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

TL;DR

This paper applies a fourth-order indirect integration method to analyze the self-force effects on a radial fall, confirming the method's convergence and accuracy in a self-consistent framework.

Contribution

It extends the indirect integration method to fourth order for self-force calculations in radial fall, validating its effectiveness and consistency.

Findings

Convergence of the integration method is confirmed.

Self-force effects are accurately modeled with iterative correction.

Results support the method's validity for self-force problems.

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).