Initial Value Problems and Signature Change

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.

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

References in corpus (1)

• Self-adjoint extensions and Signature Change

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