Beyond the geodesic approximation: conservative effects of the gravitational self-force in eccentric orbits around a Schwarzschild black hole

Beyond the geodesic approximation: conservative effects of the gravitational self-force in eccentric orbits around a Schwarzschild black hole

We study conservative finite-mass corrections to the motion of a particle in a bound (eccentric) strong-field orbit around a Schwarzschild black hole. We assume the particle's mass $\mu$ is much smaller than the black hole mass $M$, and explore post-geodesic corrections of $O(\mu/M)$. Our analysis uses numerical data from a recently developed code that outputs the Lorenz-gauge gravitational self-force (GSF) acting on the particle along the eccentric geodesic. First, we calculate the $O(\mu/M)$ conservative correction to the periastron advance of the orbit, as a function of the (gauge dependent) semi-latus rectum and eccentricity. A gauge-invariant description of the GSF precession effect is made possible in the circular-orbit limit, where we express the correction to the periastron advance as a function of the invariant azimuthal frequency. We compare this relation with results from fully nonlinear numerical-relativistic simulations. In order to obtain a gauge-invariant measure of the GSF effect for fully eccentric orbits, we introduce a suitable generalization of Detweiler's circular-orbit "red shift" invariant. We compute the $O(\mu/M)$ conservative correction to this invariant, expressed as a function of the two invariant frequencies that parametrize the orbit. Our results are in good agreement with results from post-Newtonian calculations in the weak field regime, as we shall report elsewhere. The results of our study can inform the development of analytical models for the dynamics of strongly-gravitating binaries. They also provide an accurate benchmark for future numerical-relativistic simulations

Barack, Leor

f08e66d4-c2f7-4f2f-91b8-f2c4230d0298

Sago, Norichika

c4baa9a1-e4fb-448e-8818-f7d189ed2773

Barack, Leor

f08e66d4-c2f7-4f2f-91b8-f2c4230d0298

Sago, Norichika

c4baa9a1-e4fb-448e-8818-f7d189ed2773

Barack, Leor and Sago, Norichika
(2011)
Beyond the geodesic approximation: conservative effects of the gravitational self-force in eccentric orbits around a Schwarzschild black hole.
*Physical Review D*.

## Abstract

We study conservative finite-mass corrections to the motion of a particle in a bound (eccentric) strong-field orbit around a Schwarzschild black hole. We assume the particle's mass $\mu$ is much smaller than the black hole mass $M$, and explore post-geodesic corrections of $O(\mu/M)$. Our analysis uses numerical data from a recently developed code that outputs the Lorenz-gauge gravitational self-force (GSF) acting on the particle along the eccentric geodesic. First, we calculate the $O(\mu/M)$ conservative correction to the periastron advance of the orbit, as a function of the (gauge dependent) semi-latus rectum and eccentricity. A gauge-invariant description of the GSF precession effect is made possible in the circular-orbit limit, where we express the correction to the periastron advance as a function of the invariant azimuthal frequency. We compare this relation with results from fully nonlinear numerical-relativistic simulations. In order to obtain a gauge-invariant measure of the GSF effect for fully eccentric orbits, we introduce a suitable generalization of Detweiler's circular-orbit "red shift" invariant. We compute the $O(\mu/M)$ conservative correction to this invariant, expressed as a function of the two invariant frequencies that parametrize the orbit. Our results are in good agreement with results from post-Newtonian calculations in the weak field regime, as we shall report elsewhere. The results of our study can inform the development of analytical models for the dynamics of strongly-gravitating binaries. They also provide an accurate benchmark for future numerical-relativistic simulations

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## More information

Submitted date: 2011

## Identifiers

Local EPrints ID: 173671

URI: https://eprints.soton.ac.uk/id/eprint/173671

ISSN: 1550-7998

PURE UUID: 45f74acd-2752-43d5-9127-6a6e7eca5c53

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Date deposited: 08 Feb 2011 08:58

Last modified: 18 Jul 2017 12:12

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## Contributors

Author:
Norichika Sago

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