2005/12/31 by M. Iftime, Mihaela Iftime, John Stachel · 1 citation
Physics and Astronomy · #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Applications #Relativity and Gravitational Theory #gr-qc
paper · pdf · doi:10.1007/s10714-006-0303-4
published as Gen.Rel.Grav. 38 (2006) 1241-1252 · Keywords: General Relativity, Differential Geometry. to appear in the GRG
arxiv created 2006/04/08 · openalex publication_date 2006/07/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.