Transient flow of a relativistic radiating gas past a horizontal plate

The problem of unsteady flow of a relativistic radiating neutrino gas is studied by imposing a time-dependent perturbation on a basic flow. When the perturbation is small, the problem, which is ill-posed, is reduced to a well-posed spatial value problem for the transverse velocity and the temperature. Subsequently the axial velocity and number density may be obtained by straightforward integration with respect to time and imposition of the initial condition. The solution for the initial value problem is tackled by the Laplace transform technique and the results are discussed quantitatively.     

Two-dimensional fluctuating flow and heat transfer to a relativistic radiating gas

The two-dimensional ideal flow of a neutrino gas past a vertical hot flat plate subjected to temperature fluctuation, is analysed within the framework of the continuum theory. If the difference between the wall temperature and the free-stream temperature is small, the first-order perturbed set of equations is reduced to a set of well-posed coupled linear boundary value problems for the temperature and the transverse velocity. The axial velocity and number density may then be determined.     

Energy characteristics of a relativistic Fermi gas in a magnetic field

We derive expressions for the chemical potential, pressure, and mean total energy of an extremely degenerate ideal relativistic gas of charged fermions. We take into account their static anomalous magnetic moments in the presence of a quantizing magnetic field. We examine the cases of ultra-strong magnetic fields and of weak fields in which one does not need to take into account Landau quantization when describing a Fermi gas in ultra-dense matter.Translated from Astrofizika, Vol. 37, No. 1, pp. 161–165, January–March, 1994.     

The boundary-layer flow of a radiating gas by the integral equation method

The flow in the boundary layer of a very hot two-component plasma is analysed when the radiative heat flux is given by the exact integral equation expression. The basic nonlinear integro-differential equation is solved by perturbing it about the differential approximation for radiation. In this way some light is shed on the order of accuracy of the differential approximation of radiation. In fact an error of about 4% may be incurred by invoking the differential approximation.     

Rotational perturbations of relativistic perfect-fluid model universes interacting with gravitational field

Along with the presentation of several new analytic solutions, the dynamics of slowly rotating perfect-fluid model universes are investigated, and their physical and geometrical properties are discussed from all angles. The rotational perturbations of such models are examined in detail in order to substantiate the possibility that the Universe is endowed with some rotation. The nature and role of the rotational velocity (r, t) which is related to the local dragging of inertial frames and that of the matter rotation (r, t) are studied for uniform and non-uniform motions. We find out the restrictions on the radii of the models for real astrophysical situations, and the periods of physical validity of them are also obtained. Rotating models which are expanding as well are obtained, in which cases the rotational velocities are found to decay with the time; and these models may be taken as examples of real astrophysical objects in this Universe.     

Horizon-free gravitational collapse of radiating fluid sphere

In this paper we present a detailed study of BCT Ist solution Tewari (Astrophys. Space Sci. 149:233, 1988) representing time dependent balls of perfect fluid with matter-radiation in general relativity. Assuming the life time of quasar 10⁷ years our model has initial mass≈10⁸ M _Θ with an initial linear dimension≈10¹⁵ cm. Our model is radiating the energy at a constant rate i.e. L _∞=10⁴⁷ ergs/sec with the gravitational red shift, z=0.44637. In this model we have 2GM(u)/c ² R _S (u))=0.3191 i.e. the model is horizon free.     

Compressible,conductive, steady MHD flow in a gravitational field

The magnetohydrodynamics of a compressible fluid with finite electrical conductivity in a gravitational field is treated analytically. For the case of one ignorable coordinate in cylindrical and Cartesian coordinates the problem is reduced to a scalar partial differential equation. The ideal gas equation of state is considered. For simplicity, the new equation is derived for a two-component motion. The application of this result to mass flow in sunspots is discussed.     

Unsteady isothermal flow of a gas behind an exponential shock in magnetogasdynamics

A self-similar flow of a perfect gas behind a strong shock driven out by a propelling contact discontinuity surface moving with time according to an exponential law in the presence of axial component of the magnetic field is investigated. The flow between the shock and the inner-expanding surface is assumed to be isothermal. The infinite electrically conductive and uniform medium has been taken into consideration.     

The gravitational field of a disk

This note gives the gravitational potential of the disk {(x, y, z):x ² +y ² p ² , z=0} and the gravitational field at the point (x, y, z). Formulas for a ring can be obtained as the difference of our results for two different values ofp. Results are obtained in terms of elliptic integrals and we indicate how these functions can be computed efficiently. Formulas necessary for the computation of partial derivatives are also given.This paper presents the results of one phase of research carried out at the Jet Propulsion Laboratory, California Institute of Technology, under Contract NAS7-100, sponsored by the National Aeronautics and Space Administration.     

Flow behind an attached shock wave in a radiating gas

A simple method is used to determine the curvature of an attached shock wave and the flow variable gradients behind the shock curve at the tip of a straight-edged wedge placed symmetrically in a supersonic flow of a radiating gas near the optically thin limit. The shock curvature and the flow variable gradients along the wedge at the tip are computed for a wide range of upstream flow Mach numbers and wedge angles. Several interesting results are noted; in particular, it is found that the effect of an increase in the upstream flow Mach number or the radiative flux is to enhance the shock wave curvature which, however, decreases with an increase in the specific heat ratio or the wedge angle.     

Propagation of light in a Maxwell-like gravitational field

We propose a coupling between the gravitational and electromagnetic fields so that we consider the electrodynamical Maxwell's equations as the basic ones and add the four-vector of gravitational potential to the differential operators occurring in it. It is shown that by means of this coupling all well-known tests of Einstein's theory of gravitation connected with the propagation of light in gravitational field can be correctly calculated.     

The relativistic dynamics of a thin spherically symmetric radiating shell in the presence of a central body

We construct an idealized spherically symmetric relativistic model of an exploding object within the framework of the theory of surface layers in GR. A Vaidya solution for a radially radiating star is matched through a spherical shell of dust to a Schwarzschild solution. The (incomplete) equations for the motion of the spherical shell of dust and the radiation density of the Vaidya solution, as given by the matching conditions, are reduced to a first-order system and a general analysis of the characteristics of the motion is given. This system of differential equations is completed, adding a relation between the unknowns which represents the simplest way to avoid an unphysical singularity in the motion. The results of a numerical integration of the equations are presented in two cases which we think may have some relationship to stellar explosions. A comparative set of results for other solutions is also given, and some possible generalizations of the model are pointed out.     

Two-dimensional equilibrium of a neutral sheet in a gravitational field

We solve the two-dimensional MHD-equations to find the equilibrium structure of a neutral sheet having its axis parallel to the gravitational field in an atmosphere. The evolution of an initially plane sheet which is a self-consistent, non-equilibrium solution of the MHD-equations, is followed until static equilibrium of forces is obtained. The effect of field line anchoring in a cool dense layer at the bottom of the sheet is taken into account.Presently at The Auroral Observatory, Boks 953, 9001 Tromsø, Norway.     

Equilibria in the gravitational field of a triangular body

The existence, stability and bifurcation analysis is performed for equilibria of a material point in the gravitational field of three homogeneous penetrable balls fixed in absolute frame. The radii of the balls are assumed finite. In the case when the mass distribution admits a symmetry axis, analytic expressions are written out, allowing one to investigate the properties of equilibrium positions located both on the symmetry axis and outside it. The stability of solutions is studied; domains with different instability degree are described.     

Collisional theory of non-identical particles in a gravitational field

The statistical theory of partially elastic collisions and gravitational encounters is generalized for non-identical particles having different masses, internal densities, radii, elastic parameters or other properties. In those cases which are numerically studied, the differences in elasticity do not produce significant effects: essentially the same distribution of orbits is found if the mean value of the restitution coefficients is used for all the particles. Differences in the internal density lead to the equipartition of energy in the random motion, although this approximation is rather rough and affords for the lightest particles an overestimated energy. Mass differences which correspond to a dispersion of radii produce a complicated behaviour. The equipartition of the energy is occasionally possible, but if the mass differences are large, the velocity dispersion can be inversely proportional to the radius. Other distributions also occur.