arXiv subjects

Mustapha Azreg-Aïnou

Publications and source records attributed to Mustapha Azreg-Aïnou.

At least 19 recordsLinked to original sources

arXiv2026

Gravitational and kinematic redshifts of black holes in nonlinear electrodynamics

Spacetimes arising from nonlinear electrodynamics (NED) are a good laboratory for studying both the nature of regular black hole (RBH) solutions and the imprints of nonlinear electromagnetic fields within this context. Over the past few decades, NED-sourced black hole (BH) spacetimes have attracted considerable attention, but electrically charged RBHs obtained in the so-called $F$ framework have been less addressed in the literature. We consider two electrically charged, fully regular members of the h-family that are solutions to general relativity minimally coupled to NED. Because of their potential astrophysical and astronomical applications, we mainly focus our investigation on the motion of photons and its implications for the gravitational and kinematic redshifts, as well as for the shadow radius, considering the effective geometry followed by photons in NED. Moreover, we consider the observational data for Sagittarius A$^{\star}$ and Messier 87$^{\star}$ BHs to impose some constraints on the charge-to-mass ratio of the fully RBHs. We obtain the general equations that govern the gravitational and kinematic redshifts of NED-sourced BH spacetimes. In particular, for fully RBHs with BH charge-to-mass ratios above some moderate value, we observe discrepancies in their physical and geometrical properties compared to those of the Reissner--Nordström (RN) BH. Therefore, our results indicate that it is possible to distinguish NED-based RBH solutions from RN BHs, from the perspective of gravitational and kinematic redshifts, suggesting potential astrophysical relevance.

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arXiv2026

Chaotic imprints of dark matter in extreme mass-ratio inspirals

Extreme mass-ratio inspirals (EMRIs) are among the most powerful probes of strong-field gravity and of the environments surrounding supermassive compact objects. Motivated by the expected presence of dark matter near galactic centers, we investigate the emergence and gravitational-wave imprints of chaotic dynamics in EMRIs evolving in non-vacuum spacetimes. Within a unified dynamical framework, we analyze test-particle motion in a broad class ofdark-matter-embedded geometries, including singular black holes, regular black holes, naked singularities, and Einstein-cluster configurations. We show that environmental perturbations generically break integrability in the strong-field regime, giving rise to chaotic motion whose onset, duration, and termination depend sensitively on horizon structure, core regularization, and matter distribution. Using the numerical Kludge approach, we demonstrate that chaotic trajectories produce systematic qualitative modifications of the emitted gravitational radiation, such as irregular amplitude modulation and loss of phase coherence, in contrast to the smooth, quasi-periodic waveforms generated by regular motion. Our results establish the robustness of chaos in environmentally perturbed EMRIs and provide a clear conceptual link between nonlinear orbital dynamics, spacetime structure, and observable gravitational-wave signatures.

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arXiv2025

Exact Taub-NUT-like Black Holes in Einstein-bumblebee gravity: their thermodynamics and thermodynamic topology

We re-derive an exact analytic three-parameter expressions for the non-rotating metric, describing a Taub-NUT-like black hole (BH), and its associated bumblebee field that are solutions to the Einstein-bumblebee gravity. We construct a consistence thermodynamics for the Taub-NUT-like BH and determine its thermodynamic topological class. The Lorentz symmetry breaking affects the mass and temperature of the BH but does not affect its thermodynamic topological classification.

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arXiv2025

Constraints on Kalb-Ramond Gravity from EHT Observations of Rotating Black Holes in Traceless Conformal Electrodynamics

We present a phenomenological study of rotating, charged black holes in Einstein gravity coupled to a traceless (conformal) matter sector formed by ModMax nonlinear electrodynamics and a Kalb-Ramond two-form that spontaneously breaks local Lorentz symmetry. Starting from a family of obtained static, Schwarzschild-like solutions with a traceless Kalb-Ramond sector, we construct the stationary, axisymmetric counterpart via the Newman-Janis algorithm. The resulting Newman-Kerr-like metric depends on four intrinsic parameters: the electric charge $Q$, the ModMax nonlinearity $γ$, the Lorentz-violation amplitude $\ell$ and the spin $a$. We analyze horizon structure and separatrices in parameter space, derive the null geodesic equations and obtain the photon capture boundary that defines the black hole shadow. Using ray-tracing, we compute shadow silhouettes and a suite of shadow observables (areal radius, characteristic radius $R_s$, distortion $δ$, oblateness $D$) and show how $γ$ and $\ell$ produce qualitatively distinct effects: $γ$ acts as a screening factor for the electromagnetic imprint, while $\ell$ introduces angular-dependent metric rescalings that deform shadow shape beyond simple size rescaling. We confront model predictions with EHT angular-radius measurements for M87$^*$ and Sgr A$^*$ and derive conservative bounds on the combinations of $(Q,γ,\ell,a)$. Our results identify an effective charge combination $Q_{\rm eff}\simeq e^{-γ}Q^{2}/(1-\ell)^{2}$ and demonstrate that modest $Q_{\rm eff}$ remains compatible with current EHT images while large $Q_{\rm eff}$ is progressively disfavored.

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arXiv2025

Epicyclic oscillations and accretion disk around a special Buchdahl-inspired spacetime

In this paper, we consider the Buchdahl-inspired spacetime metric and investigate its aspects using the quasiperiodic oscillations and the accretion disk due to the accreting matter. First, we focus on analyzing the geodesics of particles around the Buchdahl-inspired spacetime, together with the conserved quantities such as specific energy and angular momentum for massive particles orbiting on the innermost stable circular orbits (ISCOs). We show that the effect of the Buchdahl parameter $\tilde{k}$ increases as the radii of the ISCO orbits decrease, resulting in shifting orbits toward the central object compared to the Schwarzschild black hole case. We also consider astrophysical epicyclic oscillations and derive their general expressions using implications of circular motion of massive particles around the Buchdahl-inspired spacetime. Further, we explore the astrophysical implications of observational higher-frequency QPOs of the selected galactic microquasars of X-ray binary systems to obtain the best-fit constraints on the Buchdahl-inspired spacetime parameters. Finally, we consider the accretion disk around the Buchdahl-inspired spacetime using implications of the ISCO parameters that define the accretion disk's inner edge. We explore radiation properties of the accretion disk and redshifted image and intensity of a lensed accretion disk around the Buchdahl-inspired spacetime.

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arXiv2025

Two-sided NED black-hole, naked-singularity, and soliton solutions

We consider non-linear electrodynamics (NED) minimally coupled to general relativity. We derive novel electrically charged, spherically symmetric, black-hole solutions having, for some set of parameters, all their NED fields (the electric field and the square of the electromagnetic field) regular for all values of the radial coordinate. For another set of parameters, the NED fields and the Kretschmann scalar are regular as the radial coordinate runs from one spatial infinity to another spatial infinity without the metric being a wormhole. We obtain solutions that have two distinct or the same asymptotic behaviors (two spatial infinities) with equal or unequal ADM masses and solutions with always one horizon whatever the ratio of the electric charge to mass. We comment on some regularity theorems and generalize them to multi-valued NED Lagrangians. The derived regular solutions do not violate the Weak Energy Condition.

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arXiv2025

Spin precession frequencies of a test gyroscope around a naked singularity and quasi-periodic oscillations

Various studies show that the gravitational collapse of inhomogeneous matter clouds leads to naked singularity formation. We investigate here the spin precession frequency of a test gyroscope attached to a stationary observer in a rotating naked singularity spacetime. In the weak field limit, Lense-Thirring precession for rotating naked singularity and geodetic precession in the asymptotic limit for null naked singularity are found to be equal to that of a Kerr black hole and a Schwarzschild black hole, respectively. In addition, we can distinguish a rotating naked singularity and a Kerr naked singularity for an observer in the equatorial plane using spin precession. To this end, we have found the constraints on the parameters of rotating naked singularity by employing the Monte Carlo Markov Chain simulation and using the observation from five quasi-periodic sources within the relativistic precession model. Our analysis shows that the measurement of spin parameter estimate for GRO J1655-40 is in disagreement with the value found from the continuum-fitting method, while for XTEJ1859+226 and GRS 1915+105, it is inconsistent with spectral analysis results.

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arXiv2025

Thermodynamic Topological Classes of Family of Black Holes with NUT-Charge

{We introduce new analytical methods for treating black-hole thermodynamic topology, and thus depart from the usual treatment known in the literature. As application we investigate the universal thermodynamic topological classes of a family of black holes with NUT-charge. A charge-dependent thermodynamic topological transition from one class to another class is discussed.

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arXiv2025

Gravitational Lensing by a Dark Compact Object in Modified Gravity and Observational Constraints from Einstein Rings

In this manuscript, we provide a comprehensive study of gravitational lensing by dark compact objects predicted by a Modified Gravity (MOG) based on the Scalar-Vector-Tensor action, and the aim is to analyze new insights into the nature of gravitational interactions. We compute weak and strong deflection angles for the specified static, spherically symmetric MOG spacetime. Additionally, we dedicate a section to explore observational implications in the weak field limit. By employing a supermassive galactic black hole as a gravitational lens, we compare various parameters in MOG with those of the Schwarzschild black hole as lens in strong-field scenarios. Specifically, we model the black holes M87${^*}$ and Sgr A${^*}$ as lenses within the MOG framework, calculating the corresponding lensing coefficients and distortion parameters in the weak field regime.

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arXiv2025

Periodic orbits and their gravitational wave radiations around the Schwarzschild-MOG black hole

This article explores the motion of massive particles in the gravitational field of a modified gravity (MOG) black hole (BH), characterized by the parameter $α$. Using the Hamiltonian formalism, the geodesic equations and the effective potential governing particle trajectories are derived. Key features, including the innermost stable circular orbit (ISCO) and the innermost bound circular orbit (IBCO), are analyzed, revealing their dependence on the particle's energy, angular momentum, and the MOG parameter. In the extremal case, where $α=-1$, the event horizon merges with the Cauchy horizon, forming a distinctive BH configuration. Numerical methods are employed to compute periodic orbits in this spacetime, with a comparison drawn to the Schwarzschild BH. The findings indicate that for $α>0$, periodic orbits around Schwarzschild-MOG BH exhibit lower energy requirements than those in Schwarzschild spacetime, whereas for $-1<α<0$, the energy requirements are higher. Precessing orbits near periodic trajectories are also examined, offering insights into their complex dynamical behavior. Finally, the gravitational wave (GW) radiation from the periodic orbits of a test particle around the Schwarzschild-MOG BH is examined, generating intricate waveforms that provide insights into the gravitational structure of the system.

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arXiv2024

Gravitational Lensing and Image Distortion by Buchdahl Inspired Metric in $\mathcal{R}^2$ Gravity

We investigate gravitational lensing by \textit{special} Buchdahl inspired metric with the Buchdahl parameter $\tilde{k}$. In strong deflection limit, we derive the deflection angle analytically for the light rays that diverge as photons approach the photon sphere. These are then used in order to compute the angular image positions modeling supermassive black holes, Sgr A* and M87* as lenses. The Einstein rings for the outermost relativistic images are also depicted here alongside observational constraints on $\tilde{k}$ by the Einstein radius and lens mass. Constraints on $\tilde{k}$ are obtained modelling black holes ( Sgr A* and M87*) and Canarias Einstein ring. In weak deflection limit, the analytic expression of deflection angle of the subject asymptotically flat metric in $\mathcal{R}^2$ gravity is determined using the Gauss Bonnet theorem. Considering M87* as a lens, weak deflection angle is used to study the image magnification and image distortion for primary and secondary images. It is shown that image distortion satisfies the hypothesis of Virbhadra. Moreover, it is seen that our general expression of deflection angle reduces, as a special case, to the deflection angle of Schwarzschild metric in both weak and strong deflection limits.

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arXiv2024

Hamiltonian Formulation of Relativistic Magnetohydrodynamic Accretion on a General Spherically Symmetric and Static Black Hole: Quantum effects on Shock States

In this paper, our aim is to extend our earlier work [A. K. Ahmed et al., Eur. Phys. J. C (2016) 76:280] thereby investigating an axisymmetric plasma flow with the angular momentum onto a spherical black hole. To accomplish that goal, we focus on the case that the ideal magnetohydrodynamic approximation is valid and utilizing certain conservation laws which arise from certain symmetries of the system. After formulating a Hamiltonian of the physical system, we solve the Hamilton equations and look for critical solutions of (both in and out) flows. Reflecting the difference from the Schwarzschild spacetime, the positions of sonic points (fast magnetosonic point, slow magnetosonic point, Alfvén point) are altered. We explore several kinds of flows including critical, non-critical, global, magnetically arrested and shock induced. Lastly we analyze the shock states near a specific quantum corrected Schwarzschild black hole and deduce that quantum effects do not favor shock states by pushing the shock location outward.

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arXiv2024

Revisiting Weak Energy Condition and wormholes in Brans-Dicke gravity

It is known that the formation of a wormhole typically involves a violation of the Weak Energy Condition (WEC), but the reverse is not necessarily true. In the context of Brans-Dicke gravity, the $\textit{generalized}$ Campanelli-Lousto solution, which we shall unveil in this paper, demonstrates a WEC violation that coincides with the appearance of $\textit{unbounded}$ sheets of spacetime within the "interior" section. The emergence of a wormhole in the "exterior" section is thus only an indirect consequence of the WEC violation. Additionally, we use the generalized Campanelli-Lousto solution to construct a Kruskal-Szekeres diagram, which exhibits a "gulf" sandwiched between the four quadrants in the diagram, a novel feature in Brans-Dicke gravity. Overall, our findings shed new light onto a complex interplay between the WEC and wormholes in the Brans-Dicke theory.

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arXiv2024

Observational test of ${\cal R}^{2}$ spacetimes with the S2 star in the Milky Way galactic center

A novel class of vacuum metrics expressible in analytical form was recently found for pure $\mathcal R^2$ gravity, based on a groundwork put forth by Buchdahl in 1962. These Buchdahl-inspired solutions offer a practical framework for testing ${\cal R}^2$ gravity through empirical observations. Within a subclass of asymptotically flat Buchdahl-inspired vacuum spacetimes, we identified a parameter $ε$ measuring the deviation from the classic Schwarzschild metric, which corresponds to $ε=0$. In this paper, we employ observational data from the S2 star's orbit around Sgr A* in the Milky Way galactic center and perform Monte Carlo Markov Chain simulations to probe the effects of the new metrics on the orbit of the S2 star. Our analysis presented herein reports a range at 95\% confidence level on the deviation parameter as $ε\in(-0.6690,\ 0.4452)$. While no decisive evidence either in favor or in disfavor of the asymptotically flat Buchdahl-inspired spacetimes has been achieved, the obtained bound is compatible with the tighter results using other data of different nature as recently reported in Eur.\,Phys.\,J.\,C $\bf 84$, 330 (2024). As a meaningful test probing into a strong-field regime, our present study calls for further observations with prolonged period and improved accuracy in order to tighten the bound for $ε$ using the S2 star orbit.

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arXiv2024

Joshi--Malafarina--Narayan singularity in weak magnetic field

The importance and significance of magnetic fields in the astrophysical scenario is well known. Many domains of astrophysical black hole physics such as polarized shadow image, high energy emitting processes and jet formation are dependent on the behavior of the magnetic fields in the vicinity of the compact objects. In light of this, we determine the master equation and master differential equation that determine the spatial behavior of the magnetic field inside a matter distribution or vacuum region, of general spherically symmetric metric, which is immersed in a test magnetic field. We also investigate here the case of JMN-1 singularity immersed in a uniform weak magnetic field and determine the behavior of magnetic fields by defining electromagnetic four potential vector. We find that the tangential component of the magnetic field is discontinuous at the matching surface of the JMN-1 singularity with the external Schwarzschild metric, resulting in surface currents. We define the covariant expression of surface current density in this scenario. We also analyze the behavior of center-of-mass energy of two oppositely charged particles in the geometry of the magnetized JMN-1 singularity. We briefly discuss the possible scenarios which would possess a discontinuous magnetic field and implications of the same and future possibilities in the realm of astrophysics are indicated.

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arXiv2024

Observational tests of asymptotically flat ${\cal R}^{2}$ spacetimes

A novel class of Buchdahl-inspired metrics with closed-form expressions was recently obtained based on Buchdahl's seminal work on searching for static, spherically symmetric metrics in ${\cal R}^{2}$ gravity in vacuo. Buchdahl-inspired spacetimes provide an interesting framework for testing predictions of ${\cal R}^{2}$ gravity models against observations. To test these Buchdahl-inspired spacetimes, we consider observational constraints imposed on the deviation parameter, which characterizes the deviation of the asymptotically flat Buchdahl-inspired metric from the Schwarzschild spacetime. We utilize several recent solar system experiments and observations of the S2 star in the Galactic center and the black hole shadow. By calculating the effects of Buchdahl-inspired spacetimes on astronomical observations both within and outside of the solar system, including the deflection angle of light by the Sun, gravitational time delay, perihelion advance, shadow, and geodetic precession, we determine observational constraints on the corresponding deviation parameters by comparing theoretical predictions with the most recent observations. Among these constraints, we find that the tightest one comes from the Cassini mission's measurement of gravitational time delay.

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arXiv2023

A stationary axisymmetric vacuum solution for pure $R^2$ gravity

The closed-form expression for pure $\mathcal{R}^{2}$ vacuum solution obtained in Phys. Rev. D \textbf{107}, 104008 (2023) lends itself to a generalization to axisymmetric setup via the modified Newman--Janis algorithm. We adopt the procedure put forth in Phys. Rev. D \textbf{90}, 064041 (2014) bypassing the complexification of the radial coordinate. The procedure presumes the existence of Boyer-Lindquist coordinates. Using the Event Horizon Telescope Collaboration results, we model the central black hole M87{*} by the thus obtained exact rotating metric, depending on the mass, rotation parameter and a third dimensionless parameter. The latter is constrained upon investigating the shadow angular size assuming mass and rotation parameters are those of M87{*}. Stability is investigated.

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arXiv2023

On the parameters of the spherically symmetric parametrized Rezzolla-Zhidenko spacetime through solar system tests, orbit of S2 star about Sgr A$^\star$, and quasiperiodic oscillations

In this paper, we find the higher order expansion parameters $α$ and $λ$ of spherically symmetric parametrized Rezzolla--Zhidenko (PRZ) spacetime by using its functions of the radial coordinate. We subject the parameters of this spacetime to classical tests including weak gravitational field effects in Solar System, observations of the S2 star located in the star cluster close to the Sgr A$^{\star}$ and of the frequencies of selected microquasars. Based on this spherically symmetric spacetime we perform the analytic calculations for Solar System effects like perihelion shift, light deflection, and gravitational time delay so as to determine limits on the parameters by using observational data. We restrict our attention to the limits on the two higher order expansion parameters $α$ and $λ$ that survive at the horizon or near the horizon of spherically symmetric metrics. The properties of these two small parameters expansion in PRZ parametrization are discussed. We further apply the Monte Carlo Markov Chain (MCMC) simulations to analyze and obtain the limits on the expansion parameters by using observations of phenomena of the S2 star. Finally, we consider the epicyclic motions and derive analytic expressions of the epicyclic frequencies. Applying these expressions to the quasiperiodic oscillations (QPOs) of selected microquasars allows us to set further limits on the parameters of the PRZ spacetime. Our results demonstrate that the higher order expansion parameters can be given in the range $α\, ,λ=(-0.09\, , 0.09)$ and of order $\sim 10^{-2}$ as a consequence of three various tests and observations.

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