arXiv subjects

Mokhtar Hassaine

Publications and source records attributed to Mokhtar Hassaine.

At least 19 recordsLinked to original sources

arXiv2026

Rotating black holes with primary hair in five-dimensional generalized Proca theory

This work presents a new class of exact analytic rotating black hole solutions within five-dimensional generalized Proca theories. Through a Kerr-Schild ansatz where the Proca field is set along a null geodesic congruence, the non-linear field equations reduce to a consistent set of three master equations. This geometric configuration ensures that the vector field remains light-like on-shell, effectively restricting the theory's functional couplings to discrete constants and allowing for a fully analytic treatment. The resulting solutions, incorporating a cosmological constant and two independent angular momenta, exhibit primary hair given by an arbitrary function of the non-Killing angular coordinate. We identify several solution branches defined by specific algebraic relations between the Proca coupling constants, providing a significant generalization of the Myers-Perry family. Notably, the metric retains a Kerr-Schild form identical to the Myers-Perry representation, with an additional contribution constructed from the tensor product of the Proca one-form with itself.

gr-qc↗

arXiv2026

Dynamical axisymmetric compact objects in General Relativity

The search for exact solutions describing asymptotically FLRW compact objects in General Relativity remains a challenging problem. Progress has largely been limited to the spherically symmetric case, with notable exceptions such as the Kerr--de Sitter and Thakurta solutions. In this work, we present two new results that advance the description of axisymmetric compact objects embedded in a cosmological background. First, we introduce a new solution-generating technique that allows for the construction of nonstationary, axisymmetric solutions of the self-interacting Einstein-scalar system. Using this method, we obtain the first exact solution that can describe a dynamical axisymmetric compact object in a FLRW cosmology. We then outline how a detailed analysis of its properties, particularly dynamical trapping (or anti-trapping) horizons, can be carried out. For this purpose, we employ the mean curvature vector (MCV), which provides a natural extension of the Kodama vector beyond spherical symmetry. The norm of the MCV defines a foliation-independent, though embedding-dependent, quantity that can be used to identify trapped, anti-trapped, and untrapped regions, and to characterise the causal structure of the geometry without relying on specific symmetry assumptions. The embedding dependence must be treated carefully, as it determines the extent to which the analysis can be performed analytically while minimising the use of numerical methods. Overall, the solution-generating approach and the associated analysis tools offer a framework to further investigate dynamical axisymmetric compact objects, including black holes in cosmological settings and scenarios involving dynamical scalar accretion.

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arXiv2026

An effective cosmological constant as black hole primary hair

We study Generalized Proca theories inspired by the recent regularised Proca theory of four-dimensional Gauss-Bonnet gravity. By abandoning the rigid constraints typically imposed by specific regularization schemes, we treat the coefficients of the terms in the action as free parameters. This approach uncovers a broader solution space that admits static and spherically symmetric black hole solutions characterized by primary hair, where, surprisingly, the cosmological constant arises naturally as a constant of integration even in the absence of a bare cosmological term.

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arXiv2025

A new exact rotating spacetime in vacuum: The Kerr--Levi-Civita Spacetime

We construct a new rotating solution of Einstein's theory in vacuum by exploiting the Lie point symmetries of the field equations in the complex potential formalism of Ernst. In particular, we perform a discrete symmetry transformation, known as inversion, of the gravitational potential associated with the Kerr metric. The resulting metric describes a rotating generalization of the Schwarzschild--Levi-Civita spacetime, and we refer to it as the Kerr--Levi-Civita metric. We study the key geometric features of this novel spacetime, which turns out to be free of curvature singularities, topological defects, and closed timelike curves. These attractive properties are also common to the extremal black hole and the super-spinning case. The solution is algebraically general (Petrov-type I), and its horizons lie at the horizon radii of the Kerr black hole. The ergoregions, however, are strongly influenced by the Levi-Civita-like asymptotic structure, producing an effect akin to the magnetized Kerr--Newman and swirling solutions. Interestingly, while its static counterpart permits a Kerr--Schild representation, the Kerr--Levi-Civita metric does not admit such a formulation.

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arXiv2025

The dyonic Kerr-Schild ansatz

We develop a geometric extension of the Kerr-Schild ansatz that incorporates both electric and magnetic sectors of the Maxwell field in a unified framework, without resorting to duality rotations. We start observing that the known purely electric solution satisfies Maxwell's equations due to a closedness condition obeyed by the Kerr-Schild null congruence. From the associated local exactness property, we construct a new one-form naturally linked to the congruence as a sort of Poincaré dualization. This leads us to propose a geometrically motivated dyonic vector potential within the Kerr-Schild ansatz, defined as a superposition of an electric contribution along the congruence and a magnetic one that aligns to the dualized one-form. We then show that for a stationary and axisymmetric Kerr-Schild ansatz, the electrovac circularity theorem uniquely constrains not only the scalar profile of the metric, but also those associated to the electric-magnetic splitting of the gauge field. The resulting formalism provides a transparent derivation of the dyonic Kerr-Newman solution and extends naturally to the (A)dS case, highlighting the intrinsic interplay between geometry and matter in a Kerr-Schild setting.

hep-th↗

arXiv2025

Ultrarelativistic limit of the Kerr theorem

The original Kerr theorem provides the foundation for Kerr-Schild transformations by classifying all shear-free and geodesic null congruences in flat spacetime; the key ingredient of the Kerr-Schild ansatz. However, due to the high level of degeneracy of the outcome it is often less practical than its symmetric refinements, which may single out congruences leading to physically significant spacetimes by imposing relevant symmetries. An illustrative example is the stationary axisymmetric version of Kerr theorem which has been shown to lead directly and uniquely to the Kerr black hole in vacuum. In this work, we propose a new symmetric refinement of the Kerr theorem by boosting the stationary symmetry into its ultrarelativistic limit to achieve invariance under null translations, while keeping axisymmetry. Under these assumptions, the classification yields only two distinct congruences. The first congruence is covariantly constant and, through the Kerr-Schild ansatz, evidently yields an axisymmetric pp-wave. The vacuum axisymmetric profile of this pp-wave displays a logarithmic dependence on the polar radius, characteristic of the exterior gravitational field of the Bonnor light beam, and includes as a special case the Aichelburg-Sexl ultrarelativistic limit of the Schwarzschild black hole. The Kerr-Schild transformation of the second congruence gives rise to a non-trivial vacuum solution recently reported in [Phys. Rev. D 112, 024020 (2025)]. Using circularity and appropriately fixing the reparameterization invariance of the orthogonal manifold to the Killing fields, we show that the latter solution corresponds to the well-known Taub-NUT spacetime with planar topology. These results emphasize how symmetry-based refinements of the Kerr theorem constitute a powerful tool to constructing physically essential spacetimes.

gr-qc↗

arXiv2025

Rotating spacetimes with a free scalar field in four and five dimensions

We construct explicit rotating solutions in Einstein's theory of relativity with a minimally coupled free scalar field rederiving and finding solutions in four or five spacetime dimensions. These spacetimes describe, in particular, the back-reaction of a free scalar field evolving in a Kerr spacetime. Adapting the general integrability result obtained many years ago from Eriş-Gürses to simpler spherical coordinates, we present a method for rederiving the four-dimensional Bogush-Gal'tsov solution. Furthermore, we find the five-dimensional spacetime featuring a free scalar with two distinct angular momenta. In the static limit, these five-dimensional geometries provide higher-dimensional extensions of the Zipoy-Voorhees spacetime. Last but not least, we obtain the four-dimensional version of a Kerr-Newman-NUT spacetime endowed with a free scalar, where the scalar field's radial profile is extended to incorporate dependence on the polar angular coordinate. Our results offer a comprehensive analysis of several recently proposed four-dimensional static solutions with scalar multipolar hair, representing a unified study of spacetimes with a free scalar field in both four and five dimensions under the general integrability result of Eriş-Gürses.

gr-qc↗

arXiv2025

Cardy Entropy of Charged and Rotating Asymptotically AdS and Lifshitz Solutions with a Generalized Chern-Simons term

We consider a three-dimensional gravity model that includes (non-linear) Maxwell and Chern-Simons-like terms, allowing for the existence of electrically charged rotating black hole solutions with a static electromagnetic potential. We verify that a Cardy-like formula, based not on central charges but on the mass of the uncharged and non-spinning soliton, obtained via a double Wick rotation of the neutral static black hole solution, accurately reproduces the Bekenstein-Hawking entropy. Furthermore, we show that a slight generalization of this model, incorporating a dilatonic field and extra gauge fields, admits charged and rotating black hole solutions with asymptotic Lifshitz behavior. The entropy of these solutions can likewise be derived using the Cardy-like formula, with the Lifshitz-type soliton serving as the ground state. Based on these results, we propose a generalized Cardy-like formula that successfully reproduces the semiclassical entropy in all the studied cases.

hep-th↗

arXiv2025

Thermodynamics of four-dimensional regular black holes with an infinite tower of regularized curvature corrections

We study the thermodynamics of a class of four-dimensional black hole solutions arising from the compactification of a higher-curvature gravity theory featuring an infinite tower of Lovelock-type invariants. For planar horizons, we identify two distinct branches: a regular black hole supported by a nontrivial scalar field and a non-regular general relativity (GR) solution with a trivial scalar profile. Despite their differing geometries, both branches share the same free energy at fixed temperature, revealing a thermodynamic degeneracy naturally linked to the enhanced symmetry and scale invariance of the planar base manifold. In the case of a spherical horizon, even if the scalarized branch is not obtained in closed form, one can see that the degeneracy persists in the absence of the quadratic curvature contribution. On the other hand, if this quadratic term is taken into account, the regular solution may be thermodynamically favored (or not) over the Schwarzschild-AdS solution depending on the values of the coupling constants of the theory.

gr-qc↗

arXiv2025

Proca theory of four-dimensional regularized Gauss-Bonnet gravity and black holes with primary hair

We introduce a novel, well-defined four-dimensional regularized Gauss-Bonnet theory of gravity by applying a dimensional regularization procedure. The resulting theory is a vector-tensor theory within the generalized Proca class. We then consider the static spherically symmetric solutions of this theory and find black hole solutions that acquire primary hair. Notably, one of the integration constants associated with the Proca field is not manifest in the original metric, but under a disformal transformation of the seed solution, it emerges as a second, independent primary hair. This additional hair acts as an effective cosmological constant in the disformed geometry, even in the absence of a bare cosmological constant term. We further generalize these black hole solutions to include electromagnetic charges and effects related to the scalar-tensor counterparts of the regularized Gauss-Bonnet theory. We discuss the implications of our findings to observations.

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arXiv2025

Non-Noetherian conformal Cheshire effect

The gravitational Cheshire effect refers to the possibility of turning off the gravitational field while still leaving an imprint of the nonminimal coupling of matter to gravity. This allows nontrivial solutions in flat spacetime for which no backreaction is possible. The effect was originally shown to manifest itself for standard nonminimal couplings, such as those allowing conventional conformally invariant scalar fields. Recently, the most general scalar field action yielding a conformally invariant second-order equation was constructed, and entails a more involved nonminimal coupling explicitly breaking the conformal invariance of the action without spoiling it in the equation. We have succeeded in fully describing the spherically symmetric stealth solutions on flat spacetime supporting the Cheshire effect within this general non-Noetherian conformal theory. The allowed configurations are divided into two branches: The first one essentially corresponds to an extension of the solutions already known for the standard Noetherian conformal theory. The second branch is only possible due to the non-Noetherian conformal contribution of the action. The complete characterization of this branch is expressed by a nonlinear first-order partial differential equation. We have found the general solution of this equation using both seemingly new and well-established mathematical tools.

hep-th↗

arXiv2024

Electromagnetized black holes and swirling backgrounds in nonlinear electrodynamics: The ModMax case

This work focuses on constructing electromagnetized black holes and vortex-like backgrounds within the framework of the ModMax theory--the unique nonlinear extension of Maxwell's theory that preserves conformal symmetry and electromagnetic duality invariance. We begin by constructing the Melvin-Bonnor electromagnetic universe in ModMax through a limiting procedure that connects the spacetime of two charged accelerating black holes with that of a gravitating homogeneous electromagnetic field. Building on this result, we proceed to construct the Schwarzschild and C-metric Melvin-Bonnor black holes within the ModMax theory, representing the first black hole solutions embedded in an electromagnetic universe in the context of nonlinear electrodynamics. While the characteristics of the Melvin-Bonnor spacetime and some of its black hole extensions have been widely examined, we demonstrate for the first time that the Schwarzschild-Melvin-Bonnor configuration exhibits an unusual Kerr-Schild representation. Following this direction, we also unveil a novel Kerr-Schild construction for the spacetime of two accelerating black holes, drawing on the intrinsic relationship between the Melvin-Bonnor spacetime and the C-metric. Finally, we expand the spectrum of exact gravitational solutions within Einstein-ModMax theory by constructing a vortex-like background that coexists with the Melvin-Bonnor universe. In this process, the Taub-NUT spacetime in ModMax has played a crucial role. We present this Taub-NUT solution in a different gauge that facilitates the comparison with the Melvin-Bonnor-Swirling case.

gr-qc↗

arXiv2024

Extremal Kerr-Schild Form

We propose a novel ansatz, where the full black hole geometry is written as a linear in mass perturbation of the associated extremal black hole base. Contrary to its "standard" version, the corresponding "extremal Kerr-Schild form" is no longer restricted to special algebraic type spacetimes, and is applicable to numerous black hole solutions with matter, such as the charged Kerr-NUT-(A)dS spacetimes, black holes of $D=5$ minimal gauged supergravity, or the charged dilaton-axion rotating solutions. This ansatz is likely to find its applications in black hole perturbation theory, shed new light on the CFT description of non-extremal black holes, as well as be useful for constructing new exact solutions.

gr-qc↗

arXiv2024

Revisiting Buchdahl transformations: New static and rotating black holes in vacuum, double copy, and hairy extensions

This paper investigates Buchdahl transformations within the framework of Einstein and Einstein-Scalar theories. Specifically, we establish that the recently proposed Schwarzschild-Levi-Civita spacetime can be obtained by means of a Buchdahl transformation of the Schwarschild metric along the spacelike Killing vector. The study extends Buchdahl's original theorem by combining it with the Kerr-Schild representation. In doing so, we construct new vacuum-rotating black holes in higher dimensions which can be viewed as the Levi-Civita extensions of the Myers-Perry geometries. Furthermore, it demonstrates that the double copy scheme within these new generated geometries still holds, providing an example of an algebraically general double copy framework. In the context of the Einstein-Scalar system, the paper extends the corresponding Buchdahl theorem to scenarios where a static vacuum seed configuration, transformed with respect to a spacelike Killing vector, generates a hairy black hole spacetime. We analyze the geometrical features of these spacetimes and investigate how a change of frame, via conformal transformations, leads to a new family of black hole spacetimes within the Einstein-Conformal-Scalar system.

gr-qc↗

arXiv2024

Nonlinearly charging the conformally dressed black holes preserving duality and conformal invariance

We start this paper by concisely rederiving ModMax, which is nothing but the unique nonlinear extension of Maxwell's equations preserving conformal and duality invariance. The merit of this new derivation is its transparency and simplicity since it is based on an approach where the elusive duality invariance is manifest. In the second part, we couple the ModMax electrodynamics to Einstein gravity with a cosmological constant together with a standard conformal scalar field, and new stationary spacetimes with dyonic charges are found. These solutions are later used as seed configurations to generate nonlinearly charged (super-)renormalizably dressed spacetimes by means of a known generating method that we extend to include any nonlinear conformal electrodynamics. We end by addressing the issue of how to generalize some of these results to include the recently studied non-Noetherian conformal scalar fields, whose equation of motion still enjoys conformal symmetry even though its action does not. It turns out that the static non-Noetherian conformally dressed black holes also become amenable to being charged by ModMax.

hep-th↗

arXiv2024

Global conformal symmetry in scalar-tensor theories

We study a subclass of Horndeski gravity which has both global conformal and shift symmetries. Global symmetries are characterised by the presence of a conserved current which has been shown to be of particular importance for the integrability features of the theory at hand yielding numerous compact object solutions. We find the general conserved current associated to global conformal symmetry of Horndeski theories. We discuss some of its properties, how it can be conveniently broken by physically relevant terms and, show how it is related to that of shift symmetry when shift symmetry is present. Given our results, we consider a particular theory and demonstrate how the presence of symmetries provides integrability for the given black hole solution. We then find the charged extension of the solution thanks to the conformal invariance of the Maxwell action.

hep-th↗

arXiv2023

Endorsing black holes with beyond Horndeski primary hair: An exact solution framework for scalarizing in every dimension

This work outlines a straightforward mechanism for endorsing primary hair into Schwarzschild black holes, resulting in a unique modification within the framework of a special scalar-tensor theory, the so-called beyond Horndeski type. The derived solutions are exact, showcase primary hair with an everywhere regular scalar field profile, and continuously connect with the vacuum geometry. Initially devised to introduce primary hair in spherically symmetric solutions within General Relativity in any dimension, our investigation also explores the conditions under which spherically symmetric black holes in alternative gravitational theories become amenable to the endorsement of primary hair through a similar pattern. As a preliminary exploration, we embark on the process of endorsing primary hair to the Reissner-Nordström black hole. Subsequently, we extend our analysis to encompass spherically symmetric solutions within Lovelock and cubic quasitopological gravity theories.

hep-th↗

arXiv2023

From static to Vaidya solutions in scalar tensor theories

We consider some classes of Horndeski theories in four dimensions for which a certain combination of the Einstein equations within a spherical ansatz splits into two distinct branches. Recently, for these theories, some integrability and compatibility conditions have been established which have made it possible to obtain black hole solutions depending on a single integration constant identified as the mass. Here, we will show that these compatibility conditions can be generalized to accommodate a time dependence by promoting the constant mass to an arbitrary function of the retarded (advanced) time. As a direct consequence, we prove that all the static black hole solutions can be naturally promoted to non static Vaidya-like solutions. We extend this study in arbitrary higher dimensions where the pure gravity part is now described by the Lovelock theory and, where the scalar field action enjoyed the conformal invariance. For these theories, the splitting in two branches is also effective, and we show that their known static black hole solutions can as well be promoted to Vaidya-like solutions.

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