General Relativity and Gravitation

, Volume 38, Issue 8, pp 1241–1252

The hole argument for covariant theories

Research Article


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.


General relativity Differential geometry 


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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1.School of Arts and SciencesMCPHSBostonUSA
  2. 2.Department of Physics and Center for Philosophy and History of ScienceBostonUSA

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