Relativity and Cosmology

Extension of Lorentz Spacetime Symmetry to Four Sectors of Flat and Curved Spacetime

Authors: Tomasz Kobierzycki

This work asks what is obtained when the observer-independent light cone isused to organise the complete orientation of a local clock--ruler frame, ratherthan only the ordinary future-timelike part of that orientation. The result isa four-sector description of one spacetime. The sectors are not paralleluniverses and do not provide four independent metrics. They are the foursuccessive orientations met when a local time axis, a spatial axis, theopposite time axis, and the opposite spatial axis are followed around oneextended Lorentz orbit.The same distinction is applied separately to matter and geometry. A particlehas a fixed sector relative to the local geometric frame and undergoes ordinaryLorentz boosts only inside that sector; it is never accelerated through thelight boundary into another particle class. Curved geometry may insteadrequire a neighbouring sector chart when one of its proper scales reaches anull limit. A tensorial scale construction identifies the affected direction,pairs it with the local clock, and replaces the failed extrapolation by thereciprocal scale of the adjacent chart while retaining the samegeneral-relativistic solution.In Schwarzschild, LTB, Kerr, and FLRW geometries this procedure turns theapparent zero of an inactive scale into an infinite proper scale measured fromthe neighbouring sector centre. Curvature regularity is then a result to bechecked with invariant scalars, not an effect assigned to a tetrad rotation.Because every sector is a reading of one geometry and one field history, thesame framework also constrains black--white-hole interpretations, cosmologicaltime reversal, and closed timelike curves. The construction is presented as acoherent classical framework whose remaining dynamical and quantum conditionsare stated explicitly.

Comments: 31 Pages.

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[v1] 2026-07-23 11:31:51

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