caa a22 4500 467887551 CHVBK 20180406152739.0 cr unu---uuuuu 170328e20060801xx s 000 0 eng 10.1007/s10714-006-0303-4 doi (NATIONALLICENCE)springer-10.1007/s10714-006-0303-4 The hole argument for covariant theories [Elektronische Daten] [M. Iftime, J. Stachel] 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. Springer Science+Business Media, Inc., 2006 General relativity nationallicence Differential geometry nationallicence Iftime M. School of Arts and Sciences, MCPHS, Boston, MA, USA aut Stachel J. Department of Physics and Center for Philosophy and History of Science, Boston, MA, USA aut General Relativity and Gravitation Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 38/8(2006-08-01), 1241-1252 0001-7701 38:8<1241 2006 38 10714 https://doi.org/10.1007/s10714-006-0303-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10714-006-0303-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Iftime M. School of Arts and Sciences, MCPHS, Boston, MA, USA aut NATIONALLICENCE 700 1- Stachel J. Department of Physics and Center for Philosophy and History of Science, Boston, MA, USA aut NATIONALLICENCE 773 0- General Relativity and Gravitation Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 38/8(2006-08-01), 1241-1252 0001-7701 38:8<1241 2006 38 10714 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer