The Hole Argument for Covariant Theories

Abstract

The hole argument was developed by Einstein in 1913 while he was searching for a relativistic theory of gravitation. Einstein used the language of coordinate systems and coordinate invariance, rather than the language of manifolds and diffeomorphism invariance. He formulated the hole argument against covariant field equations and later found a way to avoid it using coordinate language. In this paper we shall use the invariant language of categories, manifolds and natural objects to give a coordinate-free description of the hole argument and a way of avoiding it. Finally we shall point out some important implications of further extensions of the hole argument to sets and relations for the problem of quantum gravity.

Keywords: General Relativity, Differential Geometry. to appear in the GRG

References in corpus (4)

• Background independent quantizations: the scalar field I
• Background independent quantizations: the scalar field II
• Fibered Manifolds, Natural Bundles, Structured Sets, G-Sets and all that: The Hole Story from Space Time to Elementary Particles
• Topics in Born-Infeld Electrodynamics

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