The Patchwork Divergence Theorem

Abstract

The divergence theorem in its usual form applies only to suitably smooth vector fields. For vector fields which are merely piecewise smooth, as is natural at a boundary between regions with different physical properties, one must patch together the divergence theorem applied separately in each region. We give an elegant derivation of the resulting "patchwork divergence theorem" which is independent of the metric signature in either region, and which is thus valid if the signature changes. (PACS numbers 4.20.Cv, 04.20.Me, 11.30.-j, 02.40.Hw)

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References in corpus (4)

• The Scalar Field Equation in the Presence of Signature Change
• Failure of Standard Conservation Laws at a Classical Change of Signature
• The Geometry of classical change of signature
• Tensor Distributions in the Presence of Degenerate Metrics

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