Dynamical Determination of the Metric Signature in Spacetime of Nontrivial Topology

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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 Rᵈ⁻¹ × T¹, for varying D. It is shown that a dynamical origin for the Lorentzian signature is possible in the five-dimensional space R⁴ × T¹ 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, multidimensional and of Lorentzian signature.