Causality in noncommutative two-sheeted space-times

Nicolas Franco, Michał Eckstein

Research output: Contribution to journalArticlepeer-review


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 detail 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.

Original languageEnglish
Pages (from-to)42-58
Number of pages17
JournalJournal of Geometry and Physics
Early online date6 Jun 2015
Publication statusPublished - 1 Oct 2015
Externally publishedYes


  • Causal structures
  • Lorentzian spectral triples
  • Noncommutative geometry


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