Quantum gravity on the event horizon

Black holes have been a prominent research interest in the past decades. Attempts at combining general relativity and quantum field theory to construct a theory of quantum gravity have to this day not yielded conclusive results without problems, either we run into infinities, or in the case of black holes run into a triad of paradoxes. The most well-known is the information paradox, in which black holes appear to evaporate over time due to quantum effects and thus lose information. 't Hooft proposed that introduction of (gravitational) interactions could exchange the missing information and be a key component to solving the paradox. In this thesis we develop a new field theory based on canonical quantization of gravity, describing scalar particles interacting through gravitons. We calculate three relevant processes and their scattering amplitudes. For the first we use that near the horizon the particles have extremely high energy, and use this to calculate non-perturbative effects in the Eikonal limit. We write down a new many-particle N-N Eikonal scattering diagram and calculate this for the first time, and find the gravitons are manifestly soft (avoiding divergences) and find that this amplitude matches 't Hooft's semi-classical amplitude. For our second calculation we introduce inelastic effects, and calculate the 2-2N amplitude at tree level. We find that the likeliest process is one involving evaporation into a large amount of particles Nmax, in which case the amplitude becomes exponential, possibly counteracting the thermal effects of Hawking radiation. Combining the inelastic amplitude with the Eikonal one, we find that the time delay of the processes of the order of magnitude of the Page time, which is not visible at tree level, showing combining both effects is important. Finally for the last process we calculate the IR triangle on the black hole horizon. The flat space IR triangle relates past and future charges using null infinity as asymptotic surface. The horizon is also an asymptotic null surface, and we calculate similar conserved charges. Their Ward identity appears to be related to the black hole soft theorem, that we calculate using our new field theory. Using our calculations, we have shown that even using only general relativity and quantum field theory, there is still a lot to learn about black holes. We have clear proof of concepts that introduction of non-perturbative and inelastic effects could be key to solving the information paradox, and that there may be a strong hidden symmetry structure embedded in the horizon itself in terms of soft charges.