A Weyl Entropy of Pure Spacetime Regions

We focus on the Penrose's Weyl Curvature Hypothesis in a general framework encompassing many specific models discussed in literature. We introduce a candidate density for the Weyl entropy in pure spacetime perfect fluid regions and show that it is monotonically increasing in time under very general assumptions. Then we consider the behavior of the Weyl entropy of compact regions, which is shown to be monotone in time as well under suitable hypotheses, and also maximal in correspondence with vacuum static metrics. The minimal entropy case is discussed too

Quantum properties of the Dirac field on BTZ black hole backgrounds

We consider a Dirac field on a $(1 + 2)$-dimensional uncharged BTZ black hole background. We first find out the Dirac Hamiltonian, and study its self-adjointness properties. We find that, in analogy to the Kerr-Newman-AdS Dirac Hamiltonian in $(1+3)$ dimensions, essential self-adjointness on $C_0^{\infty}(r_+,\infty)^2$ of the reduced (radial) Hamiltonian is implemented only if a suitable relation between the mass $\mu$ of the Dirac field and the cosmological radius $l$ holds true. The very presence of a boundary-like behaviour of $r=\infty$ is at the root of this problem. Also, we determine in a complete way qualitative spectral properties for the non-extremal case, for which we can infer the absence of quantum bound states for the Dirac field. Next, we investigate the possibility of a quantum loss of angular momentum for the $(1 + 2)$-dimensional uncharged BTZ black hole. Unlike the corresponding stationary four-dimensional solutions, the formal treatment of the level crossing mechanism is much simpler. We find that, even in the extremal case, no level crossing takes place. Therefore, no quantum loss of angular momentum via particle pair production is allowed.Comment: 19 pages; IOP styl

Perturbative Approach to Analog Hawking Radiation in dielectric media in subcritical regime

We take into account the subcritical case for dielectric media by exploiting an approximation allowing us to perform perturbative analytical calculations and still not implying low dispersive effects. We show that in the background of a specific soliton-like solution, pair-creation occurs and can display a thermal behaviour governed by an effective temperature. The robustness of the approach is also corroborated by the analysis of the $\phi\psi$-model related to the standard Hopfield model, for which analogous results are obtained.Comment: 22 pages, 6 figure

Absence of Normalizable Time-periodic Solutions for The Dirac Equation in Kerr-Newman-dS Black Hole Background

We consider the Dirac equation on the background of a Kerr-Newman-de Sitter black hole. By performing variable separation, we show that there exists no time-periodic and normalizable solution of the Dirac equation. This conclusion holds true even in the extremal case. With respect to previously considered cases, the novelty is represented by the presence, together with a black hole event horizon, of a cosmological (non degenerate) event horizon, which is at the root of the possibility to draw a conclusion on the aforementioned topic in a straightforward way even in the extremal case.Comment: 12 pages. AMS styl

Homogeneity: From Caratheodory's approach to Gibbs thermodynamics

We consider thermodynamics of homogeneous systems in the frame- work of Carath ́odory’s approach. We work in a configuration space where independent variables are all extensive, and we show that the requirement for homogeneity symmetry of the integrable 1-form δQrev , which represents the infinitesimal heat exchanged reversibly by a thermodynamic system, allows to find immediately and explicitly an integrating factor by means of elementary tools of differential geometry. The foliation of the thermodynamic manifold is associated in a natural way with an extensive potential, which is then identified with the metrical entropy S. Both S and the absolute temperature T are derived quantities in this framework. The entropy S corresponds to the fundamental relation in the entropy representation according to Gibbs’ approach to thermodynamics, thus an explicit connection between Carath ́odory’s approach and Gibbs’ approach to thermodynamics is obtained. The relation with statistical mechanical formalism is also pointed out