Recently, the relationship between (geodesics) convexity, connectedness, and completeness properties in Riemannian manifolds (∑; h) and the causal properties in Lorentzian static spacetimes (M; g) = (R × ∑; -dt2 + h) is studied. In this paper, some sufficient conditions are introduced to (∑; h) be geodesically convex.
1. A. Bautista, A. Ibort, J. Lafuente, and R. Low, A conformal boundary for space-times based on light- like geodesics: The 3-dimensional case, J. Math. Phys. 58(2017), 022503.
2. J. K. Beem and P.E. Parker, Klein–Gordon solvability and the geometry of geodesics, Pacific J. Math. 107(1983), 1–14.
3. J. K. Beem, and P. E. Parker, Pseudoconvexity and general relativity, J. Geom. Phys. 4(1987), 71–80.
4. J. K. Beem and P. E. Parker, Pseudoconvexity and geodesic connectedness, Ann. Mat. Pura Appl. 155(1989), 137–142.
5. J. K. Beem and A. Krolak, Cosmic censorship and pseudoconvexity, J. Math. Phys., 33(1992), 2249–2253.
6. J. K. Beem, P. E. Ehrlich, and K. L. Easley, Global Lorentzian Geometry, Marcel Dekker, New York, 1996.
7. J. Hedicke, E. Minguzzi, B. Schinnerl, R. Steinbauer, and S. Suhr, Causal simplicity and (maximal) null pseudoconvexity, Class. Quantum Grav. 38(2021), 227002 .
8. R. J. Low, The geometry of the space of null geodesics, J. Math. Phys. 30(1989), 809–811.
9. R. J. Low, Spaces of causal paths and naked singularities, Class. Quantum Grav 7(1990), 943–954.
10. E. Minguzzi, Lorentzian causality theory, Living Reviews in Relativity, 22(1):3(2019).
11. R. Pourkhandani and Y. Bahrampour, The space of causal curves and separation axioms, Class. Quantum Grav, 29(2012).
12. M. Sanchez, Geodesic connectedness of semi–Riemannian manifolds, Nonlinear Anal, 47 (5)(2001), 3085–3102.
13. M. Sanchez, On the geometry of static spacetimes, Nonlinear Anal, 63(2005).
14. H. J. Seifert, Global connectivity by timetike geodesics, Zs. fur Naturforsch. 22a(1967), 1356–1360.
15. M. Vatandoost and Y. Bahrampour, Some necessary and sufficient conditions for admitting a continuous sphere order representation of two-dimensional space-times, J. Math. Phys., 53(2012), 122501.
16. M. Vatandoost, R. Pourkhandani, and N. Ebrahimi, On null and causal pseudoconvex space-times, J. Math. Phys., 60(2019), 012502.
17. M. Vatandoost, R. Pourkhandani, and N. Ebrahimi, Causaly simple spacetimes and Naked Singularities, arXiv:2105.03730v1 [gr-qc] 8 May 2021.
18. F. Treves, lntroduction to Pseudodifferential and Fourier Integral Operatorss, vols. 1 and 2, Plenum, New York and London, 1980.
Vatandoost, M., & Pourkhandani, R. (2022). On pseudoconvexity conditions and static spacetimes. Journal of Finsler Geometry and its Applications, 3(1), 42-48. doi: 10.22098/jfga.2022.10526.1064
MLA
Mehdi Vatandoost; Rahimeh Pourkhandani. "On pseudoconvexity conditions and static spacetimes", Journal of Finsler Geometry and its Applications, 3, 1, 2022, 42-48. doi: 10.22098/jfga.2022.10526.1064
HARVARD
Vatandoost, M., Pourkhandani, R. (2022). 'On pseudoconvexity conditions and static spacetimes', Journal of Finsler Geometry and its Applications, 3(1), pp. 42-48. doi: 10.22098/jfga.2022.10526.1064
VANCOUVER
Vatandoost, M., Pourkhandani, R. On pseudoconvexity conditions and static spacetimes. Journal of Finsler Geometry and its Applications, 2022; 3(1): 42-48. doi: 10.22098/jfga.2022.10526.1064