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Causality in noncommutative two-sheeted space-times

By Nicolas Franco and Michał Eckstein

Abstract

We investigate the causal structure of two-sheeted space-times using the tools of Lorentzian spectral triples. We show that the noncommutative geometry of these spaces allows for causal relations between the two sheets. The computation is given in details when the sheet is a 2- or 4-dimensional globally hyperbolic spin manifold. The conclusions are then generalised to a point-dependent distance between the two sheets resulting from the fluctuations of the Dirac operator.Comment: 26 pages, 2 figure

Topics: Mathematical Physics, General Relativity and Quantum Cosmology, 58B34, 53C50, 54F05
Publisher: 'Elsevier BV'
Year: 2015
DOI identifier: 10.1016/j.geomphys.2015.05.008
OAI identifier: oai:arXiv.org:1502.04683

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