Infinitesimal Minkowskianity for manifolds with continuous Lorentzian metrics

TL;DR

This paper proves that causally simple manifolds with continuous Lorentzian metrics are infinitesimally Minkowskian, extending the understanding of local geometric structure in such spacetimes.

Contribution

It establishes that continuous Lorentzian metrics on causally simple manifolds are locally Minkowskian, providing new insights into the local geometry of non-smooth spacetimes.

Findings

Any causally simple spacetime with a continuous Lorentzian metric is infinitesimally Minkowskian.

The result extends local geometric properties known for smooth metrics to continuous metrics.

Supports the idea that causally simple spacetimes have well-behaved local structures.

Abstract

We prove that any metric measure spacetime arising from a smooth manifold $M$ endowed with a continuous Lorentzian metric $g$ is infinitesimally Minkowskian, under the assumption that $(M, g)$ is causally simple.