A brief introduction to non-regular spacetime geometry

TL;DR

This paper provides a concise, non-technical overview of non-regular spacetime geometry, explaining how curvature and gravity can be understood without relying on smooth differential calculus.

Contribution

It introduces a novel approach to defining curvature and gravity in non-regular spacetimes without smooth differential geometric tools.

Findings

Curvature can be characterized without smooth calculus.

Gravity concepts extend to non-regular geometries.

Provides foundational insights for non-smooth spacetime analysis.

Abstract

We give a brief non-technical introduction to non-regular spacetime geometry. In particular, we discuss how curvature, and hence gravity, can be defined without a smooth (differential geometric) calculus.