Einstein's Equations in the Presence of Signature Change

Abstract

We discuss Einstein's field equations in the presence of signature change using variational methods, obtaining a generalization of the Lanczos equation relating the distributional term in the stress tensor to the discontinuity of the extrinsic curvature. In particular, there is no distributional term in the stress tensor, and hence no surface layer, precisely when the extrinsic curvature is continuous, in agreement with the standard result for constant signature.

REVTeX, 8 pages; to appear in JMP

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Cited by in corpus (20)

• Avoiding singularities in Lorentzian-Euclidean black holes: the role of atemporality
• Gravity and Signature Change
• Signature change events: A challenge for quantum gravity?
• On Singular Semi-Riemannian Manifolds
• Metrics with distributional curvature
• Tensor Distributions in the Presence of Degenerate Metrics
• General solutions of Einstein's spherically symmetric gravitational equations with junction conditions
• Note on Signature Change and Colombeau Theory
• Comment on `Smooth and Discontinuous Signature Type Change in General Relativity'
• Tensor distributions on signature-changing space-times
• Riemann-Cartan gravity with dynamical signature
• Singular General Relativity
• Emergent spacetimes
• Piecewise Conserved Quantities
• On metric-connection compatibility and the signature change of space-time
• Alternative route towards the change of metric signature
• Isochronous Spacetimes
• Singularity at the demise of a black hole
• Isochronous solutions of Einstein's equations and their Newtonian limit
• The emergent Big Bang scenario