The Bern-Carrasco-Johansson (BCJ) double copy, which relates the scattering amplitudes of 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 field equations of motion, rather than scattering amplitudes. One first approach relies on a family of solutions to the Einstein equations, namely Kerr-Schild metrics, which linearise the Ricci tensor. Using them we propose a simple ansatz to construct a gauge theory vector field which, in a stationary limit, satisfies linearised Yang-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 and Kerr black holes. We extend this formalism to describe the Taub-NUT solution (which is dual to an electromagnetic dyon), perturbations over curved backgrounds and accelerating particles, both in gauge and gravity theories. A second, more utilitarian approach consists on using the relative simplicity of gauge theory to efficiently compute relevant quantities in a theory of perturbative gravity. Working along this lines, we review an exercise by Duff to obtain a spacetime metric using tree-level graphs of a quantum theory of perturbative gravity, and repeat it using a BCJ inspired gravity Lagrangian. We find that the computation is notably simplified, but a new formalism must be developed to remove the unwanted dilaton information, that naturally appears in the double copy.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:732784 |
| Date | January 2018 |
| Creators | Luna Godoy, Andres |
| Publisher | University of Glasgow |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://theses.gla.ac.uk/8716/ |
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