arXiv subjects

Hernando Quevedo

Publications and source records attributed to Hernando Quevedo.

At least 55 records · Page 3Linked to original sources

arXiv2024

A thermodynamic model of inflation without inflaton field

In the framework of geometrothermodynamics, we explore how to construct an inflationary cosmic fluid without requiring inflaton fields. To do so, we employ standard radiation and matter as barotropic background, speculating on the existence of a further real fluid, interpreted as a possible matter with pressure constituent. We thus illustrate its main characteristics, showing how it may face the flatness and horizon problems, yielding an equivalent number of e-foldings, compatible with theoretical expectations. Moreover, we calculate the associated equilibrium and kinetic temperatures, and compute out-of-equilibrium properties, in terms of particle production and effective reheating mechanism. Accordingly, we revise how inflation ends and how to fix the free parameters of our model from observations. Last but not least, we propose how to obtain a bare cosmological constant that could relate the late-time acceleration to inflation, aiming to unify the two approaches. Finally, we discuss the corresponding theoretical implications of our treatment in contrast to the standard approach reliant on scalar field potentials, emphasizing the main advantages and disadvantages.

gr-qc↗

arXiv2024

$C^3$ matching conditions for anisotropic fluids

The $C^3$ approach is an invariant formalism that utilizes the eigenvalues of the Riemann curvature tensor to match spacetimes across a specific matching surface. We apply this approach to match an anisotropic fluid with an exterior vacuum solution, including the case in which discontinuities appear on the matching surface. As a particular example, a class of analytic solutions, which describe the gravitational field of realistic neutron stars, is matched to the exterior Schwarzschild spacetime.

gr-qc↗

arXiv2024

Anisotropic Generalized Polytropic Spheres: Regular 3D Black Holes

We model gravitating relativistic 3D spheres composed of an anisotropic fluid in which the radial and transverse components of the pressure correspond to the vacuum energy and a generalized polytropic equation-of-state, respectively. By using the generalized Tolman-Oppenheimer-Volkoff (TOV) equation, and solving the complete system of equations for these anisotropic generalized polytropic spheres, for a given range of model parameters, we find three novel classes of asymptotically AdS black hole solutions with regular core. We show the regularity of the solutions using curvature scalars and the formalism of geodesic completeness. Then, using the eigenvalues of the Riemann curvature tensor, we consider the effects of repulsive gravity in the three static 3D regular black holes, concluding that their regular behavior can be explained as due to the presence of repulsive gravity near the center of the objects. Finally, we study the stability of the regular black holes under the flow of the energy through the Cauchy horizon.

gr-qc↗

arXiv2024

Ideal quantum gases: A geometrothermodynamic approach

We derive the fundamental thermodynamic equation for Fermi-Dirac and Bose-Einstein quantum gases, which contains the first order contribution due to the quantum nature of the gas particles. Then, we analyze the fundamental equation in the context of geometrothermodynamics. Although the corresponding Hamiltonian does not contain a potential, indicating the lack of classical thermodynamic interaction, we show that the curvature of the equilibrium space is non-zero and can be interpreted as a measure of the effective quantum interaction between the gas particles. In the limiting case of a classical Boltzmann gas, we show that the equilibrium space becomes flat, as expected from the physical viewpoint. In addition, we derive a thermodynamic fundamental equation for the Bose-Einstein condensation and, using the Ehrenfest scheme, we show that it can be considered as a first order phase transition which in the equilibrium space corresponds to a curvature singularity. This result indicates that the curvature of the equilibrium space can be used to measure in an invariant way the thermodynamic interaction in classical and quantum ideal gases.

gr-qc↗

arXiv2024

Naked singularities and black hole Killing horizons

In this chapter, we study special photon orbits defined by means of Killing vectors and present a framework based on the properties of such null orbits. For concreteness, we restrict ourselves to the case of axially symmetric spacetimes describing either black holes with Killing horizons or naked singularities. The null-orbits framework is then applied to analyze properties of naked singularities and concepts of black hole thermodynamics.

gr-qc↗

arXiv2023

Quasi-periodic oscillations in rotating and deformed spacetimes

Quasi-periodic oscillation (QPOs) analysis is important for understanding the dynamical behavior of many astrophysical objects during transient events such as gamma-ray bursts, solar flares, magnetar flares, and fast radio bursts. In this paper, we analyze QPO data in low-mass X-ray binary (LMXB) systems, using the Lense-Thirring, Kerr, and approximate Zipoy-Voorhees metrics. We demonstrate that the inclusion of spin and quadrupole parameters modifies the well-established results for the fundamental frequencies in the Schwarzschild spacetime. We interpret the QPO data within the framework of the standard relativistic precession model, allowing us to infer the values of the mass, spin, and quadrupole parameters of neutron stars in LMXBs. We explore recent QPO data sets from eight distinct LMXBs, assess their optimal parameters, and compare our findings with results in the existing literature. Finally, we discuss the astrophysical implications of our findings.

astro-ph.HE↗

arXiv2023

Extended black hole geometrothermodynamics

Although ordinary laboratory thermodynamic systems are known to be homogeneous systems, black holes are different and cannot be considered within this class. Using the formalism of geometrothermodynamics, we show that black holes should be considered as quasi-homogeneous systems. As a consequence, we argue that coupling constants in generalized gravity theories should be considered as thermodynamic variables, giving raise to extended versions of black hole thermodynamics.

gr-qc↗

arXiv2023

Gravitational repulsive effects in 3D regular black holes

In this work, we consider the effects of repulsive gravity in an invariant way for four static 3D regular black holes, using the eigenvalues of the Riemann curvature tensor, the Ricci scalar, and the strong energy conditions. The eigenvalues of the solutions are non-vanishing asymptotically (in asymptotically AdS) and increase as the source of gravity is approached, providing a radius at which the passage from attractive to repulsive gravity might occur. We compute the onsets and the regions of repulsive gravity and conclude that the regular behavior of the solutions at the origin of coordinates can be interpreted as due to the presence of repulsive gravity, which also turns out to be related with the violation of the strong energy condition. We showed that in all of the solutions for the allowed region of parameters, gravity changes its sign, but the repulsive regions only for the non-logarithmic solution are affected by the mass that generates the regular black hole. The repulsive regions for the logarithmic solutions are dependent on electric charge and the AdS$_{3}$ length. The implications and physical consequences of these results are discussed in detail.

gr-qc↗

arXiv2023

Accretion disk in the Hartle-Thorne spacetime

We consider the circular motion of test particles in the gravitational field of a rotating deformed object described by the Hartle-Thorne metric. This metric represents an approximate solution to the vacuum Einstein field equations, accurate to second order in the angular momentum $J$ and to first order in the mass quadrupole moment $Q$. We calculate the orbital parameters of neutral test particles on circular orbits (in accretion disks) such as angular velocity, $Ω$, total energy, $E$, angular momentum, $L$, and radius of the innermost stable circular orbit, $R_{ISCO}$, as functions of the total mass, $M$, spin parameter, $j=J/M^2$ and quadrupole parameter, $q=Q/M^3$, of the source. We use the Novikov-Thorne-Page thin accretion disk model to investigate the characteristics of the disk. In particular, we analyze in detail the radiative flux, differential luminosity, and spectral luminosity of the accretion disk, which are the quantities that can be measured experimentally. We compare our results with those obtained in the literature for the Schwarzschild and Kerr metrics, and the $q$-metric. It turns out that the Hartle-Thorne metric and the Kerr metric lead to similar results for the predicted flux and the differential and spectral luminosities, whereas the q-metric predicts different values. We compare the predicted values of $M$, $j$, and $q$ with those of realistic neutron star models. Furthermore, we compare the values of $R_{ISCO}$ with the static and rotating radii of neutron stars.

gr-qc↗

arXiv2023

Geometrothermodynamic cosmology

We review the main aspects of geometrothermodynamics, a formalism that uses contact geometry and Riemannian geometry to describe the properties of thermodynamic systems. We show how to handle in a geometric way the invariance of classical thermodynamics with respect to Legendre transformations, which means that the properties of the systems do not depend on the choice of the thermodynamic potential. Moreover, we show that in geometrothermodynamics it is possible to apply a variational principle to generate thermodynamic fundamental equations, which can be used in the context of relativistic cosmology to generate cosmological models. As a particular example, we consider a fundamental equation that relates the entropy with the internal energy and the volume of the Universe, and construct cosmological models with arbitrary parameters, which can be fixed to reproduce the main aspects of the inflationary era and the standard cosmological paradigm.

gr-qc↗

arXiv2023

Adiabatic theory in Kerr spacetimes

We present the main aspects of the adiabatic theory and show that it can be used to study the motion of test particles in general relativity. The theory is based upon the use of vector elements of the orbits and adiabatic invariants. To prove the applicability of the adiabatic theory in Einstein's gravity, we derive a particular representation of the Kerr metric in harmonic coordinates, which allows us to obtain a general formula for the perihelion shift of test particles orbiting on the non-equatorial plane of a rotating central object. We show that the principle of superposition is fulfilled for the individual effects of the gravitational source mass and angular momentum up to the second order. We demonstrate that the adiabatic theory, along with its simplicity, leads to correct results, which in the limiting cases correspond to the ones reported in the literature.

gr-qc↗

arXiv2023

Repulsive gravity in regular black holes

We evaluate the effects of repulsive gravity using first order geometric invariants, \textit{i.e.}, the Ricci scalar and the eigenvalues of the Riemann curvature tensor, for three regular black holes, namely the Bardeen, Hayward, and Dymnikova spacetimes. To examine the repulsive effects, we calculate their respective onsets and regions of repulsive gravity. Afterwards, we compare the repulsive regions obtained from these metrics among themselves and then with the predictions got from the Reissner-Nordström and Schwarzschild-de Sitter. We find that the Dymnikova spacetime does not exhibit regions in which gravity changes its sign. A notable characteristic, observed in all these metrics, is that the repulsive regions appear to be unaffected by the mass that generates the regular black hole. This property emerges due to the invariants employed in our analysis, which do not change sign through \emph{linear combinations} of the mass and the free coefficients of the metrics. As a result, gravity can change sign independently of the specific values acquired by the mass. This conclusion suggests a potential \emph{incompleteness} of regular solutions, particularly in terms of their repulsive effects. To further highlight this finding, we numerically compute, for the Reissner-Nordström and Schwarzschild-de Sitter solutions, the values of mass, $M$, that emulate the repulsive effects found in the Bardeen and Hayward spacetimes. These selected values of $M$ provide evidence that regular black holes do not incorporate repulsive effects by means of the masses used to generate the solutions themselves. Implications and physical consequences of these results are then discussed in detail.

gr-qc↗

arXiv2023

Comparing metrics for mixed quantum states: Sjoqvist and Bures

It is known that there are infinitely many distinguishability metrics for mixed quantum states. This freedom, in turn, leads to metric-dependent interpretations of physically meaningful geometric quantities such as complexity and volume of quantum states. In this paper, we first present an explicit and unabridged mathematical discussion on the relation between the Sjoqvist metric and the Bures metric for arbitrary nondegenerate mixed quantum states, using the notion of decompositions of density operators by means of ensembles of pure quantum states. Then, to enhance our comprehension of the difference between these two metrics from a physics standpoint, we compare the formal expressions of these two metrics for arbitrary thermal quantum states specifying quantum systems in equilibrium with a reservoir at non-zero temperature. For illustrative purposes, we show the difference between these two metrics in the case of a simple physical system characterized by a spin-qubit in an arbitrarily oriented uniform and stationary external magnetic field in thermal equilibrium with a finite-temperature bath. Finally, we compare the Bures and Sjoqvist metrics in terms of their monotonicity property.

quant-ph↗

arXiv2023

Study of ideal gases in curved spacetimes

The influence of a curved spacetime $M$ on the physical behavior of an ideal gas of $N$ particles is analyzed by considering the phase space of the system as a region of the cotangent bundle $T^{*}M^{N}$ and using Souriau's Lie group {thermodynamics} to define the corresponding probability distribution function. While the construction of the phase space respects the separability of the system, by forcing each particle to satisfy the so-called mass-shell constraint, the probability distribution is constructed by mixing the natural symplectic structure of the cotangent bundle with a Hamiltonian description of the system. In this way, the spacetime is introduced into the statistics and its isometries turn out to be of special interest because the distributions are parameterized by the elements of the Lie algebra of the isometry group, through the momentum map of the action of the isometries in $T^{*}M^{N}$. We find the Gibbs distribution that, in the simplest case of a flat spacetime, reduces to the so-called modified Jüttner distribution, used to describe ideal gases in the regime of special relativity. We also define a temperature-like function using the norm of a Killing vector, which allows us to recover the so-called Tolman-Ehrenfest effect. As a particular example, we study the outer region of a Schwarzschild black hole, for which a power series expansion of the Schwarzschild radius allows us to represent the partition function and the Gibbs distribution in terms of the corresponding quantities of the Minkowski spacetime.

gr-qc↗

arXiv2022

Numerical analyses of M31 dark matter profiles

We reproduce the rotation curve of the Andromeda galaxy (M31) by taking into account its bulge, disk, and halo components, considering the last one to contain the major part of dark matter mass. Hence, our prescription is to split the galactic bulge into two components, namely, the inner and main bulges, respectively. Both bulges are thus modeled by exponential density profiles since we underline that the widely accepted de Vaucouleurs law fails to reproduce the whole galactic bulge rotation curve. In addition, we adopt various well-known phenomenological dark matter profiles to estimate the dark matter mass in the halo region. Moreover, we apply the least-squares fitting method to determine from the rotation curve the model free parameters, namely, the characteristic (central) density, scale radius, and consequently the total mass. To do so, we perform Markov chain Monte Carlo statistical analyses based on the Metropolis algorithm, maximizing our likelihoods adopting velocity and radii data points of the rotation curves. We do not fit separately the components for bulges, disk and halo, but we perform an overall fit including all the components and employing all the data points. Thus, we critically analyze our corresponding findings and, in particular, we employ the Bayesian Information Criterion to assess the most accredited model to describe M31 dark matter dynamics.

gr-qc↗

arXiv2022

Thermodynamics of the FLRW apparent horizon

To investigate the relationship between gravity and thermodynamics in the case of dynamic systems, we interpret the apparent horizon of the Friedmann-Lemaître-Robertson-Walker (FLRW) spacetime as a thermodynamic system. We derive the corresponding fundamental equation in the entropy representation and explore the consequences of demanding the fulfillment of the classical laws of thermodynamics. We investigate in detail the case of an FLRW spacetime with and without cosmological constant. We show that the interpretation of the apparent horizon as a thermodynamic system is possible only under certain conditions because the analogy is not always valid for all the values of the parameters entering the dynamics of the horizon and certainly not for its entire evolution.

gr-qc↗

arXiv2022

Symplectic structure of equilibrium thermodynamics

The contact geometric structure of the thermodynamic phase space is used to introduce a novel symplectic structure on the tangent bundle of the equilibrium space. Moreover, it turns out that the equilibrium space can be interpreted as a Lagrange submanifold of the corresponding tangent bundle, if the fundamental equation is known explicitly. As a consequence, Hamiltonians can be defined that describe thermodynamic processes.

gr-qc↗

arXiv2022

Adiabatic theory of motion of bodies in the Hartle-Thorne spacetime

We study the motion of test particles in the gravitational field of a rotating and deformed object within the framework of the adiabatic theory. For this purpose, the Hartle-Thorne metric written in harmonic coordinates is employed in the post-Newtonian approximation where the adiabatic theory is valid. As a result, we obtain the perihelion shift formula for test particles orbiting on the equatorial plane of a rotating and deformed object. Based on the perihelion shift expression, we show that the principle of superposition is valid for the individual effects of the gravitational source mass, angular momentum and quadrupole moment. The resulting formula was applied to the inner planets of the Solar system. The outcomes are in a good agreement with observational data. It was also shown that the corrections related to the Sun's angular moment and quadrupole moment have little impact on the perihelion shift. On the whole, it was demonstrated that the adiabatic theory, along with its simplicity, leads to correct results, which in the limiting cases correspond to the ones reported in the literature.

gr-qc↗