Failure of standard conservation laws at a classical change of signature

Charles Hellaby and Tevian Dray
Phys. Rev. D 49, 5096 – Published 15 May 1994
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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.

  • Received 17 November 1993

DOI:https://doi.org/10.1103/PhysRevD.49.5096

©1994 American Physical Society

Authors & Affiliations

Charles Hellaby

  • Department of Applied Mathematics, University of Cape Town, Rondebosch, 7700, South Africa

Tevian Dray

  • Department of Mathematics, Oregon State University, Corvallis, Oregon 97331

Comments & Replies

Reply Comment: Comparison of approaches to classical signature change

Charles Hellaby and Tevian Dray
Phys. Rev. D 52, 7333 (1995)

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Vol. 49, Iss. 10 — 15 May 1994

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