Cudek, Franciszek (2026) Small Singular Regions of Spacetime. [Preprint]

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Abstract

We prove that every open connected region of relativistic spacetime (M,g) that encloses a b-incomplete half-curve has an open connected subregion that encloses a b-incomplete half-curve and is also "small" in the following sense: it is the image, under the bundle projection map, of some open region in the (connected) orthonormal frame bundle O+M over that spacetime which is bounded, and whose closure is Cauchy incomplete, with respect to any "natural" distance function on O+M. As a corollary, it follows that every b-incomplete half-curve can be covered by a sequence of singular regions which are images of a sequence of bounded subsets of O+M whose diameter, with respect to any "natural" distance function on O+M, tends to zero. We discuss to what extent these results can be interpreted in favour of the claim that singular structure in classical general relativity is "localizable".

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Item Type:	Preprint
Creators:	Creators Email ORCID Cudek, Franciszek franciszek.cudek@philosophy.ox.ac.uk 0000-0002-9219-6199
Additional Information:	Accepted in General Relativity and Gravitation.
Keywords:	relativistic spacetimes, singularities, b-incompleteness, frame bundles, localizability
Subjects:	Specific Sciences > Physics > Relativity Theory
Depositing User:	Franciszek Cudek
Date Deposited:	03 Feb 2026 14:28
Last Modified:	05 Feb 2026 14:02
Item ID:	28073
Subjects:	Specific Sciences > Physics > Relativity Theory
Date:	2026
URI:	https://philsci-archive.pitt.edu/id/eprint/28073

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