Foliations of lightlike hypersurfaces and their physical interpretation

• Autorzy: Krishan Duggal
• Języki publikacji: EN

Abstrakty

EN

This paper deals with a family of lightlike (null) hypersurfaces (H u) of a Lorentzian manifold M such that each null normal vector ℓ of H u is not entirely in H u, but, is defined in some open subset of M around H u. Although the family (H u) is not unique, we show, subject to some reasonable condition(s), that the involved induced objects are independent of the choice of (H u) once evaluated at u = constant. We use (n+1)-splitting Lorentzian manifold to obtain a normalization of ℓ and a well-defined projector onto H, needed for Gauss, Weingarten, Gauss-Codazzi equations and calculate induced metrics on proper totally umbilical and totally geodesic H u. Finally, we establish a link between the geometry and physics of lightlike hypersurfaces and a variety of black hole horizons.

Słowa kluczowe

EN

Lightlike hypersurface; Totally umbilical hypersurface; Spacetime manifold; Isolated horizons; Black hole

Kategorie tematyczne

• 53B30: Lorentz metrics, indefinite metrics
• 83C57: Black holes
• 53C80: Applications to physics
• 53C50: Lorentz manifolds, manifolds with indefinite metrics

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2012
• Tom: 10
• Numer: 5
• Strony: 1789-1800

Daty

wydano

2012-10-01

online

2012-07-24

Twórcy

autor

Krishan Duggal

• University of Windsor

Bibliografia

• [1] Akivis M.A., Goldberg V.V., On some methods of construction of invariant normalizations of lightlike hypersurfaces, Differential Geom. Appl., 2000, 12(2), 121–143 http://dx.doi.org/10.1016/S0926-2245(00)00008-5
• [2] Arnowitt R., Deser S., Misner C.W., The dynamics of general relativity, In: Gravitation, Wiley, New York, 1962, 227–265
• [3] Ashtekar A., Beetle C., Fairhurst S., Isolated horizons: a generalization of black hole mechanics, Classical Quantum Gravity, 1999, 16(2), L1–L7 http://dx.doi.org/10.1088/0264-9381/16/2/027
• [4] Ashtekar A., Galloway G.J., Some uniqueness results for dynamical horizons, Adv. Theor. Math. Phys., 2005, 9(1), 1–30
• [5] Ashtekar A., Krishnan B., Dynamical horizons and their properties, Phys. Rev. D, 2003, 68(10), #104030 http://dx.doi.org/10.1103/PhysRevD.68.104030
• [6] Beem J.K., Ehrlich P.E., Global Lorentzian Geometry, Monogr. Textbooks Pure Appl. Math., 67, Marcel Dekker, New York, 1981
• [7] Bejancu A., Duggal K.L., Degenerated hypersurfaces of semi-Riemannian manifolds, Bul. Inst. Politehn. Iaşi Secţ. I, 1991, 37(41)(1–4), 13–22
• [8] Carter B., Extended tensorial curvature analysis for embeddings and foliations, In: Geometry and Nature, Madeira, July 30–August 5, 1995, Contemp. Math., 203, American Mathematical Society, Providence, 1997, 207–219
• [9] Damour T., Black-hole eddy currents, Phys. Rev. D, 1978, 18(10), 3598–3604 http://dx.doi.org/10.1103/PhysRevD.18.3598
• [10] Duggal K.L., Bejancu A., Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, Math. Appl., 364, Kluwer Academic, Dordrecht, 1996
• [11] Duggal K.L., Jin D.H., Null Curves and Hypersurfaces of Semi-Riemannian Manifolds, World Scientific, Hackensack, 2007 http://dx.doi.org/10.1142/6449
• [12] Galloway G.J., Maximum principles for null hypersurfaces and null splitting theorem, Ann. Henri Poincaré, 2000, 1(3), 543–567 http://dx.doi.org/10.1007/s000230050006
• [13] Gourgoulhon E., Jaramillo J.L., A 3 + 1-perspective on null hypersurfaces and isolated horizons, Phys. Rep., 2006, 423(4–5), 159–294 http://dx.doi.org/10.1016/j.physrep.2005.10.005
• [14] Hawking S.W., Ellis G.F.R., The Large Scale Structure of Space-Time, Cambridge Monogr. Math. Phys., 1, Cambridge University Press, London-New York, 1973
• [15] Kossowski M., The intrinsic conformal structure and Gauss map of a light-like hypersurface in Minkowski space, Trans. Amer. Math. Soc., 1989, 316(1), 369–383 http://dx.doi.org/10.1090/S0002-9947-1989-0938920-1
• [16] Krishnan B., Fundamental properties and applications of quasi-local black hole horizons, Classical Quantum Gravity, 2008, 25(11), #114005 http://dx.doi.org/10.1088/0264-9381/25/11/114005
• [17] Kupeli D.N., Singular Semi-Riemannian Geometry, Math. Appl., 366, Kluwer, Dordrecht, 1996
• [18] Lewandowski J., Spacetimes admitting isolated horizons, Classical Quantum Gravity, 2000, 17(4), L53–L59 http://dx.doi.org/10.1088/0264-9381/17/4/101
• [19] Swift S.T., Null limit of the Maxwell-Sen-Witten equation, Classical Quantum Gravity, 1992, 9(7), 1829–1838 http://dx.doi.org/10.1088/0264-9381/9/7/014

Identyfikatory

DOI

10.2478/s11533-012-0067-x