Simultaneity in special and general relativity

TL;DR

This paper explores the concept of simultaneity in special and general relativity, examining synchronization conventions and the challenge of defining a universal time function in curved spacetime.

Contribution

It provides a detailed analysis of simultaneity, including Weyl's proof of Einstein's synchronization and the problem of assigning a global time function in general relativity.

Findings

Weyl's proof confirms the consistency of Einstein's synchronization.

Discussion on the existence of a global time function in curved spacetime.

Insights into the structure of simultaneity in relativistic theories.

Abstract

We present some basic facts concerning simultaneity in both special and general relativity. We discuss Weyl's proof of the consistence of Einstein's synchronization convention and consider the general relativistic problem of assigning a time function to a congruence of timelike curves.