Classical General Relativity

TL;DR

This survey paper provides an overview of classical general relativity, covering its foundational structure, the nature of simultaneity in Minkowski spacetime, Newton-Cartan theory, and how spacetime geometry can be inferred from causal relations.

Contribution

It offers a comprehensive review of key topics in classical relativity, including recent insights into the causal structure and alternative formulations of gravity.

Findings

Analysis of the relativity of simultaneity in Minkowski spacetime

Discussion of Newton-Cartan theory as a geometric reformulation of Newtonian gravity

Exploration of how spacetime geometry can be reconstructed from causal structure

Abstract

This survey paper is divided into two parts. In the first (section 2), I give a brief account of the structure of classical relativity theory. In the second (section 3), I discuss three special topics: (i) the status of the relative simultaneity relation in the context of Minkowski spacetime; (ii) the "geometrized" version of Newtonian gravitation theory (also known as Newton-Cartan theory); and (iii) the possibility of recovering the global geometric structure of spacetime from its "causal structure".