Lorentzian and signature changing branes

Abstract

General hypersurface layers are considered in order to describe brane-worlds and shell cosmologies. No restriction is placed on the causal character of the hypersurface which may thus have internal changes of signature. Strengthening the results in our previous letter [1], we confirm that a good, regular and consistent description of signature change is achieved in these brane/shells scenarios, while keeping the hypersurface and the bulk completely regular. Our formalism allows for a unified description of the traditional timelike branes/shells together with the signature-changing, or pure null, ones. This allows for a detailed comparison of the results in both situations. An application to the case of hypersurface layers in static bulks is presented, leading to the general Robertson-Walker geometry on the layer --with a possible signature change. Explicit examples on anti de Sitter bulks are then studied. The permitted behaviours in different settings ($Z_2$-mirror branes, asymmetric shells, signature-changing branes) are analysed in detail. We show in particular that (i) in asymmetric shells there is an upper bound for the energy density, and (ii) that the energy density within the brane vanishes when approaching a change of signature. The description of a signature change as a `singularity' seen from within the brane is considered. We also find new relations between the fundamental constants in the brane/shell, its tension, and the cosmological and gravitational constants of the bulk, independently of the existence or not of a change of signature.

23 pages, 2 figures

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• Gravitational double layers
• Signature change from Schutz's canonical quantum cosmology and its classical analogue
• Double layers in gravity theories
• Equations for general shells
• Variational equations on mixed Riemannian-Lorentzian metrics
• Signature transition in Einstein-Cartan cosmology
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• Accelerating expansion and change of signature
• Wormhole Nucleation via Topological Surgery in Lorentzian Geometry
• On the foundations and necessity of classical gauge invariance
• The emergent nature of time and the complex numbers in quantum cosmology