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

Patxi Ritter (1, 2) , S. Aoudia (3) , Alessandro D. A. M. Spallicci (2) , Stéphane Cordier (1)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
2 LPC2E - Laboratoire de Physique et Chimie de l'Environnement et de l'Espace
3 AEI - Max-Planck-Institut für Gravitationsphysik ( Albert-Einstein-Institut )

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).

Keywords: numbers: 0260Cb; 0260Lj; 0270Bf; 0425Nx; 0430-w; 0470Bw; 9530Sf Keywords: Modelling of wave equation; General relativity; Equations of motion; Two-body problem; Gravi- tational waves; Self-force; Black holes Mathematics Subject Classification 2010: 35Q75; 35L05; 65M70; 70F05; 83C10; 83C35; 83C57

Domains: General Relativity and Quantum Cosmology [gr-qc]; Mathematical Physics [math-ph]; Sciences of the Universe [physics]

Patxi Ritter, S. Aoudia, Alessandro D. A. M. Spallicci, Stéphane Cordier. Indirect (source-free) integration method. II. Self-force consistent radial fall. International Journal of Geometric Methods in Modern Physics, 2016, 13 (02), 1650019 (59 p.). ⟨10.1142/S0219887816500195⟩. ⟨insu-01352535⟩