Determinism and general relativity

TL;DR

This paper explores the concept of determinism in general relativity, examining the role of global hyperbolicity and its implications for the physical reasonableness of spacetime models.

Contribution

It analyzes the necessity and justification of global hyperbolicity in ensuring determinism within general relativity, comparing philosophical and physical perspectives.

Findings

Global hyperbolicity may not be necessary for all physically reasonable models.

The paper discusses whether to impose global hyperbolicity by fiat or derive it from weaker assumptions.

It considers the influence of beyond-GR physics on the status of global hyperbolicity.

Abstract

We investigate the fate of determinism in general relativity (GR), comparing the philosopher's account with the physicist's well-posed initial value formulations. The fate of determinism is interwoven with the question of what it is for a spacetime to be `physically reasonable'. A central concern is the status of global hyperbolicity, a putatively necessary condition for determinism in GR. While global hyperbolicity may fail to be true of all physically reasonable models, we analyze whether global hyperbolicity should be (i) imposed by fiat; (ii) established from weaker assumptions, as in cosmic censorship theorems; or (iii) justified by beyond-GR physics.