arXiv subjects

Hernando Quevedo

Publications and source records attributed to Hernando Quevedo.

At least 37 records · Page 2Linked to original sources

arXiv2026

Quasi-Homogeneous Thermodynamics and Microscopic Structure of the Quantum-Corrected FLRW Universe

The analysis of phase transitions in cosmological spacetimes shows that their existence requires a time-dependent apparent horizon radius, which in turn implies an equation of state different from that of a dark energy fluid. This condition is not compatible with the simultaneous fulfillment of Hayward's unified gravitational first law and the fundamental thermodynamic equation of the apparent horizon. To solve this problem, we introduce an alternative formulation in which the cosmological horizon is modeled as a quasi-homogeneous thermodynamic system. We apply this approach to the Friedmann-Lemaître-Robertson-Walker (FLRW) universe under quantum gravity corrections encoded by the Generalized Uncertainty Principle (GUP), promote the deformation parameter to a thermodynamic variable, and obtain a consistent thermodynamic description without relying on the usual pressure-volume interpretation. Using Geometrothermodynamics (GTD), we show that fluctuations of the GUP parameter can induce phase transitions closely resembling those of black hole configurations. Finally, we perform a numerical analysis of the behavior of the GTD scalar curvature near the phase transition point, where we find a scaling behavior characterized by the critical exponent close to 1, independently of the dimension of the equilibrium space. This reveals that quantum gravity corrections not only modify the thermodynamic consistency of cosmological models but also strengthen the notion of thermodynamic universality across gravitational systems. Our findings confirm GTD as a powerful geometric tool to unveil the emergent thermodynamic microstructure of spacetime.

gr-qc↗

arXiv2025

Temperature definitions and phase transitions within non-minimal large and small inflationary potentials

We explore and compare two distinct temperature definitions for scalar field inflation in the context of small- and large-field potentials. The first is based on a real gas, fluid-like temperature, $T_{RG}$, while the second corresponds to a relativistic species-like temperature, $T_{RS}$. We derive the fundamental thermodynamic relations for both and analyze their implications for the most viable inflationary potentials, consistent with Planck constraints. We also investigate non-minimally coupled scenarios, finding that $T_{RS}$ is the most self-consistent choice, as it decreases during inflation, satisfies standard thermodynamic laws, and exhibits frame-independent behavior in both the Jordan and Einstein frames. Remarkably, the $T_{RS}$ approach shows that the inflaton's dynamics is well-described by Van der Waals-like isotherms, linking inflationary evolution to thermodynamic phase transitions. We find that the onset of inflation is associated with a phase transition acting as the ``trigger'' of the inflationary epoch. Our analysis highlights inconsistencies in the hilltop potential and, more generally, in small-field potentials unless a non-minimal coupling is introduced. Conversely, the Starobinsky and $α$-attractor models emerge as the most suitable paradigms. We further show that \emph{frame independence} is achieved only for coupling values $ζ\leq 1/6$, supporting very small values. Finally, our study of natural inflation with non-minimal coupling reveals a strong dependence on the coupling parameter, where bounds associated with thermodynamic phase transitions coincide with observationally viable ranges, suggesting that thermodynamic considerations may provide an additional criterion to discriminate among inflationary scenarios.

gr-qc↗

arXiv2025

Non-extensive and quasi-homogeneous geometrothermodynamics

We study the thermodynamic properties of black holes, taking into account the non-extensive character of their entropy at the thermodynamic and statistical level. To this end, we assume that the Rényi entropy determines the fundamental thermodynamic equation of black holes and is represented by a quasi-homogeneous function. As a consequence, the Rényi parameter turns out to be an independent thermodynamic variable, which must be treated in the framework of extended thermodynamics. As a particular example, we use the formalism of geometrothermodynamics to show that the Schwarzschild black hole can become stable for certain values of the Rényi parameter.

gr-qc↗

arXiv2025

A General Theory of Operator-Valued Measures

We construct a new kind of measures, called projection families, which generalize the classical notion of vector and operator-valued measures. The maximal class of reasonable functions admits an integral with respect to a projection family, where the integral is defined as an element of the second dual instead of the original space. We show that projection families possess strong enough properties to satisfy the theorems of Monotone Convergence and Dominated convergence, but are much easier to come by than the more restrictive operator-valued measures.

math.FA↗

arXiv2025

Thermodynamics of the FLRW apparent horizon in Einstein-Gauss-Bonnet gravity

We analyze the thermodynamic properties of the apparent horizon of Friedmann-Lemaître-Roberson-Walker (FLRW) spacetimes in Einstein-Gauss-Bonnet gravity. We use the generalized definition of entropy for gravity theories in higher dimensions to determine the main thermodynamic variables and to compare their behavior with the corresponding quantities in Einstein's theory, emphasizing the role of the Gauss-Bonnet coupling constant and the dimension number. By imposing the validity of the laws of thermodynamics, we show that the apparent horizon can be interpreted thermodynamically as a dark energy fluid, independently of the coupling constant and the dimension number. Using the response functions, we determine the adiabatic index and the number of thermally accesible degrees of freedom of the apparent horizon and argue that this leads to a discretization of the Gauss-Bonnet coupling constant.

gr-qc↗

arXiv2025

Constraining quadrupole deformations with relativistic effects

We investigate two general relativistic effects - namely, the Shirokov and Shapiro effects - within the framework of the Zipoy-Voorhees spacetime ($q$-metric), which generalizes the Schwarzschild solution by incorporating a quadrupole moment. By analyzing the geodesic deviation equations, we explore the oscillatory motion of test particles and demonstrate how the source's quadrupole parameter influences the Shirokov effect. Furthermore, we derive an expression for the Shapiro time delay in this deformed spacetime and examine the quadrupole moment's impact on the gravitational time delay experienced by radio waves propagating near a massive object. The first-order approximation reveals a pronounced effect of the quadrupole parameter on the time delay, in contrast to similar recent analyses. These findings deepen our understanding of how deviations from spherical symmetry influence gravitational phenomena, with potential implications for the study of compact astrophysical objects such as neutron stars and naked singularities or ''black hole mimickers'' that exhibit significant multipolar structures.

gr-qc↗

arXiv2025

Phase Transitions, Shadows, and Microstructure of Kerr-anti-de Sitter Black Holes from Geometrothermodynamics

Using the formalism of geometrothermodynamics, we investigate the phase-transition structure and microstructure of the Kerr-anti-de Sitter black hole and show the relationship with its shadow structure. By treating the curvature radius as a thermodynamic variable, we ensure scaling consistency and model the system as quasi-homogeneous. In the canonical ensemble, we identify critical points and characterize both first- and second-order phase transitions independently of pressure. In the grand-canonical ensemble, we reveal a distinct phase structure, including the Hawking-Page transition. We derive analytical expressions for the Kerr-anti-de Sitter black hole shadow and its critical parameters, using shadow thermodynamics to construct asymmetric shadow profiles that capture the phase-transition structure. Finally, we show that the singularities of the geometrothermodynamic curvature in the shadow align with divergences in thermodynamic response functions, confirming the correspondence between shadows, phase transitions, and microstructure.

gr-qc↗

arXiv2025

Geometric properties versus particle motion in the Fan-Wang spacetime

In this work, we explore general relativistic effects and geometric properties of the Fan-Wang spacetime, one of the simplest regular solutions that can be obtained in nonlinear electrodynamics. In particular, we investigate the motion of test particles, the capture cross-section of neutral massive and massless particles, such as neutrinos and photons, and the gravitational redshift. Additionally, using a perturbative approach, we derive analytical expressions for the perihelion shift and gravitational deflection of massless particles. By identifying the one-parameter corrections to the Schwarzschild spacetime, induced by the magnetic charge contained in the Fan-Wang metric, we show that this spacetime can be falsified, since it modifies classical general relativity predictions even at the local level. Moreover, we argue that these modifications could be experimentally tested with advanced observational instrumentation.

gr-qc↗

arXiv2025

Smooth Functional Calculus and Spectral Theorem in Banach Spaces

The notion of projection families generalizes the classical notions of vector- and operator-valued measures. We show that projection families are general enough to extend the Spectral Theorem to Banach algebras and operators between Banach spaces. To this end, we first develop a Smooth Functional Calculus in Banach algebras using the Cauchy-Pompeiu formula, which is further extended to a Continuous Functional Calculus. We also show that these theorems are proper generalizations of the usual result for operators between Hilbert spaces.

math.FA↗

arXiv2025

Geometrothermodynamic description of magnetic materials

We perform a statistical and geometrothermodynamic analysis of three different models of magnetic materials, namely, the translational free model, the spin model, and the mean-field model. First, we derive the fundamental equation for each model, which is then used as input to compute the metrics of the corresponding equilibrium spaces. Analyzing the corresponding geometrothermodynamic curvatures, we conclude that they can be used to describe thermodynamic interaction, stability conditions, and the phase transition structure of the modeled substances. In all the cases, we reproduce their well-known behavior close to the Curie temperature. Moreover, in the case of the model with spin, we found a curvature singularity which corresponds to a novel transition, where a particular response function diverges, indicating the presence of a second order phase transition, according to Ehrenfest classification.

cond-mat.stat-mech↗

arXiv2024

Gravitational capture cross-section in Zipoy-Voorhees spacetimes

We consider geodesics of massive and massless test particles in the gravitational field of a static and axisymmetric compact object described by the quadrupolar metric ($q$-metric), which is the simplest generalization of the Schwarzschild metric, containing an independent quadrupole parameter $q$. We analyze the effective potential profile and calculate the orbital parameters and capture cross-sections of test particles in this spacetime. Moreover, we derive the explicit expression for the escape angle of photons as a function of the quadrupole parameter. All the results reduce in the corresponding limit of vanishing quadrupole to the well-known case of the Schwarzschild spacetime. We argue that our results could be used to investigate realistic compact objects such as white dwarfs and neutron stars.

gr-qc↗

arXiv2024

On the single versus the repetitive Penrose process in a Kerr black hole

Extracting the rotational energy from a Kerr black hole (BH) is one of the crucial topics in relativistic astrophysics. Here, we give special attention to the Penrose ballistic process based on the fission of a massive particle $μ_0$ into two particles $μ_1$ and $μ_2$, occurring in the ergosphere of a Kerr BH. Bardeen et al. indicated that for the process to occur, some additional "hydrodynamical forces or superstrong radiation reactions" were needed. Wald and Chandrasekhar further expanded this idea. This animosity convinced T. Piran and collaborators to move from a simple three-body system characterizing the original Penrose process to a many-body system. This many-body approach was further largely expanded by others, some questionable in their validity. Here, we return to the simplest original Penrose process and show that the solution of the equations of motion, imposing the turning point condition on their trajectories, leads to the rotational energy extraction from the BH expected by Penrose. The efficiency of energy extraction by a single process is quantified for three different single decay processes occurring respectively at $r=1.2 M$, $r=1.5 M$, and $r=1.9 M$. An interesting repetitive model has been proposed by Misner, Thorne \& Wheeler (hereafter MTW73). Indeed, it would appear that a repetitive sequence of $246$ decays of the above injection process at $r=1.2 M$ and the corresponding ones at $r=1.5 M$ and $r=1.9 M$ could extract $100\%$ of the rotational energy of the BH, so violating energy conservation. The accompanying paper, accounting for the existence of the BH irreducible mass, introduces a non-linear approach that avoids violating energy conservation and leads to a new energy extraction process.

gr-qc↗

arXiv2024

Event horizons under the effect of the Penrose process

We investigate how test particles absorbed by a black hole affect the properties of the event horizon. We consider particles that arrive from infinity with positive energy and cross the horizon. We also study the absorption of particles with negative energy, which are generated inside the ergosphere as the result of the decay of other particles, following the dynamics of the Penrose process. We show that, in general, the absorption process leads to an increase in the horizon radius and, consequently, of any physical quantity that is proportional to the horizon radius, such as the irreducible mass or the entropy.

gr-qc↗

arXiv2024

Spherically symmetric collapse: Initial configurations

The initial state of the spherical gravitational collapse in general relativity has been studied with different methods, especially by using {\it a priori} given equations of state that describe the matter as a perfect fluid. We propose an alternative approach, in which the energy density of the perfect fluid is given as a polynomial function of the radial coordinate that is well-behaved everywhere inside the fluid. We then solve the corresponding differential equations, including the Tolman-Oppenheimer-Volkoff equilibrium condition, using a fourth-order Runge-Kutta method and obtain a consistent model with a central perfect-fluid core surrounded by dust. We analyze the Hamiltonian constraint, the mass-to-radius relation, the boundary and physical conditions, and the stability and convergence properties of the numerical solutions. The energy density and pressure of the resulting matter distribution satisfy the standard physical conditions. The model is also consistent with the Buchdahl limit and the speed of sound conditions, even by using realistic values of compact astrophysical objects such as neutron stars.

gr-qc↗

arXiv2024

Time is entropy: A geometric proof

We analyze the equilibrium space of an ideal gas using the formalism of geometrothermodynamics. We introduce the concept of thermodynamic geodesics to show that the equilibrium space around a particular initial state can be divided into two regions, one that can be reached using thermodynamic geodesics and the second one forbidden by the second law of thermodynamics. Moreover, we show that, along thermodynamic geodesics, entropy is a linear function of the affine parameter, indicating that it can be used as a time parameter with a particular arrow of time determined by the direction in which entropy increases. We argue that entropy can also be interpreted locally as time in the case of any thermodynamic system in equilibrium and systems described within the scope of linear non-equilibrium thermodynamics.

gr-qc↗

arXiv2024

Functional measures associated to operators

We show that every operator in $L^{2}$ has an associated measure on a space of functions and prove that it can be used to find solutions to abstract Cauchy problems, including partial differential equations. We find explicit formulas to compute the integral of functions with respect to this measure and develop approximate formulas in terms of a perturbative expansion. We show that this method can be used to represent solutions of classical equations, such as the diffusion and Fokker-Plank equations, as Wiener and Martin-Siggia-Rose-Jansen-de Dominics integrals, and propose an extension to paths in infinite dimensional spaces.

math-ph↗

arXiv2024

Extended thermodynamics and critical behavior of generalized dilatonic Lifshitz black holes

We study a particular Einstein-Maxwell-Dilaton black hole configuration with cosmological constant, expressed in terms of the curvature radius, from the point of view of quasi-homogeneous thermodynamics. In particular, we show that the curvature radius and the coupling constant of the matter fields can be treated as thermodynamic variables in the framework of extended thermodynamics, leading in both cases to a van der Waals-like behavior. We also investigate in detail the stability and critical properties of the black holes and obtain results, which are compatible with the mean field approach.

gr-qc↗

arXiv2024

Phase transitions, shadows, and microstructure of Reissner-Nordström-Anti-de-Sitter black holes from a geometrothermodynamic perspective

We study the thermodynamic properties of the Reissner-Nordström black hole with cosmological constant, expressed in terms of the curvature radius, by using the approach of shadow thermodynamics and the formalism of geometrothermodynamics. We derive explicit expressions for the shadow radius in terms of the horizon, photon sphere, and observer radii. The phase transition structure turns out to strongly depend on the value of the curvature radius, including configurations with zero, one, or two phase transitions. We also analyze the black hole microscopic structure and find differences between the approaches of thermodynamic geometry and geometrothermodynamics, which are due to the presence of the curvature radius. We impose the important condition that the black hole is a quasi-homogeneous thermodynamic system to guarantee the consistency of the geometrothermodynamic approach.

gr-qc↗