Thermodynamics of a black hole in a cavity

We present a unified thermodynamical description of the configurations consisting on self-gravitating radiation with or without a black hole. We compute the thermal fluctuations and evaluate where will they induce a transition from metastable configurations towards stable ones. We show that the probability of finding such a transition is exponentially small. This indicates that, in a sequence of quasi equilibrium configurations, the system will remain in the metastable states till it approaches very closely the critical point beyond which no metastable configuration exists. Near that point, we relate the divergence of the local temperature fluctuations to the approach of the instability of the whole system, thereby generalizing the usual fluctuations analysis in the cases where long range forces are present. When angular momentum is added to the cavity, the above picture is slightly modified. Nevertheless, at high angular momentum, the black hole loses most of its mass before it reaches the critical point at which it evaporates completely.Comment: 27 pages, latex file, contains 3 figures available on request at [email protected]

Discrete-time classical and quantum Markovian evolutions: Maximum entropy problems on path space

The theory of Schroedinger bridges for diffusion processes is extended to classical and quantum discrete-time Markovian evolutions. The solution of the path space maximum entropy problems is obtained from the a priori model in both cases via a suitable multiplicative functional transformation. In the quantum case, nonequilibrium time reversal of quantum channels is discussed and space-time harmonic processes are introduced.Comment: 34 page

Causal Relativistic Fluid Dynamics

We derive causal relativistic fluid dynamical equations from the relaxation model of kinetic theory as in a procedure previously applied in the case of non-relativistic rarefied gases. By treating space and time on an equal footing and avoiding the iterative steps of the conventional Chapman-Enskog --- CE---method, we are able to derive causal equations in the first order of the expansion in terms of the mean flight time of the particles. This is in contrast to what is found using the CE approach. We illustrate the general results with the example of a gas of identical ultrarelativistic particles such as photons under the assumptions of homogeneity and isotropy. When we couple the fluid dynamical equations to Einstein's equation we find, in addition to the geometry-driven expanding solution of the FRW model, a second, matter-driven nonequilibrium solution to the equations. In only the second solution, entropy is produced at a significant rate.Comment: 23 pages (CQG, in press

Attenuation and damping of electromagnetic fields: Influence of inertia and displacement current

New results for attenuation and damping of electromagnetic fields in rigid conducting media are derived under the conjugate influence of inertia due to charge carriers and displacement current. Inertial effects are described by a relaxation time for the current density in the realm of an extended Ohm's law. The classical notions of poor and good conductors are rediscussed on the basis of an effective electric conductivity, depending on both wave frequency and relaxation time. It is found that the attenuation for good conductors at high frequencies depends solely on the relaxation time. This means that the penetration depth saturates to a minimum value at sufficiently high frequencies. It is also shown that the actions of inertia and displacement current on damping of magnetic fields are opposite to each other. That could explain why the classical decay time of magnetic fields scales approximately as the diffusion time. At very small length scales, the decay time could be given either by the relaxation time or by a fraction of the diffusion time, depending whether inertia or displacement current, respectively, would prevail on magnetic diffusion.Comment: 21 pages, 1 figur

Cosmological entropy and generalized second law of thermodynamics in F(R,G)F(R,G) theory of gravity

We consider a spatially flat Friedmann-Lemaitre-Robertson-Walker space time and investigate the second law and the generalized second law of thermodynamics for apparent horizon in generalized modified Gauss Bonnet theory of gravity (whose action contains a general function of Gauss Bonnet invariant and the Ricci scalar: $F(R,G)$). By assuming that the apparent horizon is in thermal equilibrium with the matter inside it, conditions which must be satisfied by $F(R,G)$ are derived and elucidated through two examples: a quasi-de Sitter space-time and a universe with power law expansion.Comment: 10 pages, minor changes, typos corrected, accepted for publication in Europhysics Letter

Lemaitre-Tolman-Bondi dust spacetimes: Symmetry properties and some extensions to the dissipative case

We consider extensions of Lemaitre-Tolman-Bondi (LTB) spacetimes to the dissipative case. For doing that we previously carry out a systematic study on LTB. This study is based on two different aspects of LTB. On the one hand, a symmetry property of LTB will be presented. On the other hand, the description of LTB in terms of some fundamental scalar functions (structure scalars) appearing in the orthogonal splitting of Riemann tensor will be provided. We shall consider as "natural" generalizations of LTB (hereafter referred to as GLTB) either those metrics admitting some similar kind of symmetry as LTB, or those sharing structure scalars with similar dependence on the metric.Comment: 13 pages RevTex. To appear in Phys. Rev. D. Some references corrected and update

Holographic Dark Energy with Curvature

In this paper we consider an holographic model of dark energy, where the length scale is the Hubble radius, in a non flat geometry. The model contains the possibility to alleviate the cosmic coincidence problem, and also incorporate a mechanism to obtain the transition from decelerated to an accelerated expansion regime. We derive an analytic form for the Hubble parameter in a non flat universe, and using it, we perform a Bayesian analysis of this model using SNIa, BAO and CMB data. We find from this analysis that the data favored a small value for $\Omega_k$, however high enough to still produce cosmological consequences.Comment: 6 pages, 2 figure

Thermodynamics of black holes: an analogy with glasses

The present equilibrium formulation of thermodynamics for black holes has several drawbacks, such as assuming the same temperature for black hole and heat bath. Recently the author formulated non-equilibrium thermodynamics for glassy systems. This approach is applied to black holes, with the cosmic background temperature being the bath temperature, and the Hawking temperature the internal temperature. Both Hawking evaporation and absorption of background radiation are taken into account. It is argued that black holes did not form in the very early universe.Comment: 4 pages revtex; submitted to Phys. Rev. Let

The imprint of the interaction between dark sectors in galaxy clusters

Based on perturbation theory, we study the dynamics of how dark matter and dark energy in the collapsing system approach dynamical equilibrium while interacting. We find that the interaction between dark sectors cannot ensure the dark energy to fully cluster along with dark, leading to the energy non-conservation problem in the collapsing system We examine the cluster number counts dependence on the interaction between dark sectors. Furthermore, we analyze how dark energy inhomogeneities affect cluster abundances. It is shown that cluster number counts can provide specific signature of dark sectors interaction and dark energy inhomogeneities.Comment: revised version. New treatment has been provided on studying the structure formation in the spherical collapsing system where DE does not cluster together with DM. Accepted for publication in JCA

The imprint of the interaction between dark sectors in galaxy clusters

Based on perturbation theory, we study the dynamics of how dark matter and dark energy in the collapsing system approach dynamical equilibrium while interacting. We find that the interaction between dark sectors cannot ensure the dark energy to fully cluster along with dark, leading to the energy non-conservation problem in the collapsing system We examine the cluster number counts dependence on the interaction between dark sectors. Furthermore, we analyze how dark energy inhomogeneities affect cluster abundances. It is shown that cluster number counts can provide specific signature of dark sectors interaction and dark energy inhomogeneities.Comment: revised version. New treatment has been provided on studying the structure formation in the spherical collapsing system where DE does not cluster together with DM. Accepted for publication in JCA