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Wave propagation on black hole spacetimes

Dempsey, David (2017) Wave propagation on black hole spacetimes. PhD thesis, University of Sheffield.

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Abstract

This thesis studies the propagation of fundamental fields on black hole and black hole analogue spacetimes. We consider the scalar, electromagnetic, gravitational and Dirac fields, and their governing equations, in various scenarios. We initially consider an analogue gravity model, the draining bathtub vortex, that shares features with the Kerr black hole, such as a horizon and an ergoregion. We solve the wave equation approximately, via the eikonal approximation, and numerically, using the method of lines, and show that a point-like disturbance maps out the lightcone of the effective spacetime. The Schwarzschild and Kerr black hole spacetimes are then introduced and we discuss their key features. We solve the scalar wave equation for the black hole spacetimes and compare with the analogue spacetime. We then introduce the self force, the back reaction of a body's own field on its motion. The scalar self force on Kerr spacetime is calculated using the worldline integration method. This involves solving the scalar wave equation to find the Green function via the Kirchhoff representation and integrating over the entire past history of the worldline. The electromagnetic (EM) self force is calculated via the mode sum method. We use both analytical and numerical techniques to calculate EM self force for a particle held static outside of a Schwarzschild black hole. The gauge freedom of the gravitational self force is also discussed. We construct for eccentric orbits on Schwarzschild the spin precession invariant, a gauge invariant quantity. We compare the spin precession invariant calculated using numerical self force data with a post-Newtonian calculation. Finally we investigate the Dirac (fermionic) field in searching for the existence of bound states. We find that the solutions which satisfy the boundary conditions, obey a three-term recurrence-relation. Using continued-fraction methods we find a spectrum of quasi-bound states of the Dirac field exists.

Item Type: Thesis (PhD)
Academic Units: The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield)
Depositing User: Mr David Dempsey
Date Deposited: 01 Sep 2017 10:35
Last Modified: 01 Sep 2017 10:35
URI: http://etheses.whiterose.ac.uk/id/eprint/18023

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