Frequency-domain calculation of the self force: the high-frequency problem and its resolution
| dc.creator | Barack, Leor | |
| dc.creator | Ori, Amos | |
| dc.creator | Sago, Norichika | |
| dc.date | 2008-08-17 | |
| dc.date | 2008-10-10 | |
| dc.date.accessioned | 2026-07-07T11:45:32Z | |
| dc.date.available | 2026-07-07T11:45:32Z | |
| dc.description | The mode-sum method provides a practical means for calculating the self force acting on a small particle orbiting a larger black hole. In this method, one first computes the spherical-harmonic $l$-mode contributions $F^μ_l$ of the "full force" field $F^μ$, evaluated at the particle's location, and then sums over $l$ subject to a certain regularization procedure. In the frequency-domain variant of this scheme the quantities $F^μ_l$ are obtained by fully decomposing the particle's self field into Fourier-harmonic modes $l m ω$, calculating the contribution of each such mode to $F^μ_l$, and then summing over $ω$ and $m$ for given $l$. This procedure has the advantage that one only encounters {\it ordinary} differential equations. However, for eccentric orbits, the sum over $ω$ is found to converge badly at the particle's location. This problem (reminiscent of the familiar Gibbs phenomenon) results from the discontinuity of the time-domain $F^μ_l$ field at the particle's worldline. Here we propose a simple and practical method to resolve this problem. The method utilizes the {\it homogeneous} modes $l m ω$ of the self field to construct $F^μ_l$ (rather than the inhomogeneous modes, as in the standard method), which guarantees an exponentially-fast convergence to the correct value of $F^μ_l$, even at the particle's location. We illustrate the application of the method with the example of the monopole scalar-field perturbation from a scalar charge in an eccentric orbit around a Schwarzschild black hole. Our method, however, should be applicable to a wider range of problems, including the calculation of the gravitational self-force using either Teukolsky's formalism, or a direct integration of the metric perturbation equations. | |
| dc.description | 20 pages, 10 eps figures; version published in PRD | |
| dc.identifier | https://arxiv.org/abs/0808.2315 | |
| dc.identifier | http://arxiv.org/abs/0808.2315 | |
| dc.identifier | Phys.Rev.D78:084021,2008 | |
| dc.identifier | doi:10.1103/PhysRevD.78.084021 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/201910 | |
| dc.subject | General Relativity and Quantum Cosmology | |
| dc.title | Frequency-domain calculation of the self force: the high-frequency problem and its resolution | |
| dc.type | text |