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Actions for signature change
, 1995
"... 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 (weak signature change) or to vanish (strong signature ch ..."
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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 (weak signature change) or to vanish (strong signature change). Led by a Lagrangian point of view, we write down eight candidate action functionals S1,...S8 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 EinsteinHilbert Lagrangian density g  1/2 R[g]. The other four actions are constructed as sums of integrals over singesignature domains. The result is that both types of junction conditions occur in different models, i.e. are based on different first principles, none of which can be claimed to represent Work supported by the Austrian Academy of Sciences in the framework of the ”Austrian Programme for Advanced Research and Technology”. 0 the ”correct ” one, unless physical predictions are taken into account. From a point of view of naturality dictated by the variational formalism, weak signature change is slightly favoured over strong one, because it requires less à priori restrictions for the class of offshell metrics. In addition, a proposal for the use of the Lagrangian framework in cosmology is made.