Self-force on a scalar charge in radial infall from rest using the Hadamard-WKB expansion
Abstract
We present an analytic method based on the Hadamard-WKB expansion to calculate the self-force for a particle with scalar charge falling radially from rest into a Schwarzschild black hole, in the case of short duration from the start. This is possible because under this circumstance the value of the integral of the retarded Green's function over the particle's past trajectory can be expressed in terms of two integrals over the time period that the particle has been falling. This analytic result is expected to be useful as a check for numerical prescriptions including those involving mode sum regularization and for any other analytical approximations to self-force calculations.Keywords
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