arXiv subjects

Diego Fernández-Silvestre

Publications and source records attributed to Diego Fernández-Silvestre.

6 recordsLinked to original sources

arXiv2026

Penrose-Rindler equation and horizon thermodynamics of stationary black holes

Black holes are the natural arena for exploring the interplay between gravity and thermodynamics. Although the association between black hole mechanics and black hole thermodynamics is well established, the comprehensive geometric formulation of thermodynamic variables deserves further investigation. In this work, both Newman-Penrose (NP) and Geroch-Held-Penrose (GHP) formalisms are considered within the framework of horizon thermodynamics. We show that the NP formalism reformulates the horizon condition as the Penrose-Rindler equation. In this context, a Smarr-like formula for stationary black holes is recovered from the Penrose-Rindler equation reinterpreted as a horizon equilibrium of pressures, which includes a pressure associated with the horizon rotation. A complete geometric reformulation of this reinterpretation of the Penrose-Rindler equation evaluated at the horizon is developed within the GHP formalism. The GHP approach further inspires the introduction of the horizon-averaged matter pressure and its conjugate volume, thereby enabling a quasilocal realization of the Smarr-like formula for stationary black holes. This geometric formulation clarifies the connection between horizon dynamics and thermodynamics and offers a unified setting for extending black hole thermodynamics beyond spherical symmetry.

gr-qc↗

arXiv2025

Physical reinterpretation of heat capacity discontinuities for static black holes

A generic characteristic of self-gravitating systems is that they have a negative heat capacity. An important example of this behavior is given by the Schwarzschild black hole. The case of charged and rotating black holes is even more interesting since a change of sign of the specific heat takes place through an infinite discontinuity. This has been usually associated with a black hole thermodynamic phase transition appearing at the points where the heat capacity diverges, the so-called Davies points. This aspect of black hole thermodynamics has been addressed from different perspectives, motivating different interpretations since its discovery in the 1970s. In this paper, a physical reinterpretation of the heat capacity is provided for spherically symmetric and static black holes. Our analysis is partially based on a reformulation of the black hole heat capacity using the Newman-Penrose formalism. The application to the Reissner-Nordström-de Sitter black hole case reveals a clear physical interpretation of the Newman-Penrose scalars evaluated at the event horizon. This allows us to write the heat capacity as a balance of pressures defined at the horizon, in particular, a matter pressure (coming from the energy-momentum tensor) and a thermal pressure (coming from the holographic energy equipartition of the horizon). The Davies point is identified with the point where the Komar thermal energy density matches the matter pressure at the horizon. We also compare the black hole case with the case of self-gravitating objects and their corresponding thermal evolutions. We conclude that the heat capacity of black holes and self-gravitating systems can be understood qualitatively in similar terms.

gr-qc↗

arXiv2023

Cornering Quantum Gravity

After introducing the covariant phase space calculus, Noether's theorems are discussed, with particular emphasis on Noether's second theorem and the role of gauge symmetries. This is followed by the enunciation of the theory of asymptotic symmetries, and later its application to gravity. Specifically, we review how the BMS group arises as the asymptotic symmetry group of gravity at null infinity. Symmetries are so powerful and constraining that memory effects and soft theorems can be derived from them. The lectures end with more recent developments in the field: the corner proposal as a unified paradigm for symmetries in gravity, the extended phase space as a resolution to the problem of charge integrability, and eventually the implications of the corner proposal on quantum gravity.

hep-th↗

arXiv2023

Introduction to noncommutative field and gauge theory

These are lecture notes for an introductory course on noncommutative field and gauge theory. We begin by reviewing quantum mechanics as the prototypical noncommutative theory, as well as the geometrical language of standard gauge theory. Then, we review a specific approach to noncommutative field and gauge theory, which relies on the introduction of a derivations-based differential calculus. We focus on the cases of constant and linear noncommutativity, e.g., the Moyal spacetime and the so-called $\mathbb{R}^3_λ$, respectively. In particular, we review the $gφ^4$ scalar field theory and the $U(1)$ gauge theory on such noncommutative spaces. Finally, we discuss noncommutative spacetime symmetries from both the observer and particle point of view. In this context, the twist approach is reviewed and the $λ$-Minkowski $gφ^4$ model is discussed.

hep-th↗

arXiv2022

Upon the horizon's verge: Thermal particle creation between and approaching horizons

Quantum particle creation from spacetime horizons, or accelerating boundaries in the dynamical Casimir effect, can have an equilibrium, or thermal, distribution. Using an accelerating boundary in flat spacetime (moving mirror), we investigate the production of thermal energy flux despite non-equilibrium accelerations, the evolution between equilibrium states, and the "interference" between horizons. In particular, this allows us to give a complete solution to the particle spectrum of the accelerated boundary correspondence with Schwarzschild-de Sitter spacetime.

gr-qc↗

arXiv2022

On the duality of Schwarzschild-de Sitter spacetime and moving mirror

The Schwarzschild-de Sitter (SdS) metric is the simplest spacetime solution in general relativity with both a black hole event horizon and a cosmological event horizon. Since the Schwarzschild metric is the most simple solution of Einstein's equations with spherical symmetry and the de Sitter metric is the most simple solution of Einstein's equations with a positive cosmological constant, the combination in the SdS metric defines an appropriate background geometry for semi-classical investigation of Hawking radiation with respect to past and future horizons. Generally, the black hole temperature is larger than that of the cosmological horizon, so there is heat flow from the smaller black hole horizon to the larger cosmological horizon, despite questions concerning the definition of the relative temperature of the black hole without a measurement by an observer sitting in an asymptotically flat spacetime. Here we investigate the accelerating boundary correspondence (ABC) of the radiation in SdS spacetime without such a problem. We have solved for the boundary dynamics, energy flux and asymptotic particle spectrum. The distribution of particles is globally non-thermal while asymptotically the radiation reaches equilibrium.

gr-qc↗