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An imbedding of Lorentzian manifolds

Do-Hyung Kim

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A new method for imbedding a Lorentzian manifold with a non-compact Cauchy surface is presented. As an application, it is shown that any two-dimensional globally hyperbolic spacetime with a non-compact Cauchy surface can be causally isomorphically imbedded into two-dimensional Minkowski spacetime.


PACS

04.20.Gz Spacetime topology, causal structure, spinor structure

02.40.Ky Riemannian geometries

02.40.Sf Manifolds and cell complexes

MSC

53C20 Global Riemannian geometry, including pinching (See also 31C12, 58B20)

83C75 Space-time singularities, cosmic censorship, etc.

53C50 Lorentz manifolds, manifolds with indefinite metrics

51B20 Minkowski geometries

Subjects

Mathematical physics

Gravitation and cosmology

Dates

Issue 7 (7 April 2009)

Received 17 December 2008, in final form 29 January 2009

Published 27 February 2009



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