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- W1986125169 abstract "Classical general relativity takes place on a manifold with a metric of fixed, Lorentzian, signature. However, attempts to amalgamate general relativity with quantum theory frequently involve manifolds with metrics whose signatures are Lorentzian in some regions and Euclidean in others. (Indeed even more exotic possibilities are discussed frequently.) Most theoretical calculations rely on analyticity arguments to continue variables from the Euclidean to the Lorentzian regime and vice versa. This paper examines models of signature change. It looks at a single second-order quasi-linear partial differential equation on a fixed background, whose principal part is elliptic in one regime and hyperbolic in another, i.e. a mixed problem. It introduces some examples, explains heuristically the concept of a well-posed problem and then discusses the issues involved in constructing a robust numerical algorithm to solve well-posed problems. The paper includes a worked example illustrating the proposed techniques, and a discussion of the role of the potential curvature singularity on the transition hypersurface." @default.
- W1986125169 created "2016-06-24" @default.
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- W1986125169 date "2001-11-22" @default.
- W1986125169 modified "2023-09-25" @default.
- W1986125169 title "Signature change, mixed problems and numerical relativity" @default.
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- W1986125169 doi "https://doi.org/10.1088/0264-9381/18/23/301" @default.
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