Initial Value Problems and Signature Change
Abstract
Description
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
33 pages, LaTeX The introduction has been altered, and new work (relating our previous results to continuous signature change) has been included