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Initial Value Problems and Signature Change

L. J. Alty·C. J. Fewster
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Abstract

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 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 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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L. J. Alty, C. J. Fewster. 1995-07-02. Initial Value Problems and Signature Change. https://doi.org/10.1088/0264-9381%2F13%2F5%2F024

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