of the Smarr formula.

hep-th↗

arXiv2019

Axionic charged black branes with arbitrary scalar nonminimal coupling

In this paper, we construct four-dimensional charged black branes of a nonminimally coupled and self-interacting scalar field. In addition to the scalar and Maxwell fields, the model involves two axionic fields homogeneously distributed along the two-dimensional planar base manifold providing in turn a simple mechanism of momentum dissipation. Interestingly enough, the horizon of the solution can be set at two different positions, whose locations depend on the axionic parameter, and in both cases there exists a wide range of values of the nonminimal coupling parameter yielding physical acceptable solutions. For one of our solutions, the allowed nonminimal coupling parameters take discrete values and it turns out to be extremal since its has zero temperature. A complete analysis of the thermodynamical features of the solutions is also carried out. Finally, thanks to the mechanism of momentum dissipation, the holographic DC conductivities of the solutions are computed in term of the black hole horizon data, and we analyze the effects of the nonminimal coupling parameter on these conductivities. For example, we notice that for the non extremal solutions, there always exists a nonminimal coupling (which is greater than the conformal one in four dimensions) yielding perfect conductivity in the sense that the conductivity is infinite. Even more astonishing, the conductivity matrix for the extremal solutions has a Hall effect-like behavior.

hep-th↗

arXiv2019

Black holes with Lambert W function horizons

We consider Einstein gravity with a negative cosmological constant endowed with distinct matter sources. The different models analyzed here share the following two properties: (i) they admit static symmetric solutions with planar base manifold characterized by their mass and some additional Noetherian charges, and (ii) the contribution of these latter in the metric has a slower falloff to zero than the mass term, and this slowness is of logarithmic order. Under these hypothesis, it is shown that, for suitable bounds between the mass and the additional Noetherian charges, the solutions can represent black holes with two horizons whose locations are given in term of the real branches of the Lambert W functions. We present various examples of such black hole solutions with electric, dyonic or axionic charges with AdS and Lifshitz asymptotics. As an illustrative example, we construct a purely AdS magnetic black hole in five dimensions with a matter source given by three different Maxwell invariants.

hep-th↗

arXiv2018

BTZ dilatonic black holes coupled to Maxwell and Born-Infeld electrodynamics

Motivated by string theory corrections of dilatonic gravity and Born-Infeld nonlinear electromagnetic field, we consider the BTZ black holes with these two generalizations. It will be shown that the generalization to dilatonic gravity introduces novel properties into thermodynamics of the black holes which were absent in the purely gravity case. Furthermore, the possibility of tuning out part of the dilatonic effects is explored in the Born-Infeld generalization.

physics.gen-ph↗

arXiv2017

Axionic black branes in the k-essence sector of the Horndeski model

We construct new black brane solutions in the context of Horndeski gravity, in particular in its K-essence sector. These models are supported by axion scalar fields that depend only on the horizon coordinates. The dynamics of these fields is determined by a K-essence term that includes the standard kinetic term $X$ and a correction of the form $X^{k}$. We find both neutral and charged exact and analytic solutions in $D$-dimensions, which are asymptotically anti de Sitter. Then, we describe in detail the thermodynamical properties of the four-dimensional solutions and we compute the dual holographic DC conductivity.

hep-th↗

arXiv2017

Thermodynamics of dyonic black holes with Thurston horizon geometries

In five dimensions, we consider a model described by the Einstein gravity with a source given by a scalar field and various Abelian gauge fields with dilatonic-like couplings. For this model, we are able to construct two dyonic black holes whose three-dimensional horizons are modeled by two nontrivial homogeneous Thurston's geometries. The dyonic solutions are of Lifshitz type with an arbitrary value of the dynamical exponent. In fact, the first gauge field ensures the anisotropy asymptotic while the remaining Abelian fields sustain the electric and magnetic charges. Using the Hamiltonian formalism, the mass, the electric and magnetic charges are explicitly computed. Interestingly enough, the dyonic solutions behave like Chern-Simons vortices in the sense that their electric and magnetic charges turn to be proportional. The extension with an hyperscaling violating factor is also scrutinized where we notice that for specific values of the violating factor, purely magnetic solutions are possible.

hep-th↗

arXiv2017

First law and anisotropic Cardy formula for three-dimensional Lifshitz black holes

The aim of this paper is to confirm in new concrete examples that the semiclassical entropy of a three-dimensional Lifshitz black hole can be recovered through an anisotropic generalization of the Cardy formula derived from the growth of the number of states of a boundary non-relativistic field theory. The role of the ground state in the bulk is played by the corresponding Lifshitz soliton obtained by a double Wick rotation. In order to achieve this task, we consider a scalar field nonminimally coupled to new massive gravity for which we study different classes of Lifshitz black holes as well as their respective solitons, including new solutions for a dynamical exponent z=3. The masses of the black holes and solitons are computed using the quasilocal formulation of conserved charges recently proposed by Gim, Kim, Kulkarni and Yi and based on the off-shell extension of the ADT formalism. We confirm the anisotropic Cardy formula for each of these examples, providing a stronger base for its general validity. Consistently, the first law of thermodynamics together with a Smarr formula are also verified.

gr-qc↗