Does General Relativity Highlight Necessary Connections in Nature?

TL;DR

This paper examines the role of Bianchi identities in general relativity, questioning whether they reveal necessary features of physical laws and exploring their metaphysical implications.

Contribution

It clarifies the physical significance of Bianchi identities and investigates their potential to indicate a form of a posteriori necessity in the laws of nature.

Findings

Bianchi identities are not just mathematical constraints but have physical significance.

The paper suggests Bianchi identities may imply a form of necessity in the laws of physics.

Implications for the metaphysics of laws and the nature of physical necessity.

Abstract

The dynamics of general relativity is encoded in a set of ten differential equations, the so-called Einstein field equations. It is usually believed that Einstein's equations represent a physical law describing the coupling of spacetime with material fields. However, just six of these equations actually describe the coupling mechanism: the remaining four represent a set of differential relations known as Bianchi identities. The paper discusses the physical role that the Bianchi identities play in general relativity, and investigates whether these identities -- qua part of a physical law -- highlight some kind of a posteriori necessity in a Kripkean sense. The inquiry shows that general relativistic physics has an interesting bearing on the debate about the metaphysics of the laws of nature.