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Trapped surfaces as boundaries for the constraint equations

Sergio Dain

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Trapped surfaces are studied as inner boundary for the Einstein vacuum constraint equations. The trapped surface condition can be written as a nonlinear boundary condition for these equations. Under appropriate assumptions, we prove the existence and uniqueness of solutions in the exterior region for this boundary value problem. We also discuss the relevance of this result for the study of black-hole collisions.


PACS

04.20.Ex Initial value problem, existence and uniqueness of solutions

04.70.Bw Classical black holes

02.40.-k Geometry, differential geometry, and topology

02.60.Lj Ordinary and partial differential equations; boundary value problems

MSC

83C05 Einstein's equations (general structure, canonical formalism, Cauchy problems)

83C75 Space-time singularities, cosmic censorship, etc.

83C57 Black holes

Subjects

Mathematical physics

Computational physics

Gravitation and cosmology

Dates

Issue 2 (21 January 2004)

Received 5 August 2003

Published 10 December 2003


A Corrigendum for this article has been published in 2005 Class. Quantum Grav. 22 769


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