A New Class of Inhomogeneous String Cosmological Models in General Relativity

A new class of solutions of Einstein field equations has been investigated for inhomogeneous cylindrically symmetric space-time with string source. To get the deterministic solution, it has been assumed that the expansion ($\theta$) in the model is proportional to the eigen value $\sigma^{1}_{1}$ of the shear tensor $\sigma^{i}_{j}$. Certain physical and geometric properties of the models are also discussed.Comment: 12 pages, no figure. Submitted to Astrophys. Space Sci. arXiv admin note: substantial text overlap with arXiv:0705.090

Gravity wave analogs of black holes

It is demonstrated that gravity waves of a flowing fluid in a shallow basin can be used to simulate phenomena around black holes in the laboratory. Since the speed of the gravity waves as well as their high-wavenumber dispersion (subluminal vs. superluminal) can be adjusted easily by varying the height of the fluid (and its surface tension) this scenario has certain advantages over the sonic and dielectric black hole analogs, for example, although its use in testing quantum effects is dubious. It can be used to investigate the various classical instabilities associated with black (and white) holes experimentally, including positive and negative norm mode mixing at horizons. PACS: 04.70.-s, 47.90.+a, 92.60.Dj, 04.80.-y.Comment: 14 pages RevTeX, 5 figures, section VI modifie

Waveforms for Gravitational Radiation from Cosmic String Loops

We obtain general formulae for the plus- and cross- polarized waveforms of gravitational radiation emitted by a cosmic string loop in transverse, traceless (synchronous, harmonic) gauge. These equations are then specialized to the case of piecewise linear loops, and it is shown that the general waveform for such a loop is a piecewise linear function. We give several simple examples of the waveforms from such loops. We also discuss the relation between the gravitational radiation by a smooth loop and by a piecewise linear approximation to it.Comment: 16 pages, 6 figures, Revte

From bound states to resonances: analytic continuation of the wave function

Single-particle resonance parameters and wave functions in spherical and deformed nuclei are determined through analytic continuation in the potential strength. In this method, the analyticity of the eigenvalues and eigenfunctions of the Schroedinger equation with respect to the coupling strength is exploited to analytically continue the bound-state solutions into the positive-energy region by means of Pade' approximants of the second kind. The method is here applied to single-particle wave functions of the $^{154}Sm$ and $^{131}Eu$ nuclei. A comparison of the results with the direct solution of the Schroedinger equation shows that the method can be confidently applied also in coupled-channel situations requiring high numerical accuracy.Comment: 13 pages, 3 figure

Bounds from Primordial Black Holes with a Near Critical Collapse Initial Mass Function

Recent numerical evidence suggests that a mass spectrum of primordial black holes (PBHs) is produced as a consequence of near critical gravitational collapse. Assuming that these holes formed from the initial density perturbations seeded by inflation, we calculate model independent upper bounds on the mass variance at the reheating temperature by requiring the mass density not exceed the critical density and the photon emission not exceed current diffuse gamma-ray measurements. We then translate these results into bounds on the spectral index n by utilizing the COBE data to normalize the mass variance at large scales, assuming a constant power law, then scaling this result to the reheating temperature. We find that our bounds on n differ substantially (\delta n > 0.05) from those calculated using initial mass functions derived under the assumption that the black hole mass is proportional to the horizon mass at the collapse epoch. We also find a change in the shape of the diffuse gamma-ray spectrum which results from the Hawking radiation. Finally, we study the impact of a nonzero cosmological constant and find that the bounds on n are strengthened considerably if the universe is indeed vacuum-energy dominated today.Comment: 24 pages, REVTeX, 5 figures; minor typos fixed, two refs added, version to be published in PR

The Future Evolution of White Dwarf Stars Through Baryon Decay and Time Varying Gravitational Constant

Motivated by the possibility that the fundamental ``constants'' of nature could vary with time, this paper considers the long term evolution of white dwarf stars under the combined action of proton decay and variations in the gravitational constant. White dwarfs are thus used as a theoretical laboratory to study the effects of possible time variations, especially their implications for the future history of the universe. More specifically, we consider the gravitational constant $G$ to vary according to the parametric relation $G = G_0 (1 + t/t_\ast)^{-p}$, where the time scale $t_\ast$ is the same order as the proton lifetime. We then study the long term fate and evolution of white dwarf stars. This treatment begins when proton decay dominates the stellar luminosity, and ends when the star becomes optically thin to its internal radiation.Comment: 12 pages, 10 figures, accepted to Astrophysics and Space Scienc

Consistency of the mass variation formula for black holes accreting cosmological fluids

We address the spherical accretion of generic fluids onto black holes. We show that, if the black hole metric satisfies certain conditions, in the presence of a test fluid it is possible to derive a fully relativistic prescription for the black hole mass variation. Although the resulting equation may seem obvious due to a form of it appearing as a step in the derivation of the Schwarzschild metric, this geometrical argument is necessary to fix the added degree of freedom one gets for allowing the mass to vary with time. This result has applications on cosmological accretion models and provides a derivation from first principles to serve as a base to the accretion equations already in use in the literature.Comment: 4 pages, 1 figure. To appear in Gen. Rel. Gra

Oscillation damping of chiral string loops

Chiral cosmic string loop tends to the stationary (vorton) configuration due to the energy loss into the gravitational and electromagnetic radiation. We describe the asymptotic behaviour of near stationary chiral loops and their fading to vortons. General limits on the gravitational and electromagnetic energy losses by near stationary chiral loops are found. For these loops we estimate the oscillation damping time. We present solvable examples of gravitational radiation energy loss by some chiral loop configurations. The analytical dependence of string energy with time is found in the case of the chiral ring with small amplitude radial oscillations.Comment: 10 pages, 2 figures. Accepted for publication in Physical Review

Five Dimensional Cosmological Models in General Relativity

A Five dimensional Kaluza-Klein space-time is considered in the presence of a perfect fluid source with variable G and $\Lambda$. An expanding universe is found by using a relation between the metric potential and an equation of state. The gravitational constant is found to decrease with time as $G \sim t^{-(1-\omega)}$ whereas the variation for the cosmological constant follows as $\Lambda \sim t^{-2}$, $\Lambda \sim (\dot R/R)^2$ and $\Lambda \sim \ddot R/R$ where $\omega$ is the equation of state parameter and $R$ is the scale factor.Comment: 13 pages, 4 figures, accepted in Int. J. Theor. Phy

Massive cosmic strings in Bianchi type II

We study a massive cosmic strings with BII symmetries cosmological models in two contexts. The first of them is the standard one with a barotropic equation of state. In the second one we explore the possibility of taking into account variable \textquotedblleft constants\textquotedblright ($G$ and $\Lambda ).$Both models are studied under the self-similar hypothesis. We put special emphasis in calculating the numerical values for the equations of state. We find that for $\omega\in(0,1]$, $G$, is a growing time function while $\Lambda$, behaves as positive decreasing time function. If $\omega=0,$ both \textquotedblleft constants\textquotedblright, $G$ and $\Lambda,$ behave as true constants.Comment: 7 pages, RevTe