Foliations of lightlike hypersurfaces and their physical interpretation

Krishan Duggal

Open Mathematics (2012)

  • Volume: 10, Issue: 5, page 1789-1800
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Krishan Duggal. "Foliations of lightlike hypersurfaces and their physical interpretation." Open Mathematics 10.5 (2012): 1789-1800. <http://eudml.org/doc/268944>.

@article{KrishanDuggal2012,
abstract = {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.},
author = {Krishan Duggal},
journal = {Open Mathematics},
keywords = {Lightlike hypersurface; Totally umbilical hypersurface; Spacetime manifold; Isolated horizons; Black hole; light-like hypersurface; totally umbilical hypersurface; space-time manifold; isolated horizons; black hole},
language = {eng},
number = {5},
pages = {1789-1800},
title = {Foliations of lightlike hypersurfaces and their physical interpretation},
url = {http://eudml.org/doc/268944},
volume = {10},
year = {2012},
}

TY - JOUR
AU - Krishan Duggal
TI - Foliations of lightlike hypersurfaces and their physical interpretation
JO - Open Mathematics
PY - 2012
VL - 10
IS - 5
SP - 1789
EP - 1800
AB - 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.
LA - eng
KW - Lightlike hypersurface; Totally umbilical hypersurface; Spacetime manifold; Isolated horizons; Black hole; light-like hypersurface; totally umbilical hypersurface; space-time manifold; isolated horizons; black hole
UR - http://eudml.org/doc/268944
ER -

References

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