Quantum gravity on the black hole horizon

Abstract

Over the past few decades a lot of research has been done to attempt to solve the black hole information paradox, however only rarely is the gravitational interaction between particles taken into account. In this thesis we focus on perturbatively quantizing gravity on the black hole horizon. First we review past research of 't Hooft on semi-classical black hole scattering, re-derive the resulting semi-classical scattering matrix in quantum mechanics and discuss it. Then we proceed to develop a new method for calculating the black hole scattering matrix by summing over an infinite number of graviton exchange diagrams in the high-energy limit. The graviton is given by a perturbation of the metric around the Schwarzschild background close to the black hole horizon. As a result we find that the scattering matrix of our high-energy graviton exchange is almost identical to 't Hooft's semi-classical scattering matrix, providing a generalized result. We have thus shown that similar results can also be obtained solely in perturbative general relativity and quantum field theory, opening up possibilities for new research on black hole scattering.