The double copy and classical solutions

[摘要] The Bern-Carrasco-Johansson (BCJ) double copy, which relates the scattering amplitudesof gauge and gravity theories has been an active area of research for a few years now.In this thesis, we extend the formalism of BCJ to consider classical solutions to the fieldequations of motion, rather than scattering amplitudes.One first approach relies on a family of solutions to the Einstein equations, namelyKerr-Schild metrics, which linearise the Ricci tensor. Using them we propose a simpleansatz to construct a gauge theory vector field which, in a stationary limit, satisfies linearisedYang-Mills equations. Using such ansatz, that we call the Kerr-Schild double copy,we are able to relate, for example, colour charges in Yang-Mills with the Schwarzschild andKerr black holes. We extend this formalism to describe the Taub-NUT solution (which isdual to an electromagnetic dyon), perturbations over curved backgrounds and acceleratingparticles, both in gauge and gravity theories.A second, more utilitarian approach consists on using the relative simplicity of gaugetheory to efficiently compute relevant quantities in a theory of perturbative gravity. Workingalong this lines, we review an exercise by Duff to obtain a spacetime metric usingtree-level graphs of a quantum theory of perturbative gravity, and repeat it using a BCJinspired gravity Lagrangian. We find that the computation is notably simplified, but a newformalism must be developed to remove the unwanted dilaton information, that naturallyappears in the double copy.

[发布机构] University:University of Glasgow;Department:School of Physics and Astronomy

[关键词] Double copy, Classical gravity, Gauge/Gravity.