# A NOTE ON THE LORENTZIAN LIMIT CURVE THEOREM

• Yun, Jong-Gug (Department of Mathematics Education Korea National University of Education)
• Published : 2013.07.31

#### Abstract

In this paper, we extend the familiar limit curve theorem in [2] to a situation where each causal curve lies in a sequence of compact interpolating spacetimes converging to a limit Lorentz space in the sense of Lorentzian Gromov-Hausdorff distance.

#### References

1. L. Bombelli and J. Noldus, The moduli space of isometry classes of globally hyperbolic spacetimes, Classical Quantum Gravity 21 (2004), no. 18, 4429-4453. https://doi.org/10.1088/0264-9381/21/18/010
2. S. W. Hawking and G. F. R. Ellis, The Large Scale Structure of Space-Time, Cambidge University Press, 1973.
3. J. Noldus, A Lorentzian Gromov-Hausdorff notion of distance, Classical Quantum Gravity 21 (2004), no. 4, 839-850. https://doi.org/10.1088/0264-9381/21/4/007
4. J. Noldus, Lorentzian Gromov Hausdorff theory as a tool for quantum gravity kinematics, PhD 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. https://doi.org/10.1088/0264-9381/21/4/008
6. R. Penrose, R. D. Sorkin, and E. Woolgar, A positive mass theorem based on the focusing and retardation of null geodesics, gr-qc/9301015.
7. R. Sorkin and E. Woolgar, A causal order for spacetimes with $C^0$ Lorentzian metrics: proof of compactness of the space of causal curves, Classical Quantum Gravity 13 (1996), no. 7, 1971-1993. https://doi.org/10.1088/0264-9381/13/7/023