Coulomb's law in maximally symmetric spaces

TL;DR

This paper investigates how Coulomb's law is modified in n-dimensional maximally symmetric spaces, revealing additional curvature-dependent terms and exploring magnetic monopoles and charge quantization in such geometries.

Contribution

It provides analytical expressions for electric and magnetic fields in curved spaces and examines the implications for magnetic monopoles and charge quantization.

Findings

Extra curvature-dependent terms modify Coulomb's law.

Analytical magnetic field and potential expressions are derived.

Magnetic charge quantization rules are applicable in these spaces.

Abstract

We study the modifications to the Coulomb's law when the background geometry is a $n$-dimensional maximally symmetric space, by using of the $n$-dimensional version of the Gauss' theorem. It is shown that some extra terms are added to the usual expression of the Coulomb electric field due to the curvature of the background space. Also, we consider the problem of existence of magnetic monopoles in such spaces and present analytical expressions for the corresponding magnetic fields and vector potentials. We show that the quantization rule of the magnetic charges (if they exist) would be applicable to our study as well.