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E. Contreras

Publications and source records attributed to E. Contreras.

At least 19 recordsLinked to original sources
arXiv2025

Hyperbolic polytrope

In this work, we study self-gravitating objects that obey a polytropic equation of state in hyperbolic symmetry. Specifically, we describe in detail the steps to derive the Lane-Emden equation from the structure equations of the system. To integrate the equations numerically, we propose the Cosenza-Herrera-Esculpi-Witten anisotropy and study the cases $\gamma \ne 1$ and $\gamma = 1$ in the parameter space of the models. We find that the matter sector exhibits the usual and expected behavior for certain values in this parameter space: energy density (in absolute value) and radial pressure are decreasing functions and vanish at the surface, while the mass function is increasing toward the surface. We find that the anisotropy of the system is positive and decreasing, consistent with the behavior of the radial pressure, which reaches a local minimum at the surface (i.e., the pressure gradient is zero at the surface). We also study the compactness of the dense objects as a function of the polytropic index and obtain that it has an upper bound given by the maximum value it reaches for a certain $n$. Some extensions of the work and future proposals are discussed.

gr-qc↗
arXiv2025

A topological invariant in the context of the loop representation of the massive Kalb-Ramond-Klein-Gordon model

We employ the Dirac procedure to quantize the self-dual massive Kalb-Ramond-Klein-Gordon model in $2+1$ dimensional spacetimes. The canonical fields are expressed in terms of $2$-surfaces and signed points, ensuring the automatic realization of the quantum algebra. As the duality rotation preserving the action can be implemented infinitesimally, we derive the conserved quantity that generates the transformation. Given that such a generator is a two dimensional topological quantity, its representation in terms of geometrical operators yields a two dimensional invariant (reminiscent of a projection of Gauss's law in electrodynamics), which encodes the same information of the well-known winding number.

hep-th↗
arXiv2025

Fractional Einstein field equations in $2+1$ dimensional spacetime

In this work, we introduce a new fractional derivative that modifies the conventional Riemann-Liouville operator to obtain a set of fractional Einstein field equations within a 2+1 dimensional spacetime by assuming a static and circularly symmetric metric. The main reason for introducing this new derivative stems from addressing the divergence encountered during the construction of Christoffel symbols when using the Caputo operator and the appearance of unwanted terms when using the Riemann-Liouville derivative because of the well-known fact that its action on constants does not vanish, as expected. The key innovation of the new operator ensures that the derivative of a constant is zero. As a particular application, we explore whether the Ba\~nados-Teitelboim-Zanelli black hole metric is a solution to fractional Einstein equations. Our results reveal that for values of the fractional parameter close to one, the effective matter sector corresponds to a charged BTZ solution with an anisotropic cosmological constant.

gr-qc↗
arXiv2025

Traversable wormholes with multiple unstable critical curves

The number and position of unstable critical curves, as well as the nature of the accretion disk around compact objects, play a fundamental role in their optical appearance. Identifying differences in the optical spectrum of various observed compact objects can help classify them as black holes or black hole mimickers, such as traversable wormholes. Although multiple unstable critical curves have been reported to appear in asymmetric traversable wormholes, in this work we construct symmetric traversable wormholes with multiple unstable critical curves. We propose a general rational redshift function that allows us to trace the number of critical points of the effective potential and determine their nature as maxima or minima. The ray tracing method is used to study the trajectories of massless particles, particularly their behavior near the unstable critical points. Finally, a thin accretion disk model is implemented to analyze the optical appearance of the solution.

gr-qc↗
arXiv2024

The four-components link invariant in the framework of topological field theories

In this work, we undertake a perturbative analysis of the topological non-Abelian Chern-Simons-Wong model with the aim to explicitly construct the second-order on-shell action. The resulting action is a topological quantity depending solely on closed curves, so it correspond to an analytical expression of a link invariant. Additionally, we construct an Abelian model that reproduces the same second-order on-shell action as its non-Abelian Chern-Simons-Wong counterpart so it functions as an intermediate model, featuring Abelian fields generated by currents supported on closed paths. By geometrically analyzing each term, we demonstrate that this topological invariant effectively detects the knotting of a four-component link.

hep-th↗
arXiv2024

Spontaneous scalarization in Einstein--power--Maxwell--scalar models

We study the spontaneous scalarization of charged black holes in Einstein's gravity minimally coupled to power--Maxwell electrodynamics which, in turn, is non--minimally coupled to a real scalar field. We point out the existence of a specific power for which the scalarized solution is well-behaved, and entropically preferred in comparison to the scalar-free charged black hole solution.

gr-qc↗
arXiv2023

A fractional matter sector for general relativity

In this work, we construct a fractional matter sector for general relativity. In particular, we propose a suitable fractional anisotropy function relating both the tangential and radial pressure of a spherically symmetric fluid based on the Gr\"unwald-Letnikov fractional derivative. The system is closed by implementing the polytropic equation of state for the radial pressure. We solve the system of integro-differential equations by Euler's method and explore the behavior of the physical quantities, namely, the normalized density energy, the normalized mass function, and the compactness.

gr-qc↗
arXiv2023

Geodesic analysis and steady accretion on a traversable wormhole

In this work, we analyze the behavior of light and matter as they pass near and through a traversable wormhole. In particular, we study the trajectories of massive and massless particles and the dust accretion around a traversable wormhole previously reported in Eur. Phys. J. C \textbf{82} (2022) no.7, 605. For massive particles, we integrate the trajectory equation for ingoing and outgoing geodesics and classify the orbits of particles scattered by the wormhole in accordance with their asymptotic behavior far from the throat. We represent all the time--like trajectories in an embedding surface where it is shown explicitly the trajectories of i) particles that deviate from the throat and remain in the same universe, ii) particles that traverse the wormhole to another universe, and iii) particles that get trapped in the wormhole in unstable circular orbits. For the massless particles, we numerically integrate the trajectory equation to show the ray-tracing around the wormhole specifying the particles that traverse the wormhole and those that are only deviated by the throat. For the study of accretion, we consider the steady and spherically symmetric accretion of dust. Our results show that the wormhole parameters can significantly affect the behavior of light and matter near the wormhole. Some comparisons with the behavior of matter around black holes are made.

gr-qc↗
arXiv2023

A vacuum solution of modified Einstein equations based on fractional calculus

In this work, we construct a modified version of the Einstein field equations for a vacuum and spherically symmetric spacetime in terms of the Riemann-Louville fractional derivative. The main difference between our approach and other works is that we ensure that both the classical differential equations and the classical solutions are exactly recovered in the limit when the fractional parameter is turned off. We assume that the fractional equations are valid inside and near the horizon radius and match the classical solution at the horizon. Our approach resembles the Herrera--Witten strategy shown in Adv.High Energy Phys. 2018 (2018) 3839103, where the authors constructed an alternative black hole solution by assuming that inside the horizon the spacetime is hyperbolically symmetric and matches the classical spherically symmetric exterior solution at one point at the horizon. We obtain that, depending on the value of the fractional parameter, the solutions can be interpreted as a regular black hole or a gravatar. As a final step, we compute the fractional curvature scalars and show that the solution is regular everywhere inside the horizon.

gr-qc↗
arXiv2023

A static and spherically symmetric hairy black hole in the framework of the Gravitational Decoupling

In this work we construct a static and spherically symmetric black hole geometry supported by a family of generic mono-parametric sources thorough the Gravitational Decoupling. The parameter characterizing the matter sector can be interpreted as hair which cannot be associated to any global charge. Although the solution is constructed by demanding the weak energy condition, we find that the resulting matter sector satisfies all the energy conditions at and outside the horizon. We study the effect of the hair on the periastron advance and the gravitational lensing of the black hole. We estimate the best WKB order to compute the quasinormal frequencies for scalar, vector and tensor perturbation fields.

gr-qc↗
arXiv2023

Double relativistic master polytrope for anisotropic matter

We present a detailed analysis of a general relativistic static spherical symmetric distribution in which both the radial and tangential pressures follow a master polytropic equation of state that generalizes the standard treatment and avoids the appearance of singularities in the system. In particular, we find the corresponding Lane-Emden equation and integrate it for a wide range of values of the parameters involved. We explore the parameter space with the aim to find the set of parameters leading to reasonable physical solutions. Also, we considered the effect of spherically symmetric perturbations of the matter variables in order to analyze the possible apparition of cracking within the compact distribution.

gr-qc↗
arXiv2022

Anisotropic star models in the context of vanishing complexity

We use the definition of complexity for static and self--gravitating objects to build up three physical general relativistic anisotropic models fulfilling the vanishing complexity condition which serves to provide the extra information needed to close the system of Einstein field equations. We evaluate the physical acceptability of these models by testing some of the conditions that the geometric and material sector must satisfy in order to be considered as reasonable realistic models. We present the results of this analysis by asserting that the studied cases demonstrate to be feasible and stable under the chosen set of parameters. Furthermore, the $P_{\perp}=0$ and the Consenza's anisotropy models that seem not satisfying the expect conditions are also discussed.

gr-qc↗
arXiv2022

Complexity factor for black holes in the framework of the Newman-Penrose formalism

In this work, we introduce the {\it complexity factor} in the context of self--gravitating fluid distributions for the case of black holes by employing the Newman-Penrose formalism. In particular, by working with spherically symmetric and static AdS black holes, we show that the complexity factor can be interpreted in a natural way at the event horizon. Specifically, a thermodynamic interpretation for the aforementioned complexity factor in terms of a pressure partially supporting a Van der Waals-like equation of state is given.

gr-qc↗
arXiv2022

Uncharged and charged anisotropic like--Durgapal stellar model with vanishing complexity

In this work we use the vanishing complexity factor as a supplementary condition to construct uncharged and charged like--Durgapal models. We provide the $g_{tt}$ component of the metric of the well-known Durgapal IV and V solutions and a particular form for the anisotropy, related to the electric charge, to close the system of differential equations. The physical acceptance of the models is discussed.

gr-qc↗
arXiv2022

Traversable wormholes with like--Casimir complexity supported with arbitrarily small amount of exotic matter

In this work we construct traversable wormholes geometries in the framework of the complexity factor. We provide the redshift function of a Casimir traversable wormhole which, in combination with a non--vanishing complexity factor, leads to a traversable wormhole with a minimum amount of exotic matter. The shape function and the embedding diagram are shown and discussed. The tidal accelerations and the time required to get through the wormholes are estimated.

gr-qc↗
arXiv2022

Construction of a traversable wormhole from a suitable embedding function

In this work, we construct a traversable wormhole by providing a suitable embedding function ensuring the fulfilling of the flaring--out condition. The solution contains free parameters that are reduced through the study of the acceptable conditions of a traversable wormhole. We compute both the quantifier of exotic matter and the quasi--normal modes through the $13^{th}$ order WKB as a function of the remaining free parameters. We obtain that the wormhole geometry can be sustained by a finite amount of exotic matter and seems to be stable under scalar perturbations.

gr-qc↗
arXiv2022

Integration of the Lane-Emden equation for relativistic anisotropic polytropes through Gravitational Decoupling: a novel approach

In this work we propose a novel approach to integrate the Lane-Emden equations for relativistic anisotropic polytropes. We take advantage of the fact that Gravitational Decoupling allows to decrease the number of degrees of freedom once a well known solution of the Einstein field equations is provided as a seed so after demanding the polytropic equation for the radial pressure the system is automatically closed. The approach not only allows to extend both isotropic or anisotropic known solutions but simplifies the computation of the Tolman mass whenever the Minimal Geometric Deformation is considered given that the $g_{tt}$ component of the metric remains unchanged. We illustrate how the the method works by analyzing the solutions obtained from Tolman IV, Durgapal IV and Wymann IIa isotropic systems as a seed for the integration.

gr-qc↗