Newtonian Gravity on an N-Sphere

TL;DR

This paper explores Newtonian gravity and electrostatics on an N-sphere, focusing on fundamental properties like the shell theorem, to understand how classical laws extend to curved spherical geometries.

Contribution

It introduces the formulation and analysis of Newtonian gravity and electrostatics on an N-sphere, highlighting the shell theorem in this context as a novel extension.

Findings

Shell theorem holds on an N-sphere

Electrostatics behaves similarly to Euclidean space in this setting

Insights into gravitational behavior in curved geometries

Abstract

We consider some elementary features of Newtonian gravity, or electrostatics, as defined on an N-sphere. In particular, we present and discuss "the shell theorem" for this system.