Numerical Solutions of Inflating Higher Dimensional Global Defects

We find numerical solutions of Einstein equations and scalar field equation for a global defect in higher dimensional spacetimes ($\geq 6$). We examine in detail the relation among the expansion rate $H$ and the symmetry-breaking scale $\eta$ and the number of extra dimensions $n$ for these solutions. We find that even if the extra dimensions do not have a cigar geometry, the expansion rate $H$ grows as $\eta$ increases, which is opposite to what is needed for the recently proposed mechanism for solving the cosmological constant problem. We also find that the expansion rate $H$ decreases as $n$ increases.Comment: 6 pages, 7 figures, ReVTeX4, Accepted for publication in PR

Axially Symmetric Cosmological Mesonic Stiff Fluid Models in Lyra's Geometry

In this paper, we obtained a new class of axially symmetric cosmological mesonic stiff fluid models in the context of Lyra's geometry. Expressions for the energy, pressure and the massless scalar field are derived by considering the time dependent displacement field. We found that the mesonic scalar field depends on only $t$ coordinate. Some physical properties of the obtained models are discussed.Comment: 13 pages, no figures, typos correcte

Scaling Law for the Cosmological Constant from Quantum Cosmology with Seven Extra Dimensions

According to a model of quantum cosmology the maximum number of degrees of freedom allowed in our three dimensions was determined by the size of seven extra dimensions in an initial excited state before inflation. The size of the extra dimensions can be inferred from a simple scheme for unifying the strong force and gravity. Coupled with the Bekenstein-Hawking entropy bound, these considerations lead to a scaling law for the cosmological constant that has been proposed independently by several authors.Comment: matches published version in IJT

Scattering of scalar particles by a black hole

The absorption cross section for scalar particle impact on a Schwarzschild black hole is found. The process is dominated by two physical phenomena. One of them is the well-known greybody factor that arises from the energy-dependent potential barrier outside the horizon that filters the incoming and outgoing waves. The other is related to the reflection of particles on the horizon (Kuchiev 2003). This latter effect strongly diminishes the cross section for low energies, forcing it to vanish in the infrared limit. It is argued that this is a general property, the absorption cross section vanishes in the infrared limit for scattering of particles of arbitrary spin.Comment: 7 pages, revtex, 1 figur

Reflection, radiation and interference for black holes

Black holes are capable of reflection: there is a finite probability for any particle that approaches the event horizon to bounce back. The albedo of the black hole depends on its temperature and the energy of the incoming particle. The reflection shares its physical origins with the Hawking process of radiation, both of them arise as consequences of the mixing of the incoming and outgoing waves that takes place on the event horizon.Comment: 10 pages, 1 figure, Revte

Quantum radiation by electrons in lasers and the Unruh effect

In addition to the Larmor radiation known from classical electrodynamics, electrons in a laser field may emit pairs of entangled photons -- which is a pure quantum effect. We investigate this quantum effect and discuss why it is suppressed in comparison with the classical Larmor radiation (which is just Thomson backscattering of the laser photons). Further, we provide an intuitive explanation of this process (in a simplified setting) in terms of the Unruh effect.Comment: 4 pages, 3 figure

Some Bianchi Type III String Cosmological Models with Bulk Viscosity

We investigate the integrability of cosmic strings in Bianchi III space-time in presence of a bulk viscous fluid by applying a new technique. The behaviour of the model is reduced to the solution of a single second order nonlinear differential equation. We show that this equation admits an infinite family of solutions. Some physical consequences from these results are also discussed.Comment: 12 pages, no figure. To appear in Int. J. Theor. Phy

Evolution of a Primordial Black Hole Population

We reconsider in this work the effects of an energy absorption term in the evolution of primordial black holes (hereafter PBHs) in the several epochs of the Universe. A critical mass is introduced as a boundary between the accreting and evaporating regimes of the PBHs. We show that the growth of PBHs is negligible in the Radiation-dominated Era due to scarcity of energy density supply from the expanding background, in agreement with a previous analysis by Carr and Hawking, but that nevertheless the absorption term is large enough for black holes above the critical mass to preclude their evaporation until the universe has cooled sufficiently. The effects of PBH motion are also discussed: the Doppler effect may give rise to energy accretion in black-holes with large peculiar motions relative to background. We discuss how cosmological constraints are modified by the introduction of the critical mass since that PBHs above it do not disturb the CMBR. We show that there is a large range of admissible masses for PBHs above the critical mass but well below the cosmological horizon. Finally we outline a minimal kinetic formalism, solved in some limiting cases, to deal with more complicated cases of PBH populationsComment: RevTex file, 8 pp., 3 .ps figures available upon request from [email protected]

Completeness of the Coulomb scattering wave functions

Completeness of the eigenfunctions of a self-adjoint Hamiltonian, which is the basic ingredient of quantum mechanics, plays an important role in nuclear reaction and nuclear structure theory. However, until now, there was no a formal proof of the completeness of the eigenfunctions of the two-body Hamiltonian with the Coulomb interaction. Here we present the first formal proof of the completeness of the two-body Coulomb scattering wave functions for repulsive unscreened Coulomb potential. To prove the completeness we use the Newton's method [R. Newton, J. Math Phys., 1, 319 (1960)]. The proof allows us to claim that the eigenfunctions of the two-body Hamiltonian with the potential given by the sum of the repulsive Coulomb plus short-range (nuclear) potentials also form a complete set. It also allows one to extend the Berggren's approach of modification of the complete set of the eigenfunctions by including the resonances for charged particles. We also demonstrate that the resonant Gamow functions with the Coulomb tail can be regularized using Zel'dovich's regularization method.Comment: 12 pages and 1 figur

Universality in the distribution of caustics in the expanding Universe

We numerically investigate the long--time evolution of density perturbations after the first appearance of caustics in an expanding cosmological model with one--dimensional `single--wave' initial conditions. Focussing on the time--intervals of caustic appearances and the spatial distribution of caustics at subsequent times, we find that the time--intervals of caustic appearances approach a constant, i.e., their time--subsequent ratio converges to 1; it is also found that the spatial distribution of caustics at a given time features some universality rules, e.g., the ratio between the position of the nearest caustic from the center and that of the second nearest caustic from the center approaches a constant. Furthermore we find some rules for the mass distribution for each caustic. Using these universality constants we are in the position to predict the spatial distribution of caustics at an arbitrary time in order to give an estimate for the power spectral index in the fully--developed non--dissipative turbulent (`virialized') regime.Comment: 23 pages, 19 figure