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Self-force effects on the marginally bound zoom-whirl orbit in Schwarzschild spacetime

Self-force effects on the marginally bound zoom-whirl orbit in Schwarzschild spacetime
Self-force effects on the marginally bound zoom-whirl orbit in Schwarzschild spacetime
For a Schwarzchild black hole of mass
M
, we consider a test particle falling from rest at infinity and becoming trapped, at late time, on the unstable circular orbit of radius
r
=
4
G
M
/
c
2
. When the particle is endowed with a small mass,
μ

M
, it experiences an effective gravitational self-force, whose conservative piece shifts the critical value of the angular momentum and the frequency of the asymptotic circular orbit away from their geodesic values. By directly integrating the self-force along the orbit (ignoring radiative dissipation), we numerically calculate these shifts to
O
(
μ
/
M
)
. Our numerical values are found to be in agreement with estimates first made within the effective one-body formalism and with predictions of the first law of black-hole-binary mechanics (as applied to the asymptotic circular orbit). Our calculation is based on a time-domain integration of the Lorenz-gauge perturbation equations, and it is a first such calculation for an unbound orbit. We tackle several technical difficulties specific to unbound orbits, illustrating how these may be handled in more general cases of unbound motion. Our method paves the way to calculations of the self-force along hyperbolic-type scattering orbits. Such orbits can probe the two-body potential down to the “light ring” and could thus supply strong-field calibration data for eccentricity-dependent terms in the effective one-body model of merging binaries.
2470-0010
Barack, Leor
f08e66d4-c2f7-4f2f-91b8-f2c4230d0298
Colleoni, Marta
0143a70e-604c-4df8-8517-5a69b3218bd1
Damour, Thibault
9e7fe76d-f668-4e67-a399-c806a02838d6
Isoyama, Soichiro
7644902e-6e3d-4bf3-a0a4-8b66ea4df46d
Sago, Norichika
50641559-f289-4ffa-810b-fe4ec8c26e26
Barack, Leor
f08e66d4-c2f7-4f2f-91b8-f2c4230d0298
Colleoni, Marta
0143a70e-604c-4df8-8517-5a69b3218bd1
Damour, Thibault
9e7fe76d-f668-4e67-a399-c806a02838d6
Isoyama, Soichiro
7644902e-6e3d-4bf3-a0a4-8b66ea4df46d
Sago, Norichika
50641559-f289-4ffa-810b-fe4ec8c26e26

Barack, Leor, Colleoni, Marta, Damour, Thibault, Isoyama, Soichiro and Sago, Norichika (2019) Self-force effects on the marginally bound zoom-whirl orbit in Schwarzschild spacetime. Physical Review D, 100 (12), [124015]. (doi:10.1103/PhysRevD.100.124015).

Record type: Article

Abstract

For a Schwarzchild black hole of mass
M
, we consider a test particle falling from rest at infinity and becoming trapped, at late time, on the unstable circular orbit of radius
r
=
4
G
M
/
c
2
. When the particle is endowed with a small mass,
μ

M
, it experiences an effective gravitational self-force, whose conservative piece shifts the critical value of the angular momentum and the frequency of the asymptotic circular orbit away from their geodesic values. By directly integrating the self-force along the orbit (ignoring radiative dissipation), we numerically calculate these shifts to
O
(
μ
/
M
)
. Our numerical values are found to be in agreement with estimates first made within the effective one-body formalism and with predictions of the first law of black-hole-binary mechanics (as applied to the asymptotic circular orbit). Our calculation is based on a time-domain integration of the Lorenz-gauge perturbation equations, and it is a first such calculation for an unbound orbit. We tackle several technical difficulties specific to unbound orbits, illustrating how these may be handled in more general cases of unbound motion. Our method paves the way to calculations of the self-force along hyperbolic-type scattering orbits. Such orbits can probe the two-body potential down to the “light ring” and could thus supply strong-field calibration data for eccentricity-dependent terms in the effective one-body model of merging binaries.

Text
1909.06103 - Accepted Manuscript
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More information

Accepted/In Press date: 13 September 2019
e-pub ahead of print date: 6 December 2019
Published date: 15 December 2019

Identifiers

Local EPrints ID: 436973
URI: http://eprints.soton.ac.uk/id/eprint/436973
ISSN: 2470-0010
PURE UUID: a7a06b15-f31f-4562-996c-3e1c356924f0
ORCID for Leor Barack: ORCID iD orcid.org/0000-0003-4742-9413

Catalogue record

Date deposited: 14 Jan 2020 18:33
Last modified: 27 Jan 2020 13:40

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