Geodesic Motion in the 5D Magnetized Schwarzschild-Like Solutions

TL;DR

This paper investigates the geodesic behavior in a five-dimensional magnetized Schwarzschild-like spacetime, comparing it to the classic Schwarzschild solution and visualizing the geometry through embedding diagrams, with implications for string and Brans-Dicke theories.

Contribution

It introduces an analysis of geodesics in a novel 5D magnetized Schwarzschild-like solution, extending understanding of higher-dimensional and magnetized gravitational fields.

Findings

Geodesic motion characterized by an effective potential.

Embedding diagrams visualizing the spacetime geometry.

Results applicable to string and Brans-Dicke theories.

Abstract

Geodesics for a 5D magnetized Schwarzschild-like solution are analyzed by reducing the problem to the motion of a test particle in an effective potential. In absence of magnetic field comparison is established with Schwarzschild's geometry. Embedding diagrams are constructed in order to visualize the geometry of the metric. The study performed here is also valid, when the electromagnetic interactions are neglected, for the low energy superstring theory and the Brans-Dicke theory.