Perihelion advance for orbits with large eccentricities in the Schwarzschild black hole

TL;DR

This paper introduces a new formula for calculating the perihelion advance of a test particle orbiting a Schwarzschild black hole, effective for both weak and strong gravitational fields through a novel non-linear transformation.

Contribution

It develops a new non-linear transformation that extends the applicability of perihelion advance formulas into the strong-field regime near black hole horizons.

Findings

Derived a formula valid for large eccentricities

Extended perihelion advance calculations into strong gravitational fields

Applicable to orbits close to the black hole horizon

Abstract

We deduce a new formula for the perihelion advance of a test particle in the Schwarzschild black hole by applying a newly developed non-linear transformation within the Schwarzschild space-time. By this transformation we are able to apply the well-known formula valid in the weak-field approximation near infinity also to trajectories in the strong-field regime near the horizon of the black hole.