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Lorentz cobordism

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Abstract

A Lorentz cobordism between two (in general nondiffeomorphic) 3-manifoldsM 0,M 1 is a pair (M,v), whereM is a differentiable 4-manifold andv is a differentiable vector field onM, such that 1) the boundary ofM is the disjoint union ofM 0 andM 1, 2)v is everywhere nonzero, 3)v is interior normal onM 0 and exterior normal onM 1. Such a manifoldM admits a Lorentz tensor with respect to whichM 0 andM 1 are spacelike hypersurfaces; thus a Lorentz cobordism is a model of a portion of a spacetime in which “the topology of spacelike hypersurfaces is changing”. We discuss the form that these changes can take, and give two methods for constructing a Lorentz cobordism between two nondiffeomorphic 3-manifolds. We comment on the possible relevance of Lorentz cobordism to the problem of gravitational collapse.

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Authors and Affiliations

  1. School of Theoretical Physics, Dublin Institute for Advanced Studies, Dublin, Ireland

    P. Yodzis

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  1. P. Yodzis
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Yodzis, P. Lorentz cobordism. Commun.Math. Phys. 26, 39–52 (1972). https://doi.org/10.1007/BF01877546

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  • DOI: https://doi.org/10.1007/BF01877546

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