| First, this dissertation will examine a problem in classical relativity, the effect of global expansion upon local systems. The orbit equations or geodesics around the McVittie metric will be examined. However, as will be discussed the McVittie metric is unphysical. A perturbative approach where dust is placed around a Schwarzschild black hole written in the Painleve' Gullstrand form and the solution is forced to appear similar to that of Robertson Walker in the limit of r → ∞ is presented.; Next, the dissertation will discuss homogeneous but anisotropic cosmologies known as Bianchi models. These models may be used as useful toy models for studying quantum gravity. It will discuss these models and how one might define the semi-classical states and the corresponding expectation values associated to some physical observables with these states. First, it will examine coherent states as defined in the kinematical Hilbert space. Secondly, physical coherent states as defined via group averaging will be examined. |
