On lightlike hypersurfaces and lightlike focal sets of null Cartan curves in Lorentz-Minkowski spacetime
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Authors
Xinran Liu
- School of Mathematical Sciences, Harbin Normal University, Harbin 150500, P. R. China.
Zhigang Wang
- School of Mathematical Sciences, Harbin Normal University, Harbin 150500, P. R. China.
- College of Mathematics, Jilin University, Changchun, 130012, P. R. China.
Abstract
In this paper, as a type of event horizons in astrophysics, a class of lightlike hypersurfaces that is generated by
null curves will be investigated and discussed. Based on discussions of the properties of the local differential
geometry of null curves and singularity theory, we provide classifications of the singularities of lightlike
hypersurfaces and lightlike focal sets. In addition, we reveal the facts that the types of these singularities
and the order of contact between a null Cartan curve and a pseudosphere are related closely to null Cartan
curvatures. Finally, examples of lightlike hypersurfaces and lightlike focal set are used to demonstrate our
theoretical results.
Share and Cite
ISRP Style
Xinran Liu, Zhigang Wang, On lightlike hypersurfaces and lightlike focal sets of null Cartan curves in Lorentz-Minkowski spacetime, Journal of Nonlinear Sciences and Applications, 8 (2015), no. 5, 628--639
AMA Style
Liu Xinran, Wang Zhigang, On lightlike hypersurfaces and lightlike focal sets of null Cartan curves in Lorentz-Minkowski spacetime. J. Nonlinear Sci. Appl. (2015); 8(5):628--639
Chicago/Turabian Style
Liu, Xinran, Wang, Zhigang. "On lightlike hypersurfaces and lightlike focal sets of null Cartan curves in Lorentz-Minkowski spacetime." Journal of Nonlinear Sciences and Applications, 8, no. 5 (2015): 628--639
Keywords
- null Cartan curve
- lightlike hypersurface
- singularity
MSC
References
-
[1]
J. M. Bardeen, B. Carter, S. W. Hawking, The four laws of black hole mechanics, Comm. Math. Phys., 31 (1973), 161-170.
-
[2]
J. W. Bruce, P. J. Giblin, Curves and Singularities, Cambridge University Press, Cambridge (1992)
-
[3]
A. C. CÖken, Ü. CiftCi, On the Cartan curvatures of a null curve in Minkowski spacetime, Geom. Dedicata, 114 (2005), 71-78.
-
[4]
G. Clement , Black holes with a null Killing vector in three-dimensional massive gravity, Class. Quantum Grav., 2009 (2009), 11pages.
-
[5]
M. M. de Souza, The Lorentz-Dirac equation and the structures of spacetime, Braz. J. Phys., 28 (1998), 250-256.
-
[6]
K. L. Duggal, A. Bejancu, Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, Dordrecht, The Netherlands (1996)
-
[7]
K. L. Duggal, Constant curvature and warped product globally null manifolds, J. Geom. Phy. , 43 (2002), 327-340.
-
[8]
K. L. Duggal, On scalar curvature in lightlike geometry, J. Geom. Phy., 57 (2007), 473-481.
-
[9]
K. L. Duggal, A Report on canonical null curves and screen distributions for lightlike geometry, Acta Appl. Math., 95 (2007), 135-149.
-
[10]
E. Gourgoulhon, J. L. Jaramillo, A 3 + 1 perspective on null hypersurfaces and isolated horizons, Phys. Rep., 423 (2006), 159-294.
-
[11]
S. W. Hawking, Black holes in general relativity, Comm. Math. Phys., 25 (1972), 152-166.
-
[12]
S. Izumiya, T. Sato, Lightlike hypersurfaces along spacelike submanifolds in Minkowski space-time, J. Geom. Phys., 71 (2013), 30-52.
-
[13]
M. Korzynski, J. Lewandowski, T. Pawlowski, Mechanics of multidimensional isolated horizons, Class. Quantum Grav., 22 (2005), 2001-2016.
-
[14]
A. Nersessian, E. Ramos, Massive spinning particles and the geometry of null curves, Phys. Lett. B, 445 (1998), 123-128.
-
[15]
A. Nersessian, E. Ramos, A geometrical particle model for anyons, Modern Phys. Lett. A, 14 (1999), 2033-2037.
-
[16]
W. Rudnicki , Black hole interiors cannot be totally vicious , Phys. Lett. A, 208 (1995), 53-58.
-
[17]
W. Rudnicki, R. J. Budzynski, W. Kondracki, Generalized strong curvature singularities and weak cosmic censorship in cosmological space-times, Mod. Phys. Lett. A., 21 (2006), 1501-1509.
-
[18]
J. Sultana, C. C. Dyer, Cosmological black holes: A black hole in the Einstein-de Sitter universe, Gen. Relativ. Gravit., 37 (2005), 1349-1370.
-
[19]
J. Sun, D. Pei, Null Cartan Bertrand curves of AW(k)-type in Minkowski 4-space, Phys. Lett. A, 376 (2012), 2230-2233.
-
[20]
J. Sun, D. Pei, Some new properties of null curves on 3-null cone and unit semi-Euclidean 3-spheres, J. Nonlinear Sci. Appl., 8 (2015), 275-284.
-
[21]
S. I. Tertychniy , The black hole formed by electromagnetic radiation, Phys. Lett. A, 96 (1983), 73-75.
-
[22]
M. Vincent, I. James, Symmetries of cosmological Cauchy horizons, Comm. Math. Phys., 89 (1983), 387-413.
-
[23]
Z. Wang, D. Pei , Singularities of ruled null surfaces of the principal normal indicatrix to a null Cartan curve in de Sitter 3-space, Phys. Lett. B, 689 (2010), 101-106.
-
[24]
Z. Wang, D. Pei, Geometry of 1-lightlike submanifolds in anti de Sitter n-space, Proc. Roy. Soc. Edinburgh Sect. A, 143 (2013), 1089-1113
-
[25]
Z. Wang, D. Pei, L. Kong, Gaussian surfaces and nullcone dual surfaces of null curves in a three-dimensional nullcone with index 2, J. Geom. Phys., 73 (2013), 166-186.