Self-similar space-times

An exact solution of the transport equation in radiative transfer for an axially symmetric Rayleigh scattering problem in semi-infinite planetary atmosphere both for emergent intensity and intensity at any optical depth has been derived with the help of the Laplace transform and the Wiener-Hopf technique, and by use of the constancy of net flux. Chandrasekhar's results for emergent intensity have been verified. New expressions for theH _l andH _r functions have been obtained.     

Electromagnetic variations in curved space-times

The concept of a static index of refraction is being used to demonstrate that the quantities describing the vibrational ellipse vary because of the torsion induced by the index of refraction. Further, the idea is exploited that in relativistic objects such variations can be induced by the non-Euclidean character of the external geometry. Expressions are given for the induced curvature and torsion and, finally the Hamilton-Jacobi equation is used to derive the effective index of refraction for Kerr's geometry.     

Non-singular coordinates of some Kiselev space-times

In this article, non-singular Kruskal-like coordinates of some Kiselev space-times are presented. Also, non-singular Carter-like coordinates are constructed for the extreme case of Kiselev space-time.     

Quantum string theory in curved space-times

A general method to quantize strings in curved space-times is exposed. It treats the space-time metric exactly and the string excitations small as compared with the energy scale of the geometry. The method is applied to cosmological (de Sitter) and black-hole (Schwarzschild) geometries. The critical dimension decreases in one for de Sitter and stays unaltered for black-holes as compared with flat space-time values. Bogoliubov transformations in the context of string theory are derived and the Bogoliubov coefficients describing elastic and inelastic scattering and excitation of modes are computed explicitely. The string-black-hole cross section is derived and a pair mode creation phenomena is found. The quantization and scattering of strings in shockwave geometries (ultrarelativistic boosted black-holes or Aichelburg-Sexl space time) is found to be exactly solvable.     

Self-similar expansion of white dwarfs

Properties of plasma expansion that propagates in an electron-positron-ion dense plasma are investigated. Suitable hydrodynamic equations for the ions and ultrarelativistic degenerate electrons and positrons are used. Using self-similar transformation, the basic set of nonlinear equations is solved numerically. Typical values of white dwarf stars are used to estimate the behavior of the ion number density and ion fluid velocity. The positive ions are found to initially slowly escape with high velocity when the ion-to-electron density ratio increases. For higher values of the electron number density, the self-similar solution validity domain decreases. The relevance of the results to white dwarf expansion and collapse is highlight.     

Self-similar chameleon Jordan-Brans-Dicke cosmological models

In this paper we study the chameleon Jordan-Brans-Dicke (JBD) cosmological models under the hypothesis of self-similarity. Since there are several ways to define the matter Lagrangian for a perfect fluid: L _m =?ρ and L _m =γρ, we show that they bring us to obtain two completely different cosmological models. In the first approach, L _m =?ρ, there is ordinary matter conservation, while in the second approach, L _m =γρ, we get matter creation processes. We deduce for each approach the behaviour of each physical quantity, under the self-similar hypothesis, by employing the Lie group method. The results are quite general and valid for any homogeneous geometry (FRW, Bianchi types, etc.). As example, we calculate exact solutions for each approach by considering the case of a Bianchi II geometry. In this way we can determine the exact behaviour of each physical quantity and in particular of G _eff and U (the potential that mimics the cosmological constant).We compare the solutions with the obtained ones in the framework of the usual JBD models.     

The LRS Bianchi type-I perfect fluids space-times

An algorithm is derived for constructing spatially-homogeneous perfect fluid solutions of Einstein's field equations which are of Bianchi type-I and are locally rotationally-symmetric. Starting from Bayin and Krisch solution a new exact solution is obtained. Some physical and kinematic properties of the cosmological model are discussed.     

A class of Szekeres space-times with cosmological constant

We present a generalization of a class of Szekeres space-times. The new solutions satisfy Einstein's equations with a cosmological constant and have the same geometrical properties as the corresponding class found by Szekeres. Particular cases leading to known solutions are considered.     

Self-similar spherical collapse with non-radial motions

We derive the asymptotic mass profile near the collapse centre of an initial spherical density perturbation, δ ∝ M ^{− ε} , of collisionless particles with non-radial motions. We show that angular momenta introduced at the initial time do not affect the mass profile. Alternatively, we consider a scheme in which a particle moves on a radial orbit until it reaches its turnaround radius, r ∗. At turnaround the particle acquires an angular momentum L =ℒ√ GM _* r _* per unit mass, where M ∗ is the mass interior to r ∗. In this scheme, the mass profile is M ∝ r ^{3/(1+3 ε )} for all ε >0 , in the region r / r _t ≪ℒ , where r _t is the current turnaround radius. If ℒ≪1 then the profile in the region ℒ≪ r / r _t ≪1 is M ∝ r for ε <2/3 , and remains M ∝ r ^{3/(1+3 ε )} for ε ≥2/3 . The derivation relies on a general property of non-radial orbits which is that the ratio of the pericentre to apocentre is constant in a force field k ( t ) r ⁿ with k ( t ) varying adiabatically.     

Deviation of circular geodesics in static spherically symmetric space-times

For static spherically symmetric space-times the equations of geodesic deviation are solved for circular geodesics. We discuss the connection between the obtained solutions and the stability behaviour of the geodesics. The perihelion shift for test bodies moving on nearly circular geodesics is also derived.     

Self-similar magnetogasdynamic cylindrical shock waves,I

Similarity solutions describing the flow of a perfect gas behind a cylindrical shock wave with transverse magnetic field are investigated in an inhomogeneous medium. The total energy of the shock wave is assumed to be constant. A comparative study has been made between the results with and without magnetic field.     

Two-fluid cosmological models in a Bianchi type I space-times

In this paper we present anisotropic, homogeneous two-fluid cosmological models in a Bianchi I space-time. These classes of cosmological models picture two different scenarios of cosmic history; viz., when the radiation and matter content of the universe are in interactive phase and another when the two are non-interacting. The universe is highly anisotropic in the initial stages, however, anisotropy tapers out to insignificance in due course of cosmic evolution. In every model the anisotropy of the space-time is determined by the density parameter Ω₀ at the present epoch. For Ω₀=1, the anisotropy is washed out before long. An interesting class of models, having an inflationary epoch in finite future, is discovered.      

Self-similar dynamics of a magnetized polytropic gas

In broad astrophysical contexts of large-scale gravitational collapses and outflows and as a basis for various further astrophysical applications, we formulate and investigate a theoretical problem of self-similar magnetohydrodynamics (MHD) for a non-rotating polytropic gas of quasi-spherical symmetry permeated by a completely random magnetic field. Within this framework, we derive two coupled nonlinear MHD ordinary differential equations (ODEs), examine properties of the magnetosonic critical curve, obtain various asymptotic and global semi-complete similarity MHD solutions, and qualify the applicability of our results. Unique to a magnetized gas cloud, a novel asymptotic MHD solution for a collapsing core is established. Physically, the similarity MHD inflow towards the central dense core proceeds in characteristic manners before the gas material eventually encounters a strong radiating MHD shock upon impact onto the central compact object. Sufficiently far away from the central core region enshrouded by such an MHD shock, we derive regular asymptotic behaviours. We study asymptotic solution behaviours in the vicinity of the magnetosonic critical curve and determine smooth MHD eigensolutions across this curve. Numerically, we construct global semi-complete similarity MHD solutions that cross the magnetosonic critical curve zero, one, and two times. For comparison, counterpart solutions in the case of an isothermal unmagnetized and magnetized gas flows are demonstrated in the present MHD framework at nearly isothermal and weakly magnetized conditions. For a polytropic index γ=1.25 or a strong magnetic field, different solution behaviours emerge. With a strong magnetic field, there exist semi-complete similarity solutions crossing the magnetosonic critical curve only once, and the MHD counterpart of expansion-wave collapse solution disappears. Also in the polytropic case of γ=1.25, we no longer observe the trend in the speed-density phase diagram of finding infinitely many matches to establish global MHD solutions that cross the magnetosonic critical curve twice.      

Paralleltransport and geodesic deviation in static spherically symmetric space-times

Tetrads which are parallelpropagated along time-like geodesics in static spherically symmetric spce-times are constructed. Its connection with the geodesic precession is explained. Moreover, we express the solution of the equations of geodesic deviation in terms of the Killing vectors and the fourvelocity.     

A class of new Bianchi I perfect fluid space-times

A procedure to generate new exact solutions to Einstein equations for perfect fluids is applied to LRS Bianchi type I line-element. Starting from some known solutions a class of new perfect fluid solutions of Bianchi type I are presented. The physical and kinematical properties of spatially homogeneous and anisotropic cosmological models are studied.