Abstract
We show that many standard results of Lorentzian causality theory remain valid if the regularity of the metric is reduced to \(C^{1,1}\). Our approach is based on regularisations of the metric adapted to the causal structure.
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Notes
See, however, [25] where it is shown that indeed \(\exp _p\) is even strongly differentiable at \(0\) with derivative \(\text {id}_{T_pM}\).
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Acknowledgments
We would like to thank James D. E. Grant for helpful discussions. The authors acknowledge the support of FWF projects P23714 and P25326, as well as OeAD project WTZ CZ 15/2013. We are indebted to the referees of this paper for several comments that have led to substantial improvements in the presentation.
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Kunzinger, M., Steinbauer, R., Stojković, M. et al. A regularisation approach to causality theory for \(C^{1,1}\)-Lorentzian metrics. Gen Relativ Gravit 46, 1738 (2014). https://doi.org/10.1007/s10714-014-1738-7
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DOI: https://doi.org/10.1007/s10714-014-1738-7