arXiv subjects

Carlos E. Romero-Figueroa

Publications and source records attributed to Carlos E. Romero-Figueroa.

10 recordsLinked to original sources

arXiv2026

Geometrothermodynamics of Black Hole Shadows: A Review

Black-hole shadows and geometrothermodynamics (GTD) are defined in different spaces but depend on the same macroscopic black-hole parameters. We review their correspondence for Reissner--Nordström (RN), Kerr, and Kerr--AdS black holes. The three GTD metrics reveal complementary thermodynamic structures, including Davies instabilities, extremal and degenerate limits, and regular curvature zeros, which can be mapped to shadow configurations. Kerr--AdS extends this correspondence to asymmetric shadows and multidimensional equilibrium states. We formulate a local Jacobian-rank criterion for thermodynamic reconstruction from shadow observables and discuss shadow--microstructure (SM) diagrams as optical representations of GTD-classified equilibrium states. The application to Sagittarius A* illustrates the inverse problem: shadow observations constrain thermodynamic states and provide a basis for identifying additional metric-dependent observables that could distinguish among the GTD metric structures.

gr-qc↗

arXiv2026

Naked Singularities and Black Hole Thermodynamics from Shadows and Photon Rings in the Quantum Oppenheimer-Snyder Model

We investigate the optical and thermodynamic properties of quantum Oppenheimer-Snyder (qOS) spacetimes in both the black hole and naked singularity regimes. By analyzing test-particle motion and employing numerical ray tracing of thin accretion disk models, we identify their characteristic optical signatures. We find that increasing the quantum correction parameter reduces the apparent shadow size. While qOS black holes exhibit dark inner shadows, naked singularities produce central bright rings, driven by an infinite repulsive core barrier, yet still retain key optical features such as photon rings. Furthermore, using a semi-analytical approach, we obtain higher-order photon-ring impact and gap parameters that closely align with our numerical findings. Notably, the gap parameter intervals for qOS naked singularities deviate from the Schwarzschild case, providing a concrete criterion for observational tests. Finally, in the black-hole sector, the application of Geometrothermodynamics (GTD) identifies the specific-heat divergence at the Davies point. By linking photon-ring observables to GTD curvature scalars, we reveal a direct connection between qOS black hole shadows, thermodynamic stability, and microscopic interaction structures.

gr-qc↗

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.

gr-qc↗

arXiv2026

Geometric Universality and Thermodynamic Microstructure of Real Fluids in a Unified Entropic Framework

We introduce a unified entropic framework for real fluids that encompasses the van der Waals, Berthelot, Redlich Kwong, and Peng Robinson equations of state within a common thermodynamic description. The corresponding microscopic interactions are then explored using Geometrothermodynamics, GTD, through the scalar curvature $mathcal{R}$ of the equilibrium manifold. We show that curvature singularities accurately reproduce macroscopic critical phenomena, while vanishing curvature $\mathcal{R}=0$ identifies specific thermodynamic states where attractive and repulsive intermolecular forces effectively balance. Furthermore, we introduce a set of dimensionless critical-amplitude ratios $Q^i_{j}$, which reveal universal geometric features of the critical regime. Although individual critical amplitudes exhibit a logarithmic dependence on the system size, these invariant ratios organize different molecular species according to the strength of criticality and encode universal scaling features, suggesting their potential as robust classification parameters. Finally, employing Bayesian inference and Markov Chain Monte Carlo, MCMC methods, we statistically reconstruct the zero-curvature curves. The posterior distributions support the consistency of the geometric scaling behavior, demonstrating that the GTD manifold encodes non-trivial information about the underlying thermodynamical models.

cond-mat.stat-mech↗

arXiv2026

Probing Black Hole Thermodynamics and Microstructure via the Shadow of Sagittarius A*

We explore the connection between black hole shadows, thermodynamic phase structure, and microstructure of charged and rotating black holes within General Relativity and Geometrothermodynamics. Focusing on Reissner-Nordström and Kerr solutions, we establish a criterion to select the most suitable Geometrothermodynamic metric for a system, revealing that the first metric from enthalpy and the second from mass correctly reproduce heat capacity singularities. We show that the shadow radius encodes the same phase information as entropy and introduce Shadow-Microstructure diagrams to extract insights into stability and microscopic interaction types directly from observational bounds. Applying this framework to Sagittarius A*, we constrain the macroscopic parameters and the allowed microscopic thermodynamic phases. Our findings indicate that shadow measurements offer a novel probe of thermodynamic and microscopic aspects of black holes, enabling tests of alternative theories of gravity and thermodynamic frameworks.

gr-qc↗

arXiv2026

Shadow and Thermodynamics of deformed Schwarzschild-AdS black hole with a Cloud of Strings embedded in Perfect Fluid Dark Matter

We investigate the optical and thermodynamic properties of a deformed Schwarzschild Anti-de Sitter (AdS) black hole coupled to a cloud of strings and embedded in perfect fluid dark matter. We analyze the photon sphere and the corresponding black hole shadow, determining how these observables are affected by the string cloud, dark matter distribution, and geometric deformation. The thermodynamic behavior is studied through both the quasi-homogeneous fundamental equation within the classical physical approach and the geometric framework of geometrothermodynamics (GTD), showing full consistency between the two descriptions. In the extended phase space, we examine the critical structure and phase behavior of the system. Our analysis reveals that neither the geometric deformation nor the dark matter parameter generates new phase transitions; criticality emerges only in the vicinity of the Reissner--Nordström--AdS solution (RN--AdS), where the deformation parameter effectively plays the role of an electric charge squared. These results clarify the interplay between matter distributions, geometric deformations, and the phase structure of AdS black holes.

gr-qc↗

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

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↗

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↗