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Failure of standard conservation laws at a classical change of signature

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Abstract
  • The divergence theorem as usually stated cannot be applied across a change of signature unless it is reexpressed to allow for a finite source term on the signature change surface. Consequently all conservation laws must also be ‘‘modified,’’ and therefore insistence on conservation of matter across such a surface cannot be physically justified. The Darmois junction conditions normally ensure conservation of matter via Israel’s identities for the jump in the energy-momentum density, but not when the signature changes. Modified identities are derived for this jump when a signature change occurs, and the resulting surface effects in the conservation laws are calculated. In general, physical vector fields experience a jump in at least one component, and a source term may therefore appear in the corresponding conservation law. Thus current is also not conserved. These surface effects are a consequence of the change in the character of physical law. The only way to recover standard conservation laws is to impose restrictions that no realistic cosmological model can satisfy.
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  • Hellaby, C., & Dray, T. (1994). Failure of standard conservation laws at a classical change of signature. Physical Review D, 49(10), 5096-5104.
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  • 49
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  • 10
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  • T.D. was partially funded by NSF Grant No. PHY 92-08494. C.H. would like to thank the FRD for a research grant.
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