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The second-order gravitational self-force

The second-order gravitational self-force
The second-order gravitational self-force
This project makes progress towards a first calculation of the second-order gravitational self-force in extreme-mass-ratio binaries. This is an important component in the modeling of these key astrophysical sources of gravitational waves. Computing the secondorder self-force requires the second-order metric perturbation, which can be calculated by solving the Einstein field equations through second order in the mass ratio. Here we have developed, for the first time, a practical scheme for solving the second-order equations. The main ingredient is a certain “puncture” field, which describes the local metric perturbation near the small member of the binary, and for which we obtain a useful covariant-form expression. We apply this method to the case of a quasicircular binary of nonrotating black holes. As a first test we numerically solve the first-order field equations and compute the first-order self-force, finding good agreement with previous results obtained using a different method. The calculation of the second-order metric perturbation brings about two additional technical difficulties: the need for a certain regularization at infinity and on the event horizon of the large black hole, and the strong divergence of the second-order source of the field equations near the small object. We show how these issues can be resolved, first in a simple scalar-field toy model, and then in the second-order gravitational problem. We finally apply our method in full in order to numerically solve the second-order perturbation equations in the quasicircular case, focusing on the monopole piece of the perturbation as a first example.
University of Southampton
Miller, Jeremy
35ef0e88-726a-444d-b502-1c2b828fa80d
Miller, Jeremy
35ef0e88-726a-444d-b502-1c2b828fa80d
Pound, Adam
5aac971a-0e07-4383-aff0-a21d43103a70
Barack, Leor
f08e66d4-c2f7-4f2f-91b8-f2c4230d0298

Miller, Jeremy (2017) The second-order gravitational self-force. University of Southampton, Doctoral Thesis, 229pp.

Record type: Thesis (Doctoral)

Abstract

This project makes progress towards a first calculation of the second-order gravitational self-force in extreme-mass-ratio binaries. This is an important component in the modeling of these key astrophysical sources of gravitational waves. Computing the secondorder self-force requires the second-order metric perturbation, which can be calculated by solving the Einstein field equations through second order in the mass ratio. Here we have developed, for the first time, a practical scheme for solving the second-order equations. The main ingredient is a certain “puncture” field, which describes the local metric perturbation near the small member of the binary, and for which we obtain a useful covariant-form expression. We apply this method to the case of a quasicircular binary of nonrotating black holes. As a first test we numerically solve the first-order field equations and compute the first-order self-force, finding good agreement with previous results obtained using a different method. The calculation of the second-order metric perturbation brings about two additional technical difficulties: the need for a certain regularization at infinity and on the event horizon of the large black hole, and the strong divergence of the second-order source of the field equations near the small object. We show how these issues can be resolved, first in a simple scalar-field toy model, and then in the second-order gravitational problem. We finally apply our method in full in order to numerically solve the second-order perturbation equations in the quasicircular case, focusing on the monopole piece of the perturbation as a first example.

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Published date: October 2017

Identifiers

Local EPrints ID: 418264
URI: http://eprints.soton.ac.uk/id/eprint/418264
PURE UUID: 2897ce77-e68d-42e0-a0e4-b5352dce80e8
ORCID for Leor Barack: ORCID iD orcid.org/0000-0003-4742-9413

Catalogue record

Date deposited: 27 Feb 2018 17:30
Last modified: 25 Jul 2019 00:35

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