The University of Southampton
University of Southampton Institutional Repository

Second-order gravitational self-force in a highly regular gauge

Second-order gravitational self-force in a highly regular gauge
Second-order gravitational self-force in a highly regular gauge
Gravitational-wave emission from extreme-mass-ratio inspirals (EMRIs) is expected to be a key source for the Laser Interferometer Space Antenna (LISA), a future space-based gravitational-wave detector. In this thesis, we detail an approach to model these systems through a perturbative method known as gravitational self-force theory. Accurate EMRI science requires us to go to second order in perturbation theory, which introduces a number of obstacles. One major problem that we focus on ameliorating in this thesis is the strong divergence encountered on the worldline of the small object. This divergence creates a severe computational cost in numerical simulations and hinders the rapid calculations that are required for waveform generation for LISA. However, building on previous work by Pound [Phys. Rev. D 95, 104056 (2017)], we develop a class of "highly regular" gauges with a weaker singularity structure. We calculate all orders of the metric perturbations required for numerical implementation and generate fully covariant and generic coordinate-expansion expressions for the metric perturbations in this class of gauges. Not only will the weaker divergences enable quicker numerical calculations, they also allow us to rigorously derive a pointlike second-order stress-energy tensor for the small object. We demonstrate that the form of this second-order stress-energy tensor is valid in any smoothly related gauge and, using a specific distributional definition, also valid in a widely used gauge in self-force calculations, the Lorenz gauge. This stress-energy tensor can then be used as part of the source when solving for the full, physical fields at second order and we outline how this can be done through the introduction of a counter term that cancels the most singular part of the second-order source in the Lorenz gauge. Finally, we present the calculation of the gauge vector required to transform from the Lorenz gauge to the highly regular gauge and provide it in mode-decomposed form for the case of quasicircular orbits in Schwarzschild spacetime. While this work is motivated by EMRIs, much of the work in this thesis is valid for a small object in any vacuum background spacetime with an external lengthscale much larger than the size of the small object.
black holes, EMRI, perturbation theory, gravitational self-force, general relativity, gravitational waves
University of Southampton
Upton, Samuel
f0ff8ac2-2ef0-4a99-b2d6-e55772f34dcf
Upton, Samuel
f0ff8ac2-2ef0-4a99-b2d6-e55772f34dcf
Pound, Adam
5aac971a-0e07-4383-aff0-a21d43103a70
Barack, Leor
f08e66d4-c2f7-4f2f-91b8-f2c4230d0298

Upton, Samuel (2023) Second-order gravitational self-force in a highly regular gauge. University of Southampton, Doctoral Thesis, 179pp.

Record type: Thesis (Doctoral)

Abstract

Gravitational-wave emission from extreme-mass-ratio inspirals (EMRIs) is expected to be a key source for the Laser Interferometer Space Antenna (LISA), a future space-based gravitational-wave detector. In this thesis, we detail an approach to model these systems through a perturbative method known as gravitational self-force theory. Accurate EMRI science requires us to go to second order in perturbation theory, which introduces a number of obstacles. One major problem that we focus on ameliorating in this thesis is the strong divergence encountered on the worldline of the small object. This divergence creates a severe computational cost in numerical simulations and hinders the rapid calculations that are required for waveform generation for LISA. However, building on previous work by Pound [Phys. Rev. D 95, 104056 (2017)], we develop a class of "highly regular" gauges with a weaker singularity structure. We calculate all orders of the metric perturbations required for numerical implementation and generate fully covariant and generic coordinate-expansion expressions for the metric perturbations in this class of gauges. Not only will the weaker divergences enable quicker numerical calculations, they also allow us to rigorously derive a pointlike second-order stress-energy tensor for the small object. We demonstrate that the form of this second-order stress-energy tensor is valid in any smoothly related gauge and, using a specific distributional definition, also valid in a widely used gauge in self-force calculations, the Lorenz gauge. This stress-energy tensor can then be used as part of the source when solving for the full, physical fields at second order and we outline how this can be done through the introduction of a counter term that cancels the most singular part of the second-order source in the Lorenz gauge. Finally, we present the calculation of the gauge vector required to transform from the Lorenz gauge to the highly regular gauge and provide it in mode-decomposed form for the case of quasicircular orbits in Schwarzschild spacetime. While this work is motivated by EMRIs, much of the work in this thesis is valid for a small object in any vacuum background spacetime with an external lengthscale much larger than the size of the small object.

Text
SamuelUptonThesis - Version of Record
Available under License University of Southampton Thesis Licence.
Download (3MB)
Text
Final-thesis-submission-Examination-Mr-Samuel-Upton (1)
Restricted to Repository staff only

More information

Published date: March 2023
Additional Information: Parts of this work have been published as: S. D. Upton and A. Pound, ‘Second-order gravitational self-force in a highly regular gauge’, Phys. Rev. D 103, 124016 (2021), arXiv:2101.11409 [gr-qc].
Keywords: black holes, EMRI, perturbation theory, gravitational self-force, general relativity, gravitational waves

Identifiers

Local EPrints ID: 475714
URI: http://eprints.soton.ac.uk/id/eprint/475714
PURE UUID: 66584a7b-4f06-418e-a82f-4281d77b3c3a
ORCID for Samuel Upton: ORCID iD orcid.org/0000-0003-2965-7674
ORCID for Adam Pound: ORCID iD orcid.org/0000-0001-9446-0638
ORCID for Leor Barack: ORCID iD orcid.org/0000-0003-4742-9413

Catalogue record

Date deposited: 27 Mar 2023 16:30
Last modified: 13 Jun 2024 02:08

Export record

Altmetrics

Contributors

Author: Samuel Upton ORCID iD
Thesis advisor: Adam Pound ORCID iD
Thesis advisor: Leor Barack ORCID iD

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×