Abstract
A spacetime manifold generated by the pencil of conics defined by two distinct pairs of complex-conjugated lines and a pair of real lines is considered. The manifold, originally endowed with two spatial and two temporal dimensions, is shown to substantially change its properties as we change the affine properties of the pencil. Two kinds of transformation are of particular interest. A dimensionality-preserving process, characterized by the transmutation of a temporal coordinate into a spatial one and leading to familiar (3 + 1)D spacetime, and a dimensionality-reducing scenario, featuring simultaneous ‘annihilation’ of one temporal and one spatial dimension and ending up with a (1 + 1)D spacetime. A striking difference between the nature of temporal and spatial is revealed; whereas we find purely spatial manifolds, those comprising exclusively temporal dimensions do not exist.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
