Indirect (source-free) integration method. II. Self-force consistent radial fall

Abstract

We apply our method of indirect integration, described in Part I, at fourth order, to the radial fall affected by the self-force. The Mode-Sum regularisation is performed in the Regge-Wheeler gauge using the equivalence with the harmonic gauge for this orbit. We consider also the motion subjected to a self-consistent and iterative correction determined by the self-force through osculating stretches of geodesics. The convergence of the results confirms the validity of the integration method. This work complements and justifies the analysis and the results appeared in Int. J. Geom. Meth. Mod. Phys., 11, 1450090 (2014).

To appear in Int. J. Geom. Meth. Mod. Phys

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• Comment on "Acceleration of particles to high energy via gravitational repulsion in the Schwarzschild field" [Astropart. Phys. 86 (2017) 18-20]
• Particle-without-Particle: a practical pseudospectral collocation method for linear partial differential equations with distributional sources