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.

The unique compact radio source, Sgr $A^*$, at the Galactic center show many observational signs that it is powered by supermassive black hole. Recent observations also imply that it is surrounded by winds from nearby IR sources. So we explore the model in which multiwavelength spectrum from Sgr $A^*$ is due to the spherical accretion of these winds onto the central supermassive black hole. Improving upon the previous work, we allowed the possibility that ions and electrons have different temperatures, included the Compton effects and pair processes. Electrons radiate via cyclosynchrotron and bresstrahlung with comptoniztion. We find that ion approaches the virial temperature ${\sim}10^{13}K$ while electron temperature saturates at ${\sim}10^{10}K$. However, decoupling between ion and electron does not greatly affect the shape of the emission spectrum. When the mass of the black hole is ${\sim}10^6M_{\odot}$, radio, IR, X-ray, $\gamma$-ray band spectrum is reasonably explained by the model. Yet Compton effect which is neglected in previous works produces significant emission in IR band, which is marginally compatible with observations. Pair production is negligible and annihilation lines cannot be observed.

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.

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.