Two investigations in quantum gravity

Two aspects of quantum field theory in curved spacetimes are discussed. First, the limits for applicability of the equivalence principle in the context of low energy effective field theories is considered. In particular, we find three classes of higher-derivative interactions for the gravitational and electromagnetic fields which produce dispersive photon propagation. One of these classes of interactions also produces birefringent propagation. This result is illustrated by calculating the energy-dependent contribution to the bending of light. In the second part, the divergences appearing in statistical black hole entropy are analysed. Using a Pauli-Villars regulator, it is shown that 't Hooft's approach to evaluating black hole entropy through a statistical-mechanical counting of states for a scalar field propagating outside the event horizon yields precisely the one-loop renormalization of the standard Bekenstein-Hawking formula, $S = { cal A}/(4G),$ where $ cal A$ is the black hole area. The calculation also yields a constant contribution to the black hole entropy, which may be associated with the one-loop renormalization of certain higher curvature terms in the gravitational action. The calculation of black hole entropy is done for a Schwarzschild black hole as well as for a Reissner-Nordstrom black hole