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Junction Conditions for Signature Change

Sean A. Hayward
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Abstract

The change of signature of a metric is explained using simple examples and methods. The Klein-Gordon field on a signature-changing background is discussed, and it is shown how the approach of Dray et al.\ can be corrected to ensure that the Klein-Gordon equation holds. Isotropic cosmologies are discussed, and it is shown how the approach of Ellis et al.\ can be corrected to ensure that the Einstein-Klein-Gordon equations hold. A straightforward calculation shows that a well defined Ricci tensor requires the standard junction condition, namely vanishing of the second fundamental form of the junction surface.

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Sean A. Hayward. 1994-12-12. Junction Conditions for Signature Change. https://arxiv.org/abs/gr-qc/9303034

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