The double copy and classical solutions

Luna Godoy, Andres (2018) The double copy and classical solutions. PhD thesis, University of Glasgow.

Abstract

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.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Keywords: Double copy, Classical gravity, Gauge/Gravity.
• Subjects: Q Science > QC Physics
• Colleges/Schools: College of Science and Engineering > School of Physics and Astronomy
• Supervisor's Name: White, Dr. Chris D.
• Date of Award: 2018
• Depositing User: Mr. Andres Luna Godoy
• Unique ID: glathesis:2018-8716
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 30 Jan 2018 15:04
• Last Modified: 02 Mar 2018 13:05
• URI: https://theses.gla.ac.uk/id/eprint/8716