Dynamical Determination of the Metric Signature in Spacetime of Nontrivial Topology

Abstract

The formalism of Greensite for treating the spacetime signature as a dynamical degree of freedom induced by quantum fields is considered for spacetimes with nontrivial topology of the kind ${\mathbf{R}}^{D-1}\times {\mathbf{T}}^1$, for varying $D$. It is shown that a dynamical origin for the Lorentzian signature is possible in the five-dimensional space ${\mathbf{R}}^4\times {\mathbf{T}}^1$ 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, \ie multidimensional and of Lorentzian signature.

10 pages, LaTeX file, 4 figures

References in corpus (1)

• Dynamical Origin of the Lorentzian Signature of Spacetime

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