JOURNAL BROWSE
Search
Advanced SearchSearch Tips
ON THE GEOMETRY OF LORENTZ SPACES AS A LIMIT SPACE
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
ON THE GEOMETRY OF LORENTZ SPACES AS A LIMIT SPACE
Yun, Jong-Gug;
  PDF(new window)
 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 {()} of compact globally hyperbolic interpolating spacetimes with -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 {()}. 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
 References
1.
S. B. Alexander and R. L. Bishop, Lorentz and semi-Riemannian spaces with Alexandrov curvature bounds, Comm. Anal. Geom. 16 (2008), no. 2, 251-282. crossref(new window)

2.
L. Bombelli and J. Noldus, The moduli space of isometry classes of globally hyperbolic spacetimes, Classical Quantum Gravity 21 (2004), no. 18, 4429-4453. crossref(new window)

3.
J. Noldus, A Lorentzian Gromov-Hausdorff notion of distance, Classical Quantum Gravity 21 (2004), no. 4, 839-850. crossref(new window)

4.
J. Noldus, Lorentzian Gromov Hausdorff theory as a tool for quantum gravity kinematics, Ph.D. thesis, Gent University, 2004.

5.
J. Noldus, The limit space of a Cauchy sequence of globally hyperbolic spacetimes, Classical Quantum Gravity 21 (2004), no. 4, 851-874. crossref(new window)

6.
C. Plaut, Metric curvature, convergence, and topological finiteness, Duke Math. J. 66 (1992), no. 1, 43-57. crossref(new window)

7.
K. Shiohama, An Introduction to the Geometry of Alexandrov Spaces, GARC, Seoul National University, 1993.

8.
R. Sorkin and E. Woolgar, A causal order for spacetimes with Lorentzian metrics: Proof of compactness of the space of causal curves, Classical Quantum Gravity 13 (1996), no. 7, 1971-1993. crossref(new window)

9.
J.-G. Yun, Lorentzian Gromov-Hausdorff convergence and limit curve theorem, Commun. Korean Math. Soc. 28 (2013), no. 3, 589-596. crossref(new window)