Classical no-cloning theorem under Liouville dynamics by non-Csisz\'ar f-divergence

The Csisz\'ar f-divergence, which is a class of information distances, is known to offer a useful tool for analysing the classical counterpart of the cloning operations that are quantum mechanically impossible for the factorized and marginality classical probability distributions under Liouville dynamics. We show that a class of information distances that does not belong to this divergence class also allows for the formulation of a classical analogue of the quantum no-cloning theorem. We address a family of nonlinear Liouville-like equations, and generic distances, to obtain constraints on the corresponding functional forms, associated with the formulation of classical analogue of the no-cloning principle.Comment: 6 pages, revised, published versio

Naked Singularity Explosion

It is known that the gravitational collapse of a dust ball results in naked singularity formation from an initial density profile which is physically reasonable. In this paper, we show that explosive radiation is emitted during the formation process of the naked singularity.Comment: 6 pages, 3 figures, Accepted for Publication in Phys. Rev. D as a Rapid Communicatio

Physical aspects of naked singularity explosion - How does a naked singularity explode? --

The behaviors of quantum stress tensor for the scalar field on the classical background of spherical dust collapse is studied. In the previous works diverging flux of quantum radiation was predicted. We use the exact expressions in a 2D model formulated by Barve et al. Our present results show that the back reaction does not become important during the semiclassical phase. The appearance of the naked singularity would not be affected by this quantum field radiation. To predict whether the naked singularity explosion occurs or not we need the theory of quantum gravity. We depict the generation of the diverging flux inside the collapsing star. The quantum energy is gathered around the center positively. This would be converted to the diverging flux along the Cauchy horizon. The ingoing negative flux crosses the Cauchy horizon. The intensity of it is divergent only at the central naked singularity. This diverging negative ingoing flux is balanced with the outgoing positive diverging flux which propagates along the Cauchy horizon. After the replacement of the naked singularity to the practical high density region the instantaneous diverging radiation would change to more milder one with finite duration.Comment: 18 pages, 16 figure

The thermodynamic limit for fractional exclusion statistics

I discuss Haldane's concept of generalised exclusion statistics (Phys. Rev. Lett. {\bf 67}, 937, 1991) and I show that it leads to inconsistencies in the calculation of the particle distribution that maximizes the partition function. These inconsistencies appear when mutual exclusion statistics is manifested between different subspecies of particles in the system. In order to eliminate these inconsistencies, I introduce new mutual exclusion statistics parameters, which are proportional to the dimension of the Hilbert sub-space on which they act. These new definitions lead to properly defined particle distributions and thermodynamic properties. In another paper (arXiv:0710.0728) I show that fractional exclusion statistics manifested in general systems with interaction have these, physically consistent, statistics parameters.Comment: 8 page

Onset of inflation in inhomogeneous cosmology

We study how the initial inhomogeneities of the universe affect the onset of inflation in the closed universe. We consider the model of a chaotic inflation which is driven by a massive scalar field. In order to construct an inhomogeneous universe model, we use the long wavelength approximation ( the gradient expansion method ). We show the condition of the inhomogeneities for the universe to enter the inflationary phase.Comment: 22 pages including 12 eps figures, RevTe

Power, energy, and spectrum of a naked singularity explosion

Naked singularity occurs in the gravitational collapse of an inhomogeneous dust ball from an initial density profile which is physically reasonable. We show that explosive radiation is emitted during the formation process of the naked singularity. The energy flux is proportional to $(t_{\rm CH}-t)^{-3/2}$ for a minimally coupled massless scalar field, while is proportional to $(t_{\rm CH}-t)^{-1}$ for a conformally coupled massless scalar field, where $t_{\rm CH}-t$ is the `remained time' until the distant observer could observe the singularity if the naked singularity was formed. As a consequence, the radiated energy grows unboundedly for both scalar fields. The amount of the power and the energy depends on parameters which characterize the initial density profile but do not depend on the gravitational mass of the cloud. In particular, there is characteristic frequency $\nu_{s}$ of singularity above which the divergent energy is radiated. The energy flux is dominated by particles of which the wave length is about $t_{\rm CH}-t$ at each moment. The observed total spectrum is nonthermal, i.e., $\nu dN/d\nu \sim (\nu/\nu_{s})^{-1}$ for $\nu>\nu_{s}$. If the naked singularity formation could continue until a considerable fraction of the total energy of the dust cloud is radiated, the radiated energy would reach about $10^{54}(M/M_{\odot})$ erg. The calculations are based on the geometrical optics approximation which turns out to be consistent as a rough order estimate. The analysis does not depend on whether or not the naked singularity occurs in its exact meaning. This phenomenon may provide a new candidate for a source of ultra high energy cosmic rays or a central engine of gamma ray bursts.Comment: 34 pages, 13 postscript figures included, to appear in Phys. Rev. D, grammatical errors correcte

The structure of non-spacelike geodesics in dust collapse

We study here the behaviour of non-spacelike geodesics in dust collapse models in order to understand the casual structure of the spacetime. The geodesic families coming out, when the singularity is naked, corresponding to different initial data are worked out and analyzed. We also bring out the similarity of the limiting behaviour for different types of geodesics in the limit of approach to the singularity.Comment: 23 pages, 6 figures, to appear in PR

Thermodynamics of ideal quantum gas with fractional statistics in D dimensions

We present exact and explicit results for the thermodynamic properties (isochores, isotherms, isobars, response functions, velocity of sound) of a quantum gas in dimensions D>=1 and with fractional exclusion statistics 0<=g<=1 connecting bosons (g=0) and fermions (g=1). In D=1 the results are equivalent to those of the Calogero-Sutherland model. Emphasis is given to the crossover between boson-like and fermion-like features, caused by aspects of the statistical interaction that mimic long-range attraction and short-range repulsion. The full isochoric heat capacity and the leading low-T term of the isobaric expansivity in D=2 are independent of g. The onset of Bose-Einstein condensation along the isobar occurs at a nonzero transition temperature in all dimensions. The T-dependence of the velocity of sound is in simple relation to isochores and isobars. The effects of soft container walls are accounted for rigorously for the case of a pure power-law potential.Comment: 15 pages, 31 figure

Spherically symmetric perfect fluid in area-radial coordinates

We study the spherically symmetric collapse of a perfect fluid using area-radial coordinates. We show that analytic mass functions describe a static regular centre in these coordinates. In this case, a central singularity can not be realized without an infinite discontinuity in the central density. We construct mass functions involving fluid dynamics at the centre and investigate the relationship between those and the nature of the singularities.Comment: Accepted by CQG. LaTex file, 14 pages, no figure