Indirect (source-free) integration method. II: Self-force consistent radial fall. (English) Zbl 1332.83025
Summary: We apply our method of indirect integration, described in Part I [ibid. 13, No. 2, Article ID 1650021, 43 p. (2016; Zbl 1360.35276)], at fourth order, to the radial fall affected by the self-force (SF). The Mode-Sum regularization 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 SF 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 [A. D. A. M. Spallicci and P. Ritter, Int. J. Geom. Methods Mod. Phys. 11, No. 10, Article ID 1450090, 15 p. (2014; Zbl 1327.83056)].
MSC:
| 83C10 | Equations of motion in general relativity and gravitational theory |
| 83C35 | Gravitational waves |
| 35Q75 | PDEs in connection with relativity and gravitational theory |
| 35L05 | Wave equation |
| 65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
| 70F05 | Two-body problems |
| 83C57 | Black holes |
Keywords:
modeling of wave equation; general relativity; equations of motion; two-body problem; gravitational waves; self-force; black holesReferences:
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