What is a Singularity in Geometrized Newtonian Gravitation?

TL;DR

This paper explores the concept of singularities within geometrized Newtonian gravitation, proposing geodesic incompleteness as a criterion and establishing a classical singularity theorem analogous to relativistic results.

Contribution

It introduces a natural criterion for singularities in Newtonian gravity and proves a classical Raychaudhuri-Komar type singularity theorem.

Findings

Geodesic incompleteness characterizes singularities in geometrized Newtonian gravitation.

Singularities naturally occur in classical physics according to the proven theorem.

The classical singularity theorem parallels relativistic results in a Newtonian context.

Abstract

I discuss singular spacetimes in the context of the geometrized formulation of Newtonian gravitation. I argue first that geodesic incompleteness is a natural criterion for when a model of geometrized Newtonian gravitation is singular, and then I show that singularities in this sense arise naturally in classical physics by stating and proving a classical version of the Raychaudhuri-Komar singularity theorem.