Surveying Approaches to Black Hole Theory and Quantum Gravity

This thesis provides a discussion of preliminary theories of gravitation and quantum field theory as they relate to theories of quantum gravity. Mathematical methods are developed for studying the theory of stochastic quantum gravity. The theory is developed in the cases of Minkowski space, cosmological inflation space, and Rindler space. These methods are expanded and stochastic processes found for background metrics of a particular class that do not exhibit mixed space-time derivatives, including the black hole metric. Various questions related to black hole information theory, including the effects of Hawking radiation, the firewall puzzle, and the fate of information entering a black hole are discussed. The derivations of black hole entropy calculations and their interpretations from different perspectives on quantum gravity are also included.