Radiation Reaction in Schwarzschild Spacetime: Retarded Green's Function via Hadamard-WKB Expansion

Abstract

An analytic method is given for deriving the part of the retarded Green's function v(x,x') that contributes to the tail term in the radiation reaction force felt by a particle coupled to a massless minimally coupled scalar field. The method gives an expansion of v(x,x') for small separations of the points x, x' valid for an arbitrary static spherically symmetric spacetime. It is obtained by using a WKB approximation for the Euclidean Green's function for the massless minimally coupled scalar field and is equivalent to the DeWitt-Schwinger expansion for v(x,x'). The first few terms in this expansion are displayed here for the case of Schwarzschild spacetime.

17 pages, Physical Review D version along with the corrections given in the errata

References in corpus (5)

• Listening to the Universe with Gravitational-Wave Astronomy
• Gravitational self-force on a particle orbiting a Kerr black hole
• Regularization parameters for the self force in Schwarzschild spacetime: II. gravitational and electromagnetic cases
• Noise Kernel and Stress Energy Bi-Tensor of Quantum Fields in Hot Flat Space and Gaussian Approximation in the Optical Schwarzschild Metric
• Method to compute the stress-energy tensor for the massless spin 1/2 field in a general static spherically symmetric spacetime

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