Dependence of Self-force on Central Object

For a particle in orbit about a static spherically symmetric body, we study the change in self-force that results when the central body type (i.e., the choice of interior metric for the Schwarzschild exterior) is changed. While a straight self-force is difficult to compute because of the need for regularization, such a "self-force difference" may be computed directly from the mode functions of the relevant wave equations. This technique gives a simple probe of the (non)locality of the force, as well as offers the practical benefit of an easy determination of the self-force on a body orbiting an arbitrary (static spherically symmetric) central body, once the corresponding result for a black hole (or some other reference interior) is known. We derive a general expression for the self-force difference at the level of a mode-sum in the case of a (possibly non-minimally coupled) scalar charge and indicate the generalization to the electromagnetic and gravitational cases. We then consider specific choices of orbit and/or central body. Our main findings are: (1) For charges held static at a large distance from the central body, the self-force is independent of the central body type in the minimally coupled scalar case and the electromagnetic case (but dependent in the nonminimally coupled scalar case); (2) For circular orbits about a thin-shell spacetime in the scalar case, the fractional change in self-force from a black hole spacetime is much larger for the radial (conservative) force than for the angular (dissipative) force; and (3) the radial self-force difference (between these spacetimes) agrees closely for a static charge and a circular orbit of the same radius.

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