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Boundary conditions for the scalar field in the presence of signature change. (English) Zbl 0842.53068

This paper is part of a controversy about the “correct” junction conditions at a hypersurface of signature change. The purpose of the paper is to refute an attack by S. H. Hayward [Classical Quantum Gravity 11, No. 6, L87–L90 (1994; Zbl 0812.53077)] who claims that for uniqueness of solutions one has to impose strong junction conditions. Hayward also claims that two papers of the authors [Gen. Relativ. Gravitation 23, No. 8, 967-971 (1991; Zbl 0728.53067)] and [Phys. Rev. D, III. Ser. 48, No. 6, 2587-2590 (1993)] are inconsistent. This claim of inconsistency is too strong, I find. Dray et al. arrive at a consistent theory at the price of imposing quite unnatural junction conditions which are intermediate between the “weak” and the “strong” junction conditions. The present paper seeks to clarify that their approach is indeed consistent. As far as I can see, the authors do not report on any new research.
Reviewer: M.Kriele (Berlin)

MSC:

53Z05 Applications of differential geometry to physics
83C75 Space-time singularities, cosmic censorship, etc.
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
83C50 Electromagnetic fields in general relativity and gravitational theory
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