Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2005-02-28
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
11 pages, 5 figures, part of senior thesis work
Scientific paper
We numerically calculate the dissipative part of the self-force on a scalar charge moving on a circular, geodesic, equatorial orbit in Kerr spacetime. The solution to the scalar field equation is computed by separating variables and is expressed as a mode sum over radial and angular modes. The force is then computed in two ways: a direct, instantaneous force calculation which uses the half-retarded-minus-half-advanced field, and an indirect method which uses the energy and angular momentum flux at the horizon and at infinity to infer the force. We are able to show numerically and analytically that the force-per-mode is the same for both methods. To enforce the boundary conditions (ingoing radiation at the horizon and outgoing radiation at infinity for the retarded solution) numerical solutions to the radial equation are matched to asymptotic expansions for the fields at the boundaries. Recursion relations for the coefficients in the asymptotic expansions are given in an appendix.
Friedman John L.
Gralla Samuel E.
Wiseman Alan G.
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