A Splitting Theorem for non-positively curved Lorentzian spaces

TL;DR

This paper establishes a splitting theorem for Lorentzian pre-length spaces with non-positive timelike curvature and extends the first variation formula to spaces with various timelike curvature bounds.

Contribution

It introduces a splitting theorem for Lorentzian spaces with non-positive curvature and generalizes the first variation formula to broader curvature bounds.

Findings

Proves a splitting theorem for Lorentzian pre-length spaces with non-positive curvature.

Extends the first variation formula to spaces with arbitrary timelike curvature bounds.

Provides new tools for analyzing Lorentzian spaces with curvature constraints.

Abstract

We prove a splitting theorem for Lorentzian pre-length spaces with global non-positive timelike curvature. Additionally, we extend the first variation formula to spaces with any timelike curvature bound, either from above or below, and different from 0.