L J Alty and C J Fewster 1996 Class. Quantum Grav. 13 1129 doi:10.1088/0264-9381/13/5/024
Initial-value problems and signature change
L J Alty
and C J Fewster,
We make a rigorous study of classical field equations on a two-dimensional signature-changing spacetime using the techniques of operator theory. Boundary conditions at the surface of signature change are determined by forming self-adjoint extensions of the Schrödinger Hamiltonian. We show that the initial-value problem for the Klein - Gordon equation on this spacetime is ill-posed, in the sense that its solutions are unstable. Furthermore, if the initial data are smooth and compactly supported away from the surface of signature change, the solution has a divergent 
-norm after finite time.
- PACS
-
04.20.Ex Initial value problem, existence and uniqueness of solutions
04.40.-b Self-gravitating systems; continuous media and classical fields in curved spacetime
- MSC
- Subjects
- Dates
-
Issue 5 (May 1996)
Received 20 January 1995, in final form 28 June 1995
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Initial-value problems and signature change
L J Alty and C J Fewster 1996 Class. Quantum Grav. 13 1129
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