On the geometry of Lorentz spaces as a limit space
Bull. Korean Math. Soc. 2014 Vol. 51, No. 4, 957-964
https://doi.org/10.4134/BKMS.2014.51.4.957
Published online July 31, 2014
Jong-Gug Yun
Korea National University of Education
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 $\{(M_\alpha,d_\alpha)\}$ of compact globally hyperbolic interpolating spacetimes with $C^{\pm}_\alpha$-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 $\{(M_\alpha,d_\alpha)\}$. 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 compari\-son
MSC numbers : Primary 53C20; Secondary 57S20
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