A Criterion for Physically Acceptable Extra Dimensions with Boundaries

TL;DR

This paper establishes a criterion to identify which compact extra-dimensional spaces produce physically consistent Newton's law corrections, focusing on manifolds with boundary conditions.

Contribution

It introduces a criterion that excludes compact connected Riemannian manifolds with Dirichlet boundaries as viable extra dimensions.

Findings

Compact connected Riemannian manifolds with Dirichlet boundaries are excluded as extra dimensions.

The study considers both boundary and boundary-less manifolds.

Neumann boundary conditions are not explicitly excluded.

Abstract

We present a criterion for deciding which compact extra dimensional spaces yield physically reliable Newton's law corrections. We study compact manifolds with boundary and without boundary. The boundary conditions which we use on the boundaries are Dirichlet or Neumann. We find that compact connected Riemannian manifolds with Dirichlet boundaries are completely excluded as extra dimensional spaces.