From Geometric Phantom to Physical Universe — An Enrichment of the Kruskal Diagram

Abstract

Abstract: The Kruskal-Szekeres diagram is a landmark of general relativity, revealing the complete geometric structure of the Schwarzschild spacetime via maximal analytic extension. However, the standard diagram has a fundamental limitation: among its four quadrants, only the upper-right quadrant possesses a genuine physical origin; the remaining three are purely geometric extensions of the vacuum Einstein equations—long-standing “geometric phantoms” devoid of physical entities. This paper draws upon the Physical Information Cosmology (PIC) framework, which generates four causally isolated universes through a two-stage phase transition—energy bifurcation followed by matter-antimatter bifurcation. These four universes correspond one-to-one with the four quadrants of the Kruskal diagram. We thus introduce a threefold enrichment: the coordinate axes are replaced from (spacelike, timelike) to (matter property, energy property); a dynamical mechanism of light-speed recession endows the 45° horizons with physical meaning; and the three “empty” quadrants are filled with physical entities carrying real matter and energy. We term this completed version the Kruskal-PIC diagram. The isomorphism between the two diagrams corresponds precisely to the complete structure of CPT symmetry: the standard Kruskal diagram provides only the geometric skeleton of PT symmetry—the mirror universe (P) and white hole (T) are empty because they lack the physical realization of C (charge conjugation). The PIC diagram supplies both C and energy sign reversal (the physical realization of T), giving every operation of CPT symmetry its corresponding physical content. Keywords: Kruskal-Szekeres coordinates; Schwarzschild spacetime; Physical Information Cosmology (PIC); causal structure; event horizon; CPT symmetry; Kruskal-PIC diagram