Sergio Dain 2004 Class. Quantum Grav. 21 555 doi:10.1088/0264-9381/21/2/017
Sergio Dain
Show affiliationsTrapped 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.
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
83C05 Einstein's equations (general structure, canonical formalism, Cauchy problems)
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
Sergio Dain 2004 Class. Quantum Grav. 21 555
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