## Black Holes and Conformal Quantum Gravity

##### Summary

This thesis consists of a discussion on the reconciliation of black hole evolution with unitarity and locality, followed by a discussion on conformal quantum gravity. The first part of the thesis starts with a brief review of quantum field theory in curved space. Derivations of the Unruh effect and Hawking radiation are given. Hawking radiation arises from the stretching of the horizon. The reconciliation of Hawking radiation with unitarity and locality is investigated. The postulate on the existence of the S-matrix for quantum black holes, and its most significant consequence, namely the black hole-white hole complementarity, are explained. A new version of the principle of ”black hole complementarity” is studied. This principle is then used to remove the spacetime singularities and horizons in black hole geometry. Using the complementarity principle for black holes, it is argued that exact invariance under local conformal transformations is a new essential ingredient in formulating quantum gravity and also that the conformal factor behaves as a local gauge parame- ter. In the second part, perturbative canonical quantum gravity coupled to a renormalizable model for matter fields is taken into consideration. It is proposed that the functional integral over the dilaton (local conformal factor) field should be disentangled from the other integrations over the metric field. The conformal integral diverges. Renormalization counter terms violate unitarity. At a later stage, this unitary violation will be considered in light of PT-symmetric quantum mechanics. Anomalies are investigated and constrained to cancel out. When the residual metric is taken to be flat as the background, beta functions should vanish. This necessity provides a physical principle to determine and fix the couplings, masses, and the cosmological constant. The theory leads to a class of elementary particle models without any adjustable real parameters. A review of conformal quantum gravity without compensating fields is given. Finally, a comparison of conformal quantum gravity with compensating fields and without compensating fields, particularly Mannheim’s con- formal quantum gravity, is discussed. This thesis is mainly based on ’t Hooft’s latest ideas about black holes and conformal quantum gravity and tries to put them together.