I present here one approach to general relativistic radiation hydrodynamics. It is based on covariant tensor conservation equations and considers only the frequency-integrated total energy and momentum exchange between matter and the radiation field. It is also a mixed-frame formalism in the sense that, the interaction between radiation and matter is described with quantities in the comoving frame in which the interaction is often symmetric in angle while the radiation energy and momentum equations are expressed in the fixed frame quantities in which the derivatives are simpler. Hence, this approach is intuitive enough to be applied straightforwardly to any spacetime or coordinate. A few examples are provided along with caveats in this formalism.

We now have more than 70 multiple image gravitational lens systems. Since gravitational lensing occurs through gravitational distortions in cosmic space, cosmological informations can be extracted from multiple image systems. Specifically, Hubble constant can be determined by the time delay mea-surement, curvature of the universe can be measured by the distribution of image separations in lens systems, and limits on matter density and cosmological constant can be set by the statistics of gravitationallens systems. Uncertainties, however, still exist in various steps, and results may be taken with some caution. Larger systematic survey and better understanding of galaxy properties would definitely help.

Radiation hydrodynamics in high. velocity or high optical-depth flow should be treated under rigorous relativistic formalism. Relativistic radiation hydrodynamic moment equations are summarized, and its application to the near-critical accretion onto neutron star is discussed. The relativistic effects can dominate the dynamics of the flow even when the gravity is weak and the velocity is small. First order equations fail to describe the intricate relativistic effects correctly.

To examine the effect of neighboring galaxies on the gravitational lensing statistics, we performed numerical simulations of lensing by many galaxies. The models consist of a galaxy in the rich cluster like Coma, or a galaxy surrounded by field galaxies in Ω0 = 1 universe with Ωgal = 0.1, Ωgal = 0.3 or Ωgal=1.0, Ωgal is the total mass in galaxies. Field galaxies either have the same mass or follow Schechter luminosity function and luminosity-velocity relation. Each lensing galaxy is assumed to be singular isothermal sphere (SIS) with finite cutoff radius. In most simulations, the lensing is mainly due to the single galaxy. But in Ωgal = 0.3 universe, one out of five simulations have 'collective lensing' event in which more than two galaxies collectively produce multiple images. These cases cannot be incorporated into the simple 'standard' lensing statistics calculations. In cases where 'collective lensing' does not occur, distribution of image separation changes from delta function to bimodal distribution due to shear induced by the surrounding galaxies. The amount of spread in the distribution is from a few % up to ~50% of the mean image separation in case when the galaxy is in the Coma-like cluster or when the galaxy is in the field with Ωgal = 0.1 or Ωgal=0.3. The mean of the image separation changes less than 5% compared with a single lens case. Cross section for multiple image lensing turns out to be relatively insensitive to the presence of the neighboring galaxies, changing less than 5% for Coma-like cluster and Ωgal=0.1, 0.3 universe cases. So we conclude that Coma-like cluster or field galaxies whose total mass density Ωgal < 0.3 do not significantly affect the probability of multiple image lensing if we exclude the 'collective lensing' cases. However, the distribution of the image separations can be significantly affected especially if the 'collective lensing' cases are included. Therefore, the effects of surrounding galaxies may not be negligible when statistics of lensing is used to deduce the cosmological informations.

The stability of the geometrically thin, two-temperature hot accretion disk is studied. The general criterion for thermal instability is derived from the linear local analyses, allowing for advective cooling and dynamics in the vertical direction. Specifically, classic unsaturated Comptonization disk is analysed in detail. We find five eigen-modes: (1) Heating mode grows in thermal time scale, (5/3)(αω)-1, where alpha is the viscosity parameter and w the Keplerian frequency. (2) Cooling mode decays in time scale, (2/5)(Te/Ti)(αω)-1, where Te and Ti are the electron and ion temperatures, respectively. (3) Lightman-Eardley viscous mode decays in time scale, (4/3)(Λ/H)2(αω)-1, where Λ is the wavelength of the perturbation and H the unperturbed disk height. (4) Two vertically oscillating modes oscillate in Keplerian time scale, (3/8)1/2ω-1 with growth rate ∝(H/Λ)2. The inclusion of dynamics in the vertical direction does not affect the thermal instability, adding only the oscillatory modes which gradually grow for short wavelength modes. Also, the advective cooling is not strong enough to suppress the growth of heating modes, at least for geometrically thin disk. Non-linear development of the perturbation is followed for simple unsaturated Compton disk: depending on the initial proton temperature perturbation, the disk can evolve to decoupled state with hot protons and cool electrons, or to one-temperature state with very cool protons and electrons.

To extend the work of Gott, Park, and Lee (1989), statistical properties of gravitational lensing in a wide variety of cosmological models involving non-zero cosmological constant is investigated, using the redshifts of both lens and source and observed angular separation of images for gravitational lens systems. We assume singular isothermal sphere as lensing galaxy in homogenous and isotropic Friedmann­Lemaitre-Robertson- Walker universe, Schechter luminosity function, standard angular diameter distance formula and other galaxy parameters used in Fukugita and Turner (1991). To find the most adequate flat cosmological model and put a limit on the value of dimensionless cosmological constant ⋋0, the mean value of the angular separation of images, probability distribution of angular separation and cumulative probability are calculated for given source and lens redshifts and compared with the observed values through several statistical methods. When there is no angular selection effect, models with highest value of ⋋0 is preferred generally. When the angular selection effects are considered, the preferred model depends on the shape of the selection functions and statistical methods; yet, models with large ⋋0 are preferred in general. However, the present data can not rule out any of the flat universe models with enough confidence. This approach can potentially select out best model. But at the moment, we need more data.

New and improved data on the gravitational lens systems discovered so far are compared with the theoretical predictions of Gott, Park, and Lee (1989, GPL). Systems lensed by a single galaxy, compatible with assumptions of GPL, support flat or near-flat geometry for the universe. But the statistical uncertainty is too large to draw any definite conclusion. We need more lens systems. Also, the probability of multiple image lensing and mean separation of the images averaged over the source distribution are calculated for various cosmological models. Multiple-image lens systems and radio ring systems are compared with the predictions. Although the data reject exotic cosmological models, it cannot discriminate among conventional Friedmann models yet.