ON THE GEOMETRY OF LORENTZ SPACES AS A LIMIT SPACE

Title & Authors
ON THE GEOMETRY OF LORENTZ SPACES AS A LIMIT SPACE
Yun, Jong-Gug;

Abstract
In this paper, we prove that there is no branch point in the Lorentz space (M, d) which is the limit space of a sequence {($\small{M_{\alpha},d_{\alpha}}$)} of compact globally hyperbolic interpolating spacetimes with $\small{C^{\pm}_{\alpha}}$-properties and curvature bounded below. Using this, we also obtain that every maximal timelike geodesic in the limit space (M, d) can be expressed as the limit curve of a sequence of maximal timelike geodesics in {($\small{M_{\alpha},d_{\alpha}}$)}. Finally, we show that the limit space (M, d) satisfies a timelike triangle comparison property which is analogous to the case of Alexandrov curvature bounds in length spaces.
Keywords
Lorentzian Gromov-Hausdorff theory;timelike triangle comparison;
Language
English
Cited by
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