Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2002-05-20
Phys.Rev.D67:104016,2003
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
RevTex, 31 pages, 1 figure, modified abstract, more details of numerical methods
Scientific paper
10.1103/PhysRevD.67.104016
The foundations are laid for the numerical computation of the actual worldline for a particle orbiting a black hole and emitting gravitational waves. The essential practicalities of this computation are here illustrated for a scalar particle of infinitesimal size and small but finite scalar charge. This particle deviates from a geodesic because it interacts with its own retarded field $\psi^\ret$. A recently introduced Green's function $G^\SS$ precisely determines the singular part, $\psi^\SS$, of the retarded field. This part exerts no force on the particle. The remainder of the field $\psi^\R = \psi^\ret - \psi^\SS$ is a vacuum solution of the field equation and is entirely responsible for the self-force. A particular, locally inertial coordinate system is used to determine an expansion of $\psi^\SS$ in the vicinity of the particle. For a particle in a circular orbit in the Schwarzschild geometry, the mode-sum decomposition of the difference between $\psi^\ret$ and the dominant terms in the expansion of $\psi^\SS$ provide a mode-sum decomposition of an approximation for $\psi^\R$ from which the self-force is obtained. When more terms are included in the expansion, the approximation for $\psi^\R$ is increasingly differentiable, and the mode-sum for the self-force converges more rapidly.
Detweiler Steven
Messaritaki Eirini
Whiting Bernard. F.
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