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Geometric boundary data for the gravitational field
KTH, School of Computer Science and Communication (CSC).
2014 (English)In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 31, no 6, 065004- p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2014. Vol. 31, no 6, 065004- p.
Keyword [en]
Einstein's equations, boundary conditions, gravitational field
National Category
Other Physics Topics
URN: urn:nbn:se:kth:diva-144115DOI: 10.1088/0264-9381/31/6/065004ISI: 000332207100006ScopusID: 2-s2.0-84894664775OAI: diva2:712185

QC 20140414

Available from: 2014-04-14 Created: 2014-04-10 Last updated: 2014-04-14Bibliographically approved

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Kreiss, Heinz-Otto
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