
TL;DR
This paper examines the theoretical foundations of signature change in general relativity, comparing different action principles and their implications for junction conditions, with a slight favor towards weak signature change based on variational considerations.
Contribution
It introduces eight candidate action functionals to analyze signature change and investigates which junction conditions they imply, highlighting differences and preferences from a variational perspective.
Findings
Both weak and strong signature change conditions arise from different models.
Weak signature change is slightly favored due to fewer restrictions on off-shell metrics.
The study proposes using the Lagrangian framework in cosmological models.
Abstract
This is a contribution on the controversy about junction conditions for classical signature change. The central issue in this debate is whether the extrinsic curvature on slices near the hypersurface of signature change has to be continuous ({\it weak} signature change) or to vanish ({\it strong} signature change). Led by a Lagrangian point of view, we write down eight candidate action functionals ,\dots as possible generalizations of general relativity and investigate to what extent each of these defines a sensible variational problem, and which junction condition is implied. Four of the actions involve an integration over the total manifold. A particular subtlety arises from the precise definition of the Einstein-Hilbert Lagrangian density . The other four actions are constructed as sums of integrals over singe-signature domains. The result is that {\it…
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