Cauchy and uniform temporal functions of globally hyperbolic cone fields
HTML articles powered by AMS MathViewer
- by Patrick Bernard and Stefan Suhr
- Proc. Amer. Math. Soc. 148 (2020), 4951-4966
- DOI: https://doi.org/10.1090/proc/15106
- Published electronically: June 30, 2020
- PDF | Request permission
Abstract:
We study a class of time functions called uniform temporal functions in the general context of globally hyperbolic closed cone fields. We prove some existence results for uniform temporal functions, and establish the density of uniform temporal functions in Cauchy causal functions.References
- L. Aké Hau, J. L. Flores, and M. Sánchez, Structure of globally hyperbolic spacetimes with timelike boundary, arXiv:1808.04412, to appear in Rev. Mat. Iberoamericana.
- J. J. Benavides Navarro and E. Minguzzi, Global hyperbolicity is stable in the interval topology, J. Math. Phys. 52 (2011), no. 11, 112504, 8. MR 2906563, DOI 10.1063/1.3660684
- Antonio N. Bernal and Miguel Sánchez, Smoothness of time functions and the metric splitting of globally hyperbolic spacetimes, Comm. Math. Phys. 257 (2005), no. 1, 43–50. MR 2163568, DOI 10.1007/s00220-005-1346-1
- Antonio N. Bernal and Miguel Sánchez, Further results on the smoothability of Cauchy hypersurfaces and Cauchy time functions, Lett. Math. Phys. 77 (2006), no. 2, 183–197. MR 2254187, DOI 10.1007/s11005-006-0091-5
- Antonio N. Bernal and Miguel Sánchez, Globally hyperbolic spacetimes can be defined as ‘causal’ instead of ‘strongly causal’, Classical Quantum Gravity 24 (2007), no. 3, 745–749. MR 2294243, DOI 10.1088/0264-9381/24/3/N01
- Patrick Bernard and Stefan Suhr, Lyapounov functions of closed cone fields: from Conley theory to time functions, Comm. Math. Phys. 359 (2018), no. 2, 467–498. MR 3783554, DOI 10.1007/s00220-018-3127-7
- Patrick Bernard and Stefan Suhr, Smoothing causal functions, J. Phys. Conf. Ser. 968 (2018), 012001, 7. MR 3919944, DOI 10.1088/1742-6596/968/1/012001
- Albert Fathi, Partitions of unity for countable covers, Amer. Math. Monthly 104 (1997), no. 8, 720–723. MR 1476756, DOI 10.2307/2975235
- Albert Fathi and Antonio Siconolfi, On smooth time functions, Math. Proc. Cambridge Philos. Soc. 152 (2012), no. 2, 303–339. MR 2887877, DOI 10.1017/S0305004111000661
- E. Minguzzi, On the existence of smooth Cauchy steep time functions, Classical Quantum Gravity 33 (2016), no. 11, 115001, 4. MR 3499223, DOI 10.1088/0264-9381/33/11/115001
- Ettore Minguzzi, Causality theory for closed cone structures with applications, Rev. Math. Phys. 31 (2019), no. 5, 1930001, 139. MR 3955368, DOI 10.1142/S0129055X19300012
- O. Müller and M. Sánchez, Lorentzian manifolds isometrically embeddable in $\Bbb {L}^{N}$, Trans. Amer. Math. Soc. 363 (2011), no. 10, 5367–5379. MR 2813419, DOI 10.1090/S0002-9947-2011-05299-2
Bibliographic Information
- Patrick Bernard
- Affiliation: Université Paris-Dauphine, PSL Research University, École Normale Supérieure, DMA (UMR CNRS 8553) 45, rue d’Ulm 75230 Paris Cedex 05, France
- MR Author ID: 609775
- Email: patrick.bernard@ens.fr
- Stefan Suhr
- Affiliation: Fakultät für Mathematik, Ruhr-Universität Bochum, Universitätsstraße 150 44780 Bochum, Germany
- MR Author ID: 958131
- Email: stefan.suhr@rub.de
- Received by editor(s): May 14, 2019
- Received by editor(s) in revised form: March 11, 2020, March 14, 2020, and March 23, 2020
- Published electronically: June 30, 2020
- Additional Notes: This research was supported by the SFB/TRR 191 “Symplectic Structures in Geometry, Algebra and Dynamics”, funded by the Deutsche Forschungsgemeinschaft.
- Communicated by: Jia-Ping Wang
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 148 (2020), 4951-4966
- MSC (2010): Primary 53C50, 37B25
- DOI: https://doi.org/10.1090/proc/15106
- MathSciNet review: 4143406