Topics In Classical And Quantum Gravity

This thesis is composed of two separate parts. The first part is on the stability issue of a ground state geometry of Kaluza-Klein theory. A number of workers have considered semiclassical solutions, in which a Kaluza- Klein geometry has as its source the vacuum expectation value of the energy-momentum tensor associated with a set of quantum fields. In a spacetime of this kind, however, the internal space is typically unstable to collapse. Within the semiclassical approximation, the degrees of freedom associated with boson and fermion fields on the background spacetime are quantized, but the length of the internal space remains a classical variable. The present project is concerned with whether the instability to collapse is an artifact of this approximation. We consider a generalization in which the length of the internal space remains a quantum variable, beginning with a toy, minisuperspace model whose quantum geometry is coupled to a set of scalar fields; as in the semiclassical approximation these fields are described by a one-loop effective action. The scalar-field degrees of freedom can be regarded as mimicking the effect of the remaining gravitational degrees of freedom, that are frozen in a minisuperspace calculation. If one takes a classical FRW geometry as the large spacetime, then for times short compared to the Hubble time, the Wheeler- DeWitt equation becomes a time-independent Schrödinger equation for the size of the internal space, with zero energy eigenvalue. The second part of the thesis deals with the radiation reaction problem in general relativity. In this thesis we compute the self force on a non-minimally coupled scalar static charge outside a Schwarzschild black hole. It is an interesting problem because an earlier result by Zel'nikov and Frolov would, if correct, be a counter- example to a set of axioms proposed by Quinn and Wald. We not only showed that the result by Zel'nikov and Frolov has an error, but were also able to identify that the precise source of that error has a deeper relation to the generalized definition of black hole entropy