1209.6088 (Peter Taylor)

Self-force on an arbitrarily coupled static scalar particle in a
wormhole space-time    [PDF]

Peter Taylor

In this paper, we consider the problem of computing the self-force and self-energy for a static scalar charge in a wormhole space-time with throat profile $r(\rho)^{2}=\rho^{2}+a^{2}$ for arbitrary coupling of the field to the curvature. This calculation has previously been considered only in the special cases of minimal ($\xi=0$) coupling and conformal coupling ($\xi=1/8$ in three dimensions). Though it is straight-forward to obtain a closed-form representation of the Green's function and the self-force for these special cases, we believe the previous results to be erroneous due to a naive definition of the self-force as a derivative of the radiative field at coincidence, rather than the coincidence limit of the derivative of the radiative field. We present the correct expressions for the self-force in these cases, as well as presenting an analytic expression for the self-force for arbitrary coupling. We analyse our results and show that the qualitative features of the correct self-force are very different to the previous results.

View original: http://arxiv.org/abs/1209.6088