Effective potential approach to the motion of massive test particles in Kaluza-Klein gravity

TL;DR

This paper investigates the motion of massive test particles in Kaluza-Klein gravity using an effective potential approach, comparing higher-dimensional solutions to the Schwarzschild case and exploring modifications consistent with experimental data.

Contribution

It introduces an effective potential method for analyzing particle orbits in static Kaluza-Klein solutions and compares these with Schwarzschild results, highlighting potential observable differences.

Findings

Stable circular orbits are characterized in higher-dimensional solutions.

Differences from Schwarzschild orbits are identified and analyzed.

Modifications to orbits are consistent with experimental constraints.

Abstract

Effective potential for a class of static solutions of Kaluza-Klein equations with three-dimensional spherical symmetry is studied. Test particles motion is analyzed. In attempts to read the obtained results with the experimental data, particular attention is devoted to the Schwarzschild's limit of the four dimensional counterpart of these electromagnetic-free solutions. Massive particles stable circular orbits in particular are studied, and a comparison between the well known results if the Schwarzschild's case and those found for the static higher-dimensional case is performed. A modification of the circular stable orbits is investigated in agreement with the experimental constraints.