arXiv subjects

J. R. Villanueva

Publications and source records attributed to J. R. Villanueva.

At least 19 recordsLinked to original sources

arXiv2026

Dark-Sector Effects on the Phase Structure of Nonlinear Magnetic AdS Black Holes

We investigate the effects of perfect fluid dark matter (PFDM) and a dark-energy field on the phase structure of a nonlinear magnetically charged Anti--de Sitter (NLMC--AdS) black hole. The full thermodynamic system is analyzed numerically, while exact critical points are obtained for the limiting cases. Small--large black hole (SBH/LBH) phase transitions emerge in both the limiting geometries and the full solution within the quintessence regime. Moreover, the critical ratio $ρ_c=P_c v_c/T_c$ differs from the standard Reissner--Nordström--AdS (RN--AdS)/van der Waals (vdW) value, $ρ_c=3/8$. Our results show that the dark-sector parameters significantly influence the strength and persistence of the first-order transition. In the quintessence regime, a stronger dark-energy contribution enhances the swallow-tail structure of the Gibbs free energy and increases the latent heat associated with SBH/LBH coexistence. In contrast, a larger magnitude of the PFDM parameter $|λ|$ progressively suppresses the swallow-tail structure and the corresponding first-order transition, eventually leading to a single-phase regime. In the phantom regime, the system instead exhibits spinodal behavior without phase coexistence. We also find that any nonzero $λ$ prevents the formation of a regular magnetic core. Finally, geometrothermodynamics (GTD) reproduces the phase structure through singularities of the thermodynamic curvature, while the associated critical scaling is consistent with results reported for black holes, cosmological horizons, and real fluids, pointing toward a broader universality of thermodynamic critical behavior.

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arXiv2026

Inverse Reconstruction of Causal Nonlinear Electrodynamics: Functional Families, Spectral Constraints, and Single-Horizon Black Holes

Nonlinear electrodynamics (NLED) admits many causal theories, so causality alone does not provide a unique selection principle. We formulate an inverse construction in which constitutive integrability, the Maxwell weak-field limit, and causal propagation are imposed before either a Lagrangian or a spacetime geometry is chosen. An affine-separable reduction of the two-invariant Plebański class yields an infinite-dimensional causal family $\mathcal{C}_X$, characterized by a bounded logarithmic index; Born-Infeld is its unique self-dual member, while generic members are birefringent. On the magnetic axis, complete monotonicity gives a positive spectral representation. Finite monopole self-energy is equivalent to the existence of the spectral moment of order $-1/4$, whereas global magnetic causality restricts the support. Generalized-gamma spectra are simultaneously causal and finite-energy precisely for $1/4<γ\le1/2$, independently of the shape parameter, and a separate criterion determines when the magnetic law admits a causal two-invariant completion. After coupling to Einstein gravity, a positive magnetic response and characteristic factor, finite self-energy, and nonnegative residual mass imply a strictly increasing metric function, excluding more than one positive horizon; positive residual mass guarantees a unique horizon. The two optical metrics of $\mathcal{C}_X$ remain Lorentzian with overlapping timelike cones, establishing symmetric hyperbolicity of the electromagnetic subsystem. Thus inverse matter selection connects local causal consistency to global black-hole structure without prescribing the geometry.

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arXiv2026

A causal magnetic black hole with finite self-energy

We construct a nonlinear electrodynamics (NLED) model for a static magnetic black hole. Rather than imposing a regular center, we require a Maxwell weak-field limit, finite magnetic self-energy, a positive and subluminal electromagnetic cone, the standard energy conditions, and a static exterior that satisfies known sufficient stability criteria. A positive mixture of power kernels restricts the exponent to $1/4<γ\leq1/2$. For the minimal two-kernel model, with $γ_1=1/3$ and $γ_2=1/2$, the field equations admit an exact solution in terms of incomplete beta functions. For the branches with nonnegative Schwarzschild mass parameter $M_0$, the metric function is strictly increasing, so there is at most one positive-radius horizon and no inner Cauchy horizon. We construct the maximal extension and show that the black-hole, horizonless, and critical branches have spacelike, timelike, and null singularities, respectively. The representative black-hole families have positive temperature and negative fixed-charge heat capacity. Electromagnetic waves split into ordinary and extraordinary optical branches. We calculate their photon spheres, shadow radii, instability rates, and illustrative Event Horizon Telescope size bands. We also construct ISCO-truncated thin-disk images. The full images remain close, but jointly normalized residual maps and radial profiles reveal a coherent branch-dependent shift near the lensed inner edge and the critical region. The extraordinary branch moves the critical curve outward and partly compensates the shadow reduction caused by magnetic charge.

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arXiv2026

Constitutive birefringence and critical curves in the rotating García--Díaz black hole

We study high-frequency electromagnetic propagation in the rotating García--Díaz solution of Einstein gravity coupled to NLED. In this system, light is not governed only by the null cone of the spacetime metric, because the NLED field also behaves as an optical medium whose constitutive response determines the physical optical cones. Starting from the mixed electromagnetic potentials, we project the field $F$ and the excitation $P$ on a principal tetrad and obtain the aligned scalars $E$, $B$, $D$ and $H$. These scalars allow us to reconstruct the regular local constitutive branch connected with Maxwell theory through the map $(D,B)\mapsto(E,H)$. We then insert the resulting response matrix into the Fresnel characteristic problem. At the perturbative order considered here, the Fresnel quartic factorizes into two quadratic branches, each defining an effective optical metric. Both optical metrics admit Carter-type separation of the Hamilton--Jacobi equation and possess their own radial and angular potentials, critical constants and unstable critical families. By projecting these families onto the celestial sphere of a finite-distance observer, we obtain two critical contours, $Γ_+$ and $Γ_-$, which coincide in the Maxwell limit and split when the nonlinear constitutive response is active. We quantify this birefringent splitting through the maximum angular separation, the relative diameter shift and the normalized birefringent width. Numerical scans over the nonlinear coupling, spin and observer inclination show that the splitting is generated by the constitutive response, redistributed by rotation and stable under local projection changes within the perturbative domain. This provides a direct geometrical link between the local NLED response and a polarization-dependent critical structure on the observer screen.

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arXiv2026

Interacting Generalized Chaplygin-Jacobi gas: Thermodynamics approach

This work investigates a cosmological model featuring an interaction between dark energy and dark matter, where the dark energy component is described by the Generalized Chaplygin-Jacobi gas (GCJG). In this study, we establish a system in which the GCJG and a pressureless dark matter fluid exchange energy via a linear interaction term, $Q \propto ρ_x$, being $ρ_{x}$ the dark energy density. By solving the conservation equations, we derive analytical expressions for the evolution of the dark energy and dark matter densities. The thermodynamic properties of this interacting system are then thoroughly analyzed. The thermodynamic analysis reveals that both dark components maintain positive temperatures, ensuring stability. Notably, the dark energy component transitions to a phantom regime in the past, a feature of interest for recent cosmological observations, without violating thermodynamic principles. The total entropy production is shown to be in agreement with the second law of thermodynamics. Furthermore, an analysis of the specific heats suggests that while the dark matter sector remains thermodynamically stable, the dark energy sector undergoes a late-time phase transition, consistent with its entering into the phantom domain at effective level.

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arXiv2025

Quasinormal modes of a static black hole in nonlinear electrodynamics

We investigate the axial electromagnetic quasinormal modes of a static, asymptotically Anti--de Sitter (AdS) black hole sourced by a nonlinear electrodynamics model of Plebański type. Starting from the master equation governing axial perturbations, we impose ingoing boundary conditions at the event horizon and normalizable (Dirichlet) behavior at the AdS boundary. Following the approach of Jansen, we recast the radial equation into a linear generalized eigenvalue problem by using an ingoing Eddington--Finkelstein formulation, compactifying the radial domain, and regularizing the asymptotic coefficients. The resulting problem is solved using a Chebyshev--Lobatto pseudospectral discretization. We compute the fundamental quasinormal mode frequencies for both the purely electric ($Q_m=0$) and purely magnetic ($Q_e=0$) sectors, emphasizing the role of the nonlinearity parameter $β$ and the effective charge magnitude $Q$. Our results show that increasing either $β$ or $Q$ raises both the oscillation frequency $ω_R$ and the damping rate $-ω_I$, leading to faster but more rapidly decaying ringdown profiles. Nonlinear electrodynamics breaks the isospectrality between electric and magnetic configurations: magnetic modes are systematically less oscillatory and more weakly damped than their electric counterparts. For sufficiently large $β$ and small $Q_m$, the fundamental mode becomes purely imaginary ($ω_R \approx 0$), in agreement with the absence of a trapping potential barrier in this regime. These findings reveal qualitative signatures of nonlinear electromagnetic effects on black hole perturbations and may have implications for high-field or high-charge astrophysical environments.

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arXiv2025

Cosmological evolution driven by polytropic fluids in an inhomogeneous spacetime

Addressing the late-time accelerated expansion of the universe, known as the "dark energy problem", remains a central challenge in cosmology. While the cosmological constant is the standard explanation, alternative models such as quintessence, phantom fluids, and Chaplygin gas have been proposed. This work investigates the generalized Chaplygin gas (GCG) model, which is characterized by a polytropic equation of state. We explore this model within the framework of an anisotropic fluid, by means of a metric that reduces to the standard form of the Friedmann-Lemaître-Robertson-Walker (FLRW) spacetime at cosmological scales. To assess the model's viability, we derive analytical expressions for the scale factor, the Hubble parameter, and the deceleration parameter. Finally, the model is tested against observational data to constrain its parameters and evaluate its consistency.

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arXiv2025

Cosmic slowing down of acceleration with the Chaplygin-Jacobi gas as a dark fluid?

A particular generalization of the Chaplygin inflationary model, using the formalism of Hamilton-Jacobi and elliptic functions, results in a more general non-linear Chaplygin-type equation of state (Chaplygin-Jacobi model). We investigate the implementation of this model as a dark energy (DE) fluid to explain the recent acceleration of the universe. Unlike $Λ$CDM and other Chaplygin-like fluids, where the final fate of the universe is an eternal de Sitter (dS) phase, the dynamics of this model allows for the possibility of a decelerating phase in the future, following the current accelerating phase. In other words, a transient acceleration arises, accounting for the recently claimed slowing down phenomenon. This Chaplygin-Jacobi model shows important differences compared to the standard and generalized Chaplygin gas models. Additionally, we perform a Markov Chain Monte Carlo (MCMC) analysis using several datasets, including Type Ia Supernovae (SNIa), Cosmic Chronometers (CC), Fast Radio Bursts (FRBs), and Baryon Acoustic Oscillations (BAO) to examine the observational viability of the model. Our results indicate that, although a transient phase of accelerated expansion is supported by current observations in the context of the Chaplygin-Jacobi model, this model is strongly disfavored in comparison with $Λ$CDM.

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arXiv2024

Null geodesics around a black hole with weakly coupled global monopole charge

In this paper, we study an asymptotically flat black hole spacetime with weakly nonminimally coupled monopole charge. We analytically and numerically investigate light ray propagation around such a black hole by employing the common Lagrangian formalism. Our analysis encompasses both radial and angular geodesics, for which we present analytical solutions in terms of incomplete Lauricella hypergeometric functions. Additionally, we explore the impact of the coupling constant on geodesic motion. Based on observations from the Event Horizon Telescope, we constrain the black hole parameters, resulting in a coupling constant range of $-0.5\lesssim α\lesssim 0.5$. Throughout our analysis, we simulate all possible trajectories and, where necessary, perform numerical inversion of the included integrals.

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arXiv2024

Black hole in a generalized Chaplygin-Jacobi dark fluid: shadow and light deflection angle

We investigate a generalized Chaplygin-like gas with an anisotropic equation of state, characterizing a dark fluid within which a static spherically symmetric black hole is assumed. By solving the Einstein equations for this black hole spacetime, we explicitly derive the metric function. The spacetime is parametrized by two critical parameters, $\mathcal{B}$ and $α$, which measure the deviation from the Schwarzschild black hole and the extent of the dark fluid's anisotropy, respectively. We explore the behavior of light rays in the vicinity of the black hole by calculating its shadow and comparing our results with the Event Horizon Telescope observations. This comparison constrains the parameters to $0 \leq \mathcal{B} < 0.03$ and $0 < α< 0.1$. Additionally, we calculate the deflection angles to determine the extent to which light is bent by the black hole. These calculations are further utilized to formulate possible Einstein rings, estimating the angular radius of the rings to be approximately $37.6\,\mathrm{μas}$. Throughout this work, we present analytical solutions wherever feasible, and employ reliable approximations where necessary to provide comprehensive insights into the spacetime characteristics and their observable effects.

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arXiv2023

Timelike geodesics for five-dimensional Schwarzschild and Reissner-Nordström Anti-de Sitter black holes

The timelike structure of the five-dimensional Schwarzschild and Reissner-Nordström Anti-de Sitter black holes is studied in detail. Different kinds of motion are allowed and studied by using an adequate effective potential. Then, by solving the corresponding equations of motion, several trajectories and orbits are described in terms of Weierstrass elliptic functions and elementary functions for neutral particles.

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arXiv2023

Spherical particle orbits around a rotating black hole in massive gravity

In this paper, we present a rotating de Rham-Gabadadze-Tolley black hole with a positive cosmological constant in massive gravity, achieved by applying a modified Newman-Janis algorithm. The black hole exhibits stable orbits of constant radii, prompting a numerical study on the behavior of the solutions to a nonic equation governing the radii of planar orbits around the black hole. Additionally, we investigate the stability of orbits near the event horizon and provide a comprehensive analytical examination of the solutions to the angular equations of motion. This is followed by simulating some spherical particle orbits around the black hole.

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arXiv2023

Carathéodory's thermodynamics of the Schwarzschild black hole surrounded by quintessence

In this paper, we apply the Carathéodory's method of geometrothermodynamics to investigate the behavior of the main thermodynamic parameters associated with a Schwarzschild black hole surrounded by quintessence. The corresponding Pfaffian form is constructed by means of the Schwarzschild radius $r_s$, and the quintessential radius $r_γ$ as independent variables. This form is then used to characterize the thermodynamic manifold. The homogeneity of the system allows for the recognition of the empirical temperature and entropy, and thus, connects with the usual laws of thermodynamics. In particular, we show that the Helmholtz and Gibbs free energies lead to the same value for the Schwarzschild black hole, in the case of the vanishing cosmological term.

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arXiv2023

Spherical photon orbits around a rotating black hole with quintessence and cloud of strings

In this paper, we calculate the analytical solutions for the radii of planar and polar spherical photon orbits around a rotating black hole that is associated with quintessential field and cloud of strings. This includes a full analytical treatment of a quintic that describes orbits on the equatorial plane. Furthermore, The radial profile of the impact parameters is studied and the radii corresponding to the extreme cases are derived. For the more general cases, we also discuss the photon regions that form around this black hole. To simulate the orbits that appear in different inclinations, we analytically solve the latitudinal and azimuth equations of motion in terms of the Weierstrassian elliptic functions, by considering the radii of spherical orbits, in their general form, as the initial conditions. The period and the stability conditions of the orbits are also obtained analytically.

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arXiv2022

Study of null and time-like geodesics in the exterior of a Schwarzschild black hole with quintessence and cloud of strings

Recently, an analytical study of radial and circular orbits for null and time-like geodesics that propagate in the spacetime produced by a Schwarzschild black hole associated with cloud of strings, in a universe filled by quintessence, has been done in Ref. \cite{Mustafa:2021}. In this paper, we complete the aforementioned study by investigating possible analytical solutions to the equations of motion for other types of bound orbits, besides taking into account the cases of unbound orbits. This requires an extensive study of the corresponding effective potentials that categorize the test particle motion. We follow the standard Lagrangian dynamics to parametrize the radial and angular geodesics and the resultant (hyper-)elliptic integrals of motion are treated accordingly. We also simulate the orbits which correspond to different levels of energy in the effective potentials.

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arXiv2021

Analytical study of light ray trajectories in Kerr spacetime in the presence of an inhomogeneous anisotropic plasma

We calculate the exact solutions to the equations of motion that govern the light ray trajectories as they travel in a Kerr black hole's exterior that is considered to be filled with an inhomogeneous and anisotropic plasmic medium. This is approached by characterizing the plasma through conceiving a radial and an angular structure function, which are let to be constant. The description of the motion is carried out by using the Hamilton-Jacobi method, that allows defining two effective potentials, characterizing the evolution of the polar coordinates. The elliptic integrals of motion are then solved analytically, and the evolution of coordinates is expressed in terms of the Mino time. This way, the three-dimensional demonstrations of the light ray trajectories are given respectively.

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arXiv2021

The role of elliptic integrals in calculating the gravitational lensing of a charged Weyl black hole surrounded by plasma

In this paper, we mainly aim at highlighting the importance of (hyper-)elliptic integrals in the study of gravitational effects caused by strongly gravitating systems. For this, we study the application of elliptic integrals in calculating the light deflection as it passes a plasmic medium, surrounding a charged Weyl black hole. To proceed with this, we consider two specific algebraic ansatzes for the plasmic refractive index, and we characterize the photon sphere for each of the cases. This will be used further to calculate the angular diameter of the corresponding black hole shadow. We show that the complexity of the refractive index expressions, can result in substantially different types of dependencies of the light behavior on the spacetime parameters.

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arXiv2021

Probing the parameters of a Schwarzschild black hole surrounded by quintessence and cloud of strings through four standard astrophysical tests

In this paper, we concern about applying general relativistic tests on the spacetime produced by a static black hole associated with cloud of strings, in a universe filled with quintessence. The four tests we apply are precession of the perihelion in the planetary orbits, gravitational redshift, deflection of light, and the Shapiro time delay. Through this process, we constrain the spacetime's parameters in the context of the observational data, which results in about $\sim 10^{-9}$ for the cloud of strings parameter, and $\sim 10^{-20}$ m$^{-1}$ for that of quintessence. The response of the black hole to the gravitational perturbations is also discussed.

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