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

Abstract

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).

arXiv comment31 pages, 17 figures. v3 corrects typos in Eqs. (21) and (22). These typos do not propagate, and the rest of the paper remains unaffected

References in corpus (29)

• LISA Capture Sources: Approximate Waveforms, Signal-to-Noise Ratios, and Parameter Estimation Accuracy
• Gravitational Radiation Reaction to a Particle Motion
• An axiomatic approach to electromagnetic and gravitational radiation reaction of particles in curved spacetime
• The motion of point particles in curved spacetime
• Self-force via a Green's function decomposition
• Mode sum regularization approach for the self-force in black hole spacetime
• Calculating the gravitational self force in Schwarzschild spacetime
• Axiomatic approach to radiation reaction of scalar point particles in curved spacetime
• Gravitational waveforms from a point particle orbiting a Schwarzschild black hole
• Gravitational self force and gauge transformations
• Perturbations of Schwarzschild black holes in the Lorenz gauge: Formulation and numerical implementation
• Self-force of a scalar field for circular orbits about a Schwarzschild black hole
• Self force on particle in orbit around a black hole
• Perspective on gravitational self-force analyses
• Computing the gravitational self-force on a compact object plunging into a Schwarzschild black hole
• Low multipole contributions to the gravitational self-force
• Gravitational self-force on a particle orbiting a Kerr black hole
• Understanding initial data for black hole collisions
• Regularization parameters for the self force in Schwarzschild spacetime: II. gravitational and electromagnetic cases
• Radiation-reaction force on a particle plunging into a black hole
• Scalar field self-force effects on orbits about a Schwarzschild black hole
• Self force on static charges in Schwarzschild spacetime
• Gravitational self force by mode sum regularization
• A One-Parameter Family of Time-Symmetric Initial Data for the Radial Infall of a Particle into a Schwarzschild Black Hole
• Self force on a scalar charge in the spacetime of a stationary, axisymmetric black hole
• Self-force Regularization in the Schwarzschild Spacetime
• Gravitational reaction force on a particle in the Schwarzschild background
• A new analytical method for self-force regularization II. Testing the efficiency for circular orbits
• Harmonic-gauge dipole metric perturbations for weak-field circular orbits in Schwarzschild spacetime

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