cristovao correia da silva and ruth m. williams- wormholes in simplicial minisuperspace

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a r X i v : g r q c / 0 0 0 4 0 3 5 v 1 1 2 A p r 2 0 0 0 Wormholes in Simplicial Minisuperspace Crist´ ov˜ ao Correia da Silva 1 and Ruth M. Williams 2 DAMTP, Silver Street, Cambridge, CB3 9EW, England ABSTRACT We consi der a simpl icial minisupers pace modelling wor mhole configur ations. Suc h configurations result from a cut and paste procedure on two identical copies of the most relevant triangulation of our universe, namely the cone over α 4 , which is the simplest triangulation of S 3 . The connecting space where the two copies are glued, acts as the throat of a wormhole connecting tw o distinct universes. We sho w that the mo del contains both Euclidean and Lorentzian classical configurations, although the Euclidean configurations are restricted to ve ry sma ll size, while the Lore nt zia n ones exist for all size s. By computing the steepest descents contours associated with the different kind of configurations, and studying the be- haviour of the Euclidean action along these contours we are able to conclude that except for a very small range of boundary data, the semiclassical approximation is always valid, which facilitates both the computation and interpretation of the wavefunctions associated to those steepest descents contours. Having computed these semiclassical wavefunctions we could observe that in the case of the microscopic Euclidean wormhole configurations there is a stron g pred icti on of a finite throat, which seems to indicate that such configurat ions are very lik ely. For large universe there are only Lorentzian configurations. Some of them have fully complex Euclidean action and the exp(−ReI ) acts as the weighting of the Lorentzian 1 e-mail address : [email protected].ac.uk 2 e-mail address : rmw7@damtp.cam.ac.uk

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Page 1: Cristovao Correia da Silva and Ruth M. Williams- Wormholes in Simplicial Minisuperspace

8/3/2019 Cristovao Correia da Silva and Ruth M. Williams- Wormholes in Simplicial Minisuperspace

http://slidepdf.com/reader/full/cristovao-correia-da-silva-and-ruth-m-williams-wormholes-in-simplicial-minisuperspace 1/48

http://arxiv.org/abs/gr-qc/0004035v1

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http://arxiv.org/abs/gr-qc/0002084

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