Dynamical determination of the metric signature in spacetime of non-trivial topology

Abstract

The formalism of Greensite for treating the spacetime signature as a dynamical degree of freedom, induced by quantum fields in spacetimes with non-trivial topology of the kind , is considered, for varying D. It is shown that a dynamical origin for the Lorentzian signature is possible in the five-dimensional space with small torus radius (periodic boundary conditions), as well as in four-dimensional space with trivial topology. Hence the possibility exists that the early universe might have been of the Kaluza--Klein type, i.e. multi-dimensional and of Lorentzian signature.