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

Journal Article · Fri Apr 15 00:00:00 EDT 2011 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.83.084023· OSTI ID:21541489

Barack, Leor ^[1]; Sago, Norichika ^[2]

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1. School of Mathematics, University of Southampton, Southampton SO17 1BJ (United Kingdom)
2. Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502 (Japan)

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) semilatus 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 ''redshift'' 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.

• OSTI ID: 21541489
• Journal Information: Physical Review. D, Particles Fields, Vol. 83, Issue 8; Other Information: DOI: 10.1103/PhysRevD.83.084023; (c) 2011 American Institute of Physics; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
APPROXIMATIONS
BENCHMARKS
BLACK HOLES
COMPARATIVE EVALUATIONS
COMPUTERIZED SIMULATION
CORRECTIONS
GAUGE INVARIANCE
LORENTZ INVARIANCE
MASS
NONLINEAR PROBLEMS
ORBITS
PRECESSION
RED SHIFT
RELATIVISTIC RANGE
SCHWARZSCHILD METRIC
CALCULATION METHODS
ENERGY RANGE
EVALUATION
INVARIANCE PRINCIPLES
METRICS
SIMULATION