Junction Conditions for Signature Change

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.

13 pages. TeX. Revised to discuss further mistaken papers

References in corpus (2)

• The Geometry of classical change of signature
• Quantum Cosmology

Cited by in corpus (11)

• Signature change events: A challenge for quantum gravity?
• On Singular Semi-Riemannian Manifolds
• Actions for signature change
• Comment on "Failure of standard conservation laws at a classical change of signature"
• Initial Value Problems and Signature Change
• Singular General Relativity
• On metric-connection compatibility and the signature change of space-time
• Signature Changing Space-times and the New Generalised Functions
• Self-adjoint extensions and Signature Change
• Distinguished solutions for discontinuous signature change with weak junction conditions
• Black-hole models in loop quantum gravity