A reformulation of the Barrabes-Israel null-shell formalism

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dc.creatorPoisson, Eric
dc.date2002-07-25
dc.date.accessioned2026-07-07T03:27:02Z
dc.date.available2026-07-07T03:27:02Z
dc.descriptionWe consider a situation in which two metrics are joined at a null hypersurface. It often occurs that the union of the two metrics gives rise to a Ricci tensor that contains a term proportional to a Dirac delta-function supported on the hypersurface. This singularity is associated with a thin distribution of matter on the hypersurface, and following Barrabes and Israel, we seek to determine its stress-energy tensor in terms of the geometric properties of the null hypersurface. While our treatment here does not deviate strongly from their previous work, it offers a simplification of the computational operations involved in a typical application of the formalism, and it gives rise to a stress-energy tensor that possesses a more recognizable phenomenology. Our reformulation of the null-shell formalism makes systematic use of the null generators of the singular hypersurface, which define a preferred flow to which the flow of matter can be compared. This construction provides the stress-energy tensor with a simple characterization in terms of a mass density, a mass current, and an isotropic pressure. Our reformulation also involves a family of freely-moving observers that intersect the surface layer and perform measurements on it. This construction gives operational meaning to the stress-energy tensor by fixing the argument of the delta-function to be proper time as measured by these observers.
dc.description12 pages, revtex4
dc.identifierhttps://arxiv.org/abs/gr-qc/0207101
dc.identifierhttp://arxiv.org/abs/gr-qc/0207101
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/34279
dc.subjectGeneral Relativity and Quantum Cosmology
dc.titleA reformulation of the Barrabes-Israel null-shell formalism
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