Initial Value Problems and Signature Change

Details Initial Value Problems and Signature Change Initial Value Problems and Signature Change

1995-01-22

arxiv.org/abs/gr-qc/9501026v2

Class.Quant.Grav.13:1129-1148,1996

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

33 pages, LaTeX The introduction has been altered, and new work (relating our previous results to continuous signature change)

Scientific paper

10.1088/0264-9381/13/5/024

We make a rigorous study of classical field equations on a 2-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 Schr\"odinger 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 is smooth and compactly supported away from the surface of signature change, the solution has divergent $L^2$-norm after finite time.

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