Reparametrizing the relativistic Kepler equation: a bridge to Levi-Civita-type models

TL;DR

This paper connects relativistic Kepler problems with Levi-Civita models by reparameterizing solutions, revealing a shared dynamical structure with modified coefficients.

Contribution

It introduces a reparameterization method linking special relativistic Kepler solutions to Levi-Civita-type models with an added $1/r^2$ potential term.

Findings

Solutions of relativistic Kepler problems can be reparameterized as generalized Kepler equations.

The dynamics resemble Levi-Civita corrections with different coefficients.

A new mathematical link between relativistic and classical correction models is established.

Abstract

We establish a link between different relativistic variants of the Kepler problem. In particular, we show that solutions of the special relativistic model with fixed energy can be reparameterized as solutions of a generalized Kepler equation with an additional $1/r^2$ term in the gravitational potential. This yields a dynamics of the same type as the Levi-Civita correction, up to different coefficients.