Self-Force and Green Function in Schwarzschild spacetime via Quasinormal Modes and Branch Cut

Abstract

The motion of a small compact object in a curved background spacetime deviates from a geodesic due to the action of its own field, giving rise to a self-force. This self-force may be calculated by integrating the Green function for the wave equation over the past worldline of the small object. We compute the self-force in this way for the case of a scalar charge in Schwarzschild spacetime, making use of the semi-analytic method of matched Green function expansions. Inside a local neighbourhood of the compact object, this method uses the Hadamard form for the Green function in order to render regularization trivial. Outside this local neighbourhood, we calculate the Green function using a spectral decomposition into poles (quasinormal modes) and a branch cut integral in the complex-frequency plane. We show that both expansions overlap in a sufficiently large matching region for an accurate calculation of the self-force to be possible. The scalar case studied here is a useful and illustrative toy-model for the gravitational case, which serves to model astrophysical binary systems in the extreme mass-ratio limit.

23 pages, 13 figures, 3 tables. Final published version

References in corpus (8)

• Gravitational self-force correction to the innermost stable circular orbit of a Schwarzschild black hole
• Quasinormal ringing of Kerr black holes: The excitation factors
• Precession effect of the gravitational self-force in a Schwarzschild spacetime and the effective one-body formalism
• Scalar-field perturbations from a particle orbiting a black hole using numerical evolution in 2+1 dimensions
• Self-Force Calculations with Matched Expansions and Quasinormal Mode Sums
• Caustic echoes from a Schwarzschild black hole
• Pade Approximants of the Green Function in Spherically Symmetric Spacetimes
• Analytic Investigation of the Branch Cut of the Green Function in Schwarzschild Space-time

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