Propagation of High-Frequency Electromagnetic Waves Through a Magnetized Plasma in Curved Spaces-Time. II. Application of the Asymptotic Approximation

This is the second of two papers on the propagation of high-frequency electromagnetic waves through an inhomogeneous, non-stationary plasma in curved space-time. By applying the general two-scale W.K.B. method developed in part I to the basic wave equation, derived also in that paper, we here obtain the dispersion relation, the rays, the polarization states and the transport laws for the amplitudes of these waves. In an unmagnetized plasma the transport preserves the helicity and the eccentricity of the polarization state along each ray; the axes of the polarization ellipse rotate along a ray, relative to quasiparallely displaced directions, at a rate determined by the vorticity of the electron fluid; and the norm of the amplitude changes according to a conservation law which can be interpreted as the constancy of the number of quasiphotons. In a magnetized plasma the polarization state changes differently for ordinary and extraordinary waves, according to the angle between the wavenormal and the background magnetic field, and under specified approximation conditions the direction of polarization of linearly polarized waves undergoes a generalized Faraday rotation

Cosmology With A Dark Refraction Index

We review Gordon's optical metric and the transport equations for the amplitude and polarization of a geometrical optics wave traveling in a gravity field. We apply the theory to the FLRW cosmologies by associating a refraction index with the cosmic fluid. We then derive an expression for the accumulated effect of a refraction index on the distance redshift relations and fit the Hubble curve of current supernova observations with a non-accelerating cosmological model. We also show that some observational effects caused by inhomogeneities, e.g. the Sachs-Wolfe effect, can be interpreted as being caused by an effective index of refraction, and hence this theory could extend to other speed of light communications such as gravitational radiation and neutrino fluxes.Comment: 21 pages, 3 figure

Choked flow of fluid nitrogen with emphasis on the thermodynamic critical region

Experimental measurements of critical flow rate and pressure ratio for nitrogen flowing through a nozzle are presented. Data for selected stagnation isotherms from 87.5 to 234 K with pressures to 9.3 MN/m2 are compared to an equilibrium model with real fluid properties and also a nonequilibrium model. Critical flow pressure ratio along an isotherm tends to peak while the flow rate indicates an inflection. The point is closely associated with the transposed critical temperature and represents a change in the fluid structure

A Characterisation of the Weylian Structure of Space-Time by Means of Low Velocity Tests

The compatibility axiom in Ehlers, Pirani and Schild's (EPS) constructive axiomatics of the space-time geometry that uses light rays and freely falling particles with high velocity, is replaced by several constructions with low velocity particles only. For that purpose we describe in a space-time with a conformal structure and an arbitrary path structure the radial acceleration, a Coriolis acceleration and the zig-zag construction. Each of these quantities give effects whose requirement to vanish can be taken as alternative version of the compatibility axiom of EPS. The procedural advantage lies in the fact, that one can make null-experiments and that one only needs low velocity particles to test the compatibility axiom. We show in addition that Perlick's standard clock can exist in a Weyl space only.Comment: to appear in Gen.Rel.Gra

Prediction of local and integrated heat transfer in nozzles using an integral turbulent boundary layer method

An empirical modification of an existing integral energy turbulent boundary layer method is proposed in order to improve the estimates of local heat transfer in converging-diverging nozzles and consequently, provide better assessments of the total or integrated heat transfer. The method involves the use of a modified momentum-heat analogy which includes an acceleration term comprising the nozzle geometry and free stream velocity. The original and modified theories are applied to heat transfer data from previous studies which used heated air in 30 deg - 15 deg, 45 deg - 15 deg, and 60 deg - 15 deg water-cooled nozzles

On the Asymptotic Stability of De-Sitter Spacetime: a non-linear perturbative approach

We derive evolution and constraint equations for second order perturbations of flat dust homogeneous and isotropic solutions to the Einstein field equations using all scalar, vector and tensor perturbation modes. We show that the perturbations decay asymptotically in time and that the solutions converge to the De-Sitter solution. By induction, this result is valid for perturbations of arbitrary order. This is in agreement with the cosmic no-hair conjecture of Gibbons and Hawking.Comment: 11 pages, 2 figure

Distance-redshift from an optical metric that includes absorption

We show that it is possible to equate the intensity reduction of a light wave caused by weak absorption with a geometrical reduction in intensity caused by a "transverse" conformal transformation of the spacetime metric in which the wave travels. We are consequently able to modify Gordon's optical metric to account for electromagnetic properties of ponderable material whose properties include both refraction and absorption. Unlike refraction alone however, including absorption requires a modification of the optical metric that depends on the eikonal of the wave itself. We derive the distance-redshift relation from the modified optical metric for Friedman-Lema\^itre-Robertson-Walker spacetimes whose cosmic fluid has associated refraction and absorption coefficients. We then fit the current supernovae data and provide an alternate explanation (other than dark energy) of the apparent acceleration of the universe.Comment: 2 figure

Noncommutative Einstein-Maxwell pp-waves

The field equations coupling a Seiberg-Witten electromagnetic field to noncommutative gravity, as described by a formal power series in the noncommutativity parameters $\theta^{\alpha\beta}$, is investigated. A large family of solutions, up to order one in $\theta^{\alpha\beta}$, describing Einstein-Maxwell null pp-waves is obtained. The order-one contributions can be viewed as providing noncommutative corrections to pp-waves. In our solutions, noncommutativity enters the spacetime metric through a conformal factor and is responsible for dilating/contracting the separation between points in the same null surface. The noncommutative corrections to the electromagnetic waves, while preserving the wave null character, include constant polarization, higher harmonic generation and inhomogeneous susceptibility. As compared to pure noncommutative gravity, the novelty is that nonzero corrections to the metric already occur at order one in $\theta^{\alpha\beta}$.Comment: 19 revtex pages. One refrence suppressed, two references added. Minor wording changes in the abstract, introduction and conclusio

Propagation of High-Frequency Electromagnetic Waves Through a Magnetized Plasma in Curved Space-Time. I

This is the first of two papers on the propagation of high-frequency electromagnetic waves through a magnetized plasma in curved space-time. We first show that the nonlinear system of equations governing the plasma and the electromagnetic field in a given, external gravitational field has locally a unique solution for any initial data set obeying the appropriate constraints, and that this system is linearization stable at any of its solutions. Next we prove that the linearized perturbations of a `background' solution are characterized by a third-order (not strictly) hyperbolic, constraint-free system of three partial differential equations for three unknown functions of the four space-time coordinates. We generalize the algorithm for obtaining oscillatory asymptotic solutions of linear systems of partial differential equations of arbitrary order, depending polynomially on a small parameter such that it applies to the previously established perturbation equation when the latter is rewritten in terms of dimensionless variables and a small scale ratio. For hyperbolic systems we then state a sufficient condition in order that asymptotic solutions of finite order, constructed as usual by means of a Hamiltonian system of ordinary differential equations for the characteristic strips and a system of transport equations determining the propagation of the amplitudes along the rays, indeed approximate solutions of the system. The procedure is a special case of a two-scale method, suitable for describing the propagation of locally approximately plane, monochromatic waves through a dispersive, inhomogeneous medium. In the second part we shall apply the general method to the perturbation equation referred to above

Quasi-Newtonian dust cosmologies

Exact dynamical equations for a generic dust matter source field in a cosmological context are formulated with respect to a non-comoving Newtonian-like timelike reference congruence and investigated for internal consistency. On the basis of a lapse function $N$ (the relativistic acceleration scalar potential) which evolves along the reference congruence according to $\dot{N} = \alpha \Theta N$ ($\alpha = {const}$), we find that consistency of the quasi-Newtonian dynamical equations is not attained at the first derivative level. We then proceed to show that a self-consistent set can be obtained by linearising the dynamical equations about a (non-comoving) FLRW background. In this case, on properly accounting for the first-order momentum density relating to the non-relativistic peculiar motion of the matter, additional source terms arise in the evolution and constraint equations describing small-amplitude energy density fluctuations that do not appear in similar gravitational instability scenarios in the standard literature.Comment: 25 pages, LaTeX 2.09 (10pt), to appear in Classical and Quantum Gravity, Vol. 15 (1998