Gravitational self force on a particle in circular orbit around a Schwarzschild black hole

Details Gravitational self force on a particle in circular orbit around a Schwarzschild black hole Gravitational self force on a particle in circular orbit around a Schwarzschild black hole

2007-01-15

arxiv.org/abs/gr-qc/0701069v3

Phys.Rev.D75:064021,2007

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

31 pages, 17 figures. v3 corrects typos in Eqs. (21) and (22). These typos do not propagate, and the rest of the paper remains

Scientific paper

10.1103/PhysRevD.75.064021

We calculate the gravitational self force acting on a pointlike particle of mass $\mu$, set in a circular geodesic orbit around a Schwarzschild black hole. Our calculation is done in the Lorenz gauge: For given orbital radius, we first solve directly for the Lorenz-gauge metric perturbation using numerical evolution in the time domain; We then compute the (finite) back-reaction force from each of the multipole modes of the perturbation; Finally, we apply the ``mode sum'' method to obtain the total, physical self force. The {\em temporal} component of the self force (which is gauge invariant) describes the dissipation of orbital energy through gravitational radiation. Our results for this component are consistent, to within the computational accuracy, with the total flux of gravitational-wave energy radiated to infinity and through the event horizon. The {\em radial} component of the self force (which is gauge dependent) is calculated here for the first time. It describes a conservative shift in the orbital parameters away from their geodesic values. We thus obtain the $O(\mu)$ correction to the specific energy and angular momentum parameters (in the Lorenz gauge), as well as the $O(\mu)$ shift in the orbital frequency (which is gauge invariant).

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