Thermodynamics and gravitational collapse

It is known now that a typical gravitational collapse in general relativity, evolving from regular initial data and under physically reasonable conditions would end in either a black hole or a naked singularity final state. An important question that needs to be answered in this connection is, whether the analogues of the laws of thermodynamics, as formulated for relativistic horizons are respected by the dynamical spacetimes for collapse that end in the formation of a naked singularity. We investigate here the thermodynamical behaviour of the dynamical horizons that form in spherically symmetric gravitational collapse and we show that the first and second laws of black hole thermodynamics, as extended to dynamical spacetimes in a suitable manner, are not violated whether the collapse ends in a black hole or a naked singularity. We then make a distinction between the naked singularities that result from gravitational collapse, and those that exist in solutions of Einstein equations in vacuum axially symmetric and stationary spacetimes, and discuss their connection with thermodynamics in view of the cosmic censorship conjecture and the validity of the third law of black hole mechanics.Comment: 8 pages, 2 figure

Compact objects from gravitational collapse: an analytical toy model

We develop here a procedure to obtain regular static configurations as resulting from dynamical gravitational collapse of a massive matter cloud in general relativity. Under certain general physical assumptions for the collapsing cloud, we find the class of dynamical models that lead to an equilib- rium configuration. To illustrate this, we provide a class of perfect fluid collapse models that lead to a static constant density object as limit. We suggest that similar models might possibly constitute the basis for the description of formation of compact objects in nature.Comment: 9 pages, published versio

All black holes in Lemaitre-Tolman-Bondi inhomogeneous dust collapse

Within the Lemaitre-Tolman-Bondi formalism for gravitational collapse of inhomogeneous dust we analyze the parameter space that leads to the formation of a globally covered singularity (i.e. a black hole) when some physically reasonable requirements are imposed (namely positive radially decreasing and quadratic profile for the energy density and avoidance of shell crossing singularities). It turns out that a black hole can occur as the endstate of collapse only if the singularity is simultaneous as in the standard Oppenheimer-Snyder scenario. Given a fixed density profile then there is one velocity profile for the infalling particles that will produce a black hole. All other allowed velocity profiles will terminate the collapse in a locally naked singularity.Comment: 10 pages, 2 figures, matches published versio

Susceptibility analysis of complex systems

A study of electromagnetic coupling effects on systems containing distributed elements and lumped linear components is presented. The structure is decomposed into sections containing multiconductor transmission lines and interconnection blocks holding lumped elements. The external field is assumed to interfere with line sections, but mutual influences among different sections are neglected. Both the sections and the blocks are treated as multiport components and characterized by their scattering parameters. The analysis is based on a correspondence matrix that accounts for the topology of connections between sections and blocks. Closed-form solutions are derived in the Laplace domain, and the temporal evolution of voltages and currents at any of the system ports is obtained by a numerical inversion. This method makes it possible to predict the susceptibility of complex systems and to verify the intra-system compatibility (especially crosstalk). The relative influence of circuit components and of line layouts on the severity of interferences is evidenced by simulation result

Asymmetric Dark Matter in the Sun and the Diphoton Excess at the LHC

It has been recently pointed out that a momentum-dependent coupling of the asymmetric Dark Matter (ADM) with nucleons can explain the broad disagreement between helioseismological observables and the predictions of standard solar models. In this paper, we propose a minimal simplified ADM model consisting of a scalar and a pseudoscalar mediator, in addition to a Dirac fermionic DM, for generating such momentum-dependent interactions. Remarkably, the pseudoscalar with mass around 750 GeV can simultaneously explain the solar anomaly and the recent diphoton excess observed by both ATLAS and CMS experiments in the early $\sqrt s=13$ TeV LHC data. In this framework, the total width of the resonance is naturally large, as suggested by the ATLAS experiment, since the resonance mostly decays to the ADM pair. The model predicts the existence of a new light scalar in the GeV range, interacting with quarks, and observable dijet, monojet and $t\bar{t}$ signatures for the 750 GeV resonance at the LHC.Comment: 7 pages, 4 figures. Version to appear in PR

Acceleration field of a Universe modeled as a mixture of scalar and matter fields

A model of the Universe as a mixture of a scalar (inflaton or rolling tachyon from the string theory) and a matter field (classical particles) is analyzed. The particles are created at the expense of the gravitational energy through an irreversible process whereas the scalar field is supposed to interact only with itself and to be minimally coupled with the gravitational field. The irreversible processes of particle creation are related to the non-equilibrium pressure within the framework of the extended (causal or second-order) thermodynamic theory. The scalar field (inflaton or tachyon) is described by an exponential potential density added by a parameter which represents its asymptotic value and can be interpreted as the vacuum energy. This model can simulate three phases of the acceleration field of the Universe, namely,(a) an inflationary epoch with a positive acceleration followed by a decrease of the acceleration field towards zero, (b) a past decelerated period where the acceleration field decreases to a maximum negative value followed by an increase towards zero, and (c) a present accelerated epoch. For the energy densities there exist also three distinct epochs which begin with a scalar field dominated period followed by a matter field dominated epoch and coming back to a scalar field dominated phase.Comment: 9 pages, 2 figures, to be published in General Relativity and Gravitatio