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Cited article:

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

Patxi Ritter, Sofiane Aoudia, Alessandro D. A. M. Spallicci and Stéphane Cordier
International Journal of Geometric Methods in Modern Physics 13 (02) 1650019 (2016)
https://doi.org/10.1142/S0219887816500195

A fully relativistic radial fall

Alessandro D. A. M. Spallicci and Patxi Ritter
International Journal of Geometric Methods in Modern Physics 11 (10) 1450090 (2014)
https://doi.org/10.1142/S021988781450090X