Detecting ill posed boundary conditions in general relativity

Journal of Mathematical Physics

Volumn 44, Issue 9, 2003, Pages 3888-3899

  Calabrese, Gioel ^a   Sarbach, Olivier ^a  

^a LOUISIANA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0242473132     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1599056     Document Type: Article

References (29)

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25. When discussing initial-boundary value problems one sometimes demands a slightly stronger estimate that also bounds the norm of the solution at the boundary surface. For the purpose of the present article, it is sufficient to consider the weaker estimate (4) since we will show that when the determinant condition is violated, the inequality (4) cannot hold for all initial data.
26. 18 that requires that | detL_ | must be bounded away from zero. The reason why here we do not require the uniform Kreiss condition is that it might be too strong for the case of CPBCs in general relativity. As we will see in Sec. IV the well posed CPBCs that were derived in Ref. 7 do not satisfy the uniform Kreiss condition.
27. (∓)/√2
28. xA.
29. Ikij= 0. For definiteness, we take the choice that leads to the same boundary conditions as in Ref. 7.