On the Topological Connection of Inertial Systems on Space-time Manifolds

Abstract: St. Hawking proved that the conformal diffeomorphisms of the space-time manifold can be represented by autohomeomorphisms of a Zeeman topology [17]. The corresponding physical invariants to this symmetry group are well known [17]. For accelerated reference frames, there are contradictions in measurements of observables, since the locally used Lorentz transformations require inertial frames that are compatible [13]. I use a finer Zeeman topolo y generated by piecewise timelike geodesics representing inertial motions. The corresponding autohomeomorpism group preserves the Nonregularity of this topology . The non-regularity was proven by the Bulgarian topologist Strassimir Popvassilev [12], [9]. We construct the possible relationship for inertial frames by the aid of this proof .