Reply Comment: Comparison of Approaches to Classical Signature Change

Abstract

We contrast the two approaches to ``classical" signature change used by Hayward with the one used by us (Hellaby and Dray). There is (as yet) no rigorous derivation of appropriate distributional field equations. Hayward's distributional approach is based on a postulated modified form of the field equations. We make an alternative postulate. We point out an important difference between two possible philosophies of signature change --- ours is strictly classical, while Hayward's Lagrangian approach adopts what amounts to an imaginary proper ``time" on one side of the signature change, as is explicitly done in quantum cosmology. We also explain why we chose to use the Darmois-Israel type junction conditions, rather than the Lichnerowicz type junction conditions favoured by Hayward. We show that the difference in results is entirely explained by the difference in philosophy (imaginary versus real Euclidean ``time"), and not by the difference in approach to junction conditions (Lichnerowicz with specific coordinates versus Darmois with general coordinates).

10 pages, latex, no figures. Replying to - "Comment on `Failure of Standard Conservation Laws at a Classical Change of Signature'", S.A. Hayward, Phys. Rev. D52, 7331-7332 (1995) (gr-qc/9606045)

References in corpus (9)

• The Scalar Field Equation in the Presence of Signature Change
• Failure of Standard Conservation Laws at a Classical Change of Signature
• Dynamical Origin of the Lorentzian Signature of Spacetime
• Hamiltonian quantization of General Relativity with the change of signature
• On Cosmological Isotropy, Quantum Cosmology and the Weyl Curvature Hypothesis
• The Geometry of classical change of signature
• Comment on "Failure of standard conservation laws at a classical change of signature"
• Dynamical Determination of the Metric Signature in Spacetime of Nontrivial Topology
• The Patchwork Divergence Theorem

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• Signature change events: A challenge for quantum gravity?
• Einstein's Equations in the Presence of Signature Change
• Metrics with distributional curvature
• Revisiting the Darmois and Lichnerowicz junction conditions
• Variational equations on mixed Riemannian-Lorentzian metrics
• Note on Signature Change and Colombeau Theory
• Comment on `Smooth and Discontinuous Signature Type Change in General Relativity'
• Casimir effect in a two dimensional signature changing spacetime
• Isochronous Spacetimes
• Casimir effect for a spherical shell in de Sitter spacetime with signature change
• Casimir stress on parallel plates in de Sitter space with signature change
• Diffeomorphism algebra of two dimensional free massless scalar field with signature change
• Isochronous solutions of Einstein's equations and their Newtonian limit
• Casimir effect for concentric spheres in de Sitter spacetime with signature change
• Geodesic family of spherical instantons and cosmic quantum creation