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On scalar curvature in light-like geometry. (English) Zbl 1107.53047

Summary: We introduce the concept of induced scalar curvature of a class \({\mathcal C}[M]\), of light-like hypersurfaces \((M,g,S(TM))\), of a Lorentzian manifold, such that \(M\) admits a canonical screen distribution \(S(TM)\), a canonical light-like transversal vector bundle and an induced symmetric Ricci tensor. We prove that there exists such a class \({\mathcal C}[M]\) of a globally hyperbolic warped product space-time [J. K. Beem, P. E. Ehrlich, and K. L. Easley, Global Lorentzian Geometry, 2nd edition, Marcel Dekker, Inc. New York (1996; Zbl 0846.53001)] of general relativity. In particular, we calculate the scalar curvature of a member of \({\mathcal C}[M]\) in a globally hyperbolic space-time of constant curvature, supported by an example.

MSC:

53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
53C20 Global Riemannian geometry, including pinching
53B50 Applications of local differential geometry to the sciences

Citations:

Zbl 0846.53001
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References:

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