pc-Gravity as a geometric resolution of the black hole information paradox

Abstract

We investigate the black hole information paradox in the setting of pseudo-complex gravity, a covariant geometric extension of generalrelativity that introduces a minimal length scale by deforming the spacetime manifold.In thisframework, curvature invariantsstay finite, and the classicalsingularity is geometrically regularized via a smooth core. We showthat the correction term B/(6r 4 ) altersthe Schwarzschild metric, generating the regularized geometry above, yielding a finite Hawking temperature, and inducing subleading correctionsto the Bekenstein–Hawking entropy. Crucially,we demonstrate that the pseudo-complex geometric structure obstructs a clean factorization of the Hilbertspace into interior and exteriorregions, thereby removing the key assumption behind the standard derivation of the paradox. Thisstructuralreinterpretation of entanglement flowoffers a newgeometric route to unitarity preservation and information recovery. We examine the resulting effects on evaporation dynamics, entropy flow, and thermodynamic behavior. Our predictions are comparedwith those of generalized uncertainty principles(GUP), loop quantum gravity (LQG), and island-based models, and are summarized in a comparative table. Observable signatures—such asshiftsin quasi-normal mode frequencies and the appearance of gravitationalwave echoesfrom the regularized core—suggest that pseudo-complex gravity (pcGravity)is a testable, covariant approach to resolving the paradoxwithout invoking firewalls, holography, or exotic quantum states.