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 that undergoes radial infall in a Schwarzschild spacetime after being held at rest until a time t = 0. Our result is valid in the case of short duration from the start. It is possible to use the Hadamard-WKB expansion in this case because the value of the integral of the retarded Green's function over the particle's entire 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.

arXiv comment22 pages, 2 figures, Physical Review D version along with the corrections given in the erratum

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• Self-Force Calculations with Matched Expansions and Quasinormal Mode Sums
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• Noise kernel for a quantum field in Schwarzschild spacetime under the Gaussian approximation
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• Pade Approximants of the Green Function in Spherically Symmetric Spacetimes
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