# Cauchy and uniform temporal functions of globally hyperbolic cone fields

## TL;DR

This paper investigates uniform temporal functions within globally hyperbolic cone fields, establishing their existence and density among Cauchy causal functions, thereby advancing the understanding of time functions in Lorentzian geometry.

## Contribution

It introduces new existence results for uniform temporal functions and proves their density in the space of Cauchy causal functions in the context of globally hyperbolic cone fields.

## Key findings

- Existence of uniform temporal functions is established.
- Uniform temporal functions are dense in Cauchy causal functions.
- Advances the understanding of time functions in Lorentzian geometry.

## Abstract

We study a class of time functions called uniform temporal functions in the general context of globally hyperbolic closed cone fields. We prove some existence results for uniform temporal functions, and prove the density of uniform temporal functions in Cauchy causal functions.