Selected Studies in Classical and Quantum Gravity.

Abstract

This thesis is composed of two parts, one corresponding to classical and the other to quantum gravitational phenomena. In the classical part, we focus on the behavior of various classical scalar fields in the presence of black holes. New fundamental results discussed include the first confirmation of the Belinskii, Khalatnikov, and Lifschitz (BKL) conjecture for an asymptotically flat spacetime, where we find that the dynamics of a canonical test scalar field near a black hole singularity are dominated by terms with time derivatives. We also perform a numerical simulation of the gravitational collapse of a non-canonical scalar field showing that signals can escape black holes in the k-essence dark energy model and find numerical confirmation that the accretion of various scalar fields onto a black hole from generic initial conditions is stationary.

In the second part, we focus on the long distance behavior of perturbative quantum gravity. New results discussed include a proof of the cancellation of collinear divergences to all orders in the amplitudes of the theory as well as a characterization of all infrared divergent diagrams. In particular, we find that the only diagrams that can have soft divergences are ladder and crossed ladder diagrams, and that the only collinearly divergent diagrams are those with only three point vertices and no internal jet loops.

Also presented is a construction of a double copy relation between gravity and gauge theory amplitudes similar to that conjectured by Bern, Carrasco, and Johansson for the case where there is no hard momentum exchange in the scattering, which we find implies a squaring relation between the classical shockwave solutions of the two theories as well. Finally, the first calculation of a gravitational scattering amplitude through the next-to-leading eikonal order is performed. We find that this correction to the scattering amplitude exponentiates, and that these power corrections probe smaller impact parameters compared to the leading eikonal case. This suggests that researching such corrections in a general setting may yield evidence of black hole formation from the quantum theory.