| This thesis is a collection of four pieces of work on the application of general relativity to local gravitational systems and cosmological models. First piece: for weak fields at small scales like the accreting neutron star systems, the gravitational wave radiation will compete against viscosity and induce the secular instability to grow the r-mode perturbations, decrease the star's rotational energy, balance the accretion torque, and limit the star's rotation speed. Second piece: for strong fields at small scales, we set up a simple analytic model to study the gravitational collapse of spherical light shells and dust spheres to black holes, as predicted by general relativity. Third piece: combined with quantum mechanics, general relativity gives a generalized uncertainty principle and suggests that black hole remnants exist. These may evolve from primordial black holes at the end of the inflation period and correspond to the dark matter component in the current universe. The radiation and all relativistic particles emitted from the primordial black holes correspond to the normal particles today. These are investigated by a phenomenological cosmological model consisting of black holes and radiation. Final piece: treating the mysterious dark energy component of the current universe as a simple quintessence scalar field, we examine the evolution of both the background and perturbations in the quintessence and cold dark matter universe model with diverse quintessence potentials. We consider the evolution dependence on the equation-of-state parameter and spatial scale, stress the sensitivity of the structure evolution to initial conditions, and discuss its possible effects on cosmological observations. |
