Geometric boundary data for the gravitational field

Kreiss, Heinz-Otto (author): KTH,Skolan för datavetenskap och kommunikation (CSC)

Winicour, J. (author)

(creator_code:org_t)

2014-02-24
2014
English.
In: Classical and quantum gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 31:6, s. 065004-

Related links:: http://arxiv.org/pdf...; show more...; https://urn.kb.se/re...; https://doi.org/10.1...; show less...

Abstract Subject headings

An outstanding issue in the treatment of boundaries in general relativity is the lack of a local geometric interpretation of the necessary boundary data. For the Cauchy problem, the initial data is supplied by the 3-metric and extrinsic curvature of the initialCauchy hypersurface, subject to constraints. This Cauchy data determine a solution to Einstein's equations which is unique up to a diffeomorphism. Here, we show how three pieces of unconstrained boundary data, which are associated locally with the geometry of the boundary, likewise determine a solution of the initial-boundary value problem which is unique, up to a diffeomorphism. Two pieces of this data constitute a conformal class of rank-2 metrics, which represent the two gravitational degrees of freedom. The third piece, constructed from the extrinsic curvature of the boundary, determines the dynamical evolution of the boundary.

About the subject

NATURAL SCIENCES: NATURAL SCIENCES; and Physical Science ...; and Other Physics To ...

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