Pseudo-Complex Gravity as a Geometric Resolution of the Black Hole Information Paradox

TL;DR

This paper proposes pseudo-complex gravity as a geometric extension of general relativity that regularizes black hole singularities, modifies Hawking radiation, and offers a new geometric perspective on the black hole information paradox, potentially testable via gravitational wave signatures.

Contribution

It introduces pseudo-complex gravity, a covariant geometric framework that regularizes black hole singularities and redefines entanglement structure, providing a novel resolution to the information paradox.

Findings

Regularized black hole geometry with finite curvature invariants

Modified Hawking temperature and entropy corrections

Potential observable signatures like gravitational wave echoes

Abstract

We investigate the black hole information paradox in the setting of pseudo-complex gravity, a covariant geometric extension of general relativity that introduces a minimal length scale by deforming the spacetime manifold. In this framework, curvature invariants stay finite, and the classical singularity is geometrically regularized via a smooth core. We show that the correction term B/(6r**4) alters the Schwarzschild metric, generating the regularized geometry above, yielding a finite Hawking temperature, and inducing subleading corrections to the Bekenstein-Hawking entropy. Crucially, we demonstrate that the pseudo-complex geometric structure obstructs a clean factorization of the Hilbert space into interior and exterior regions, thereby removing the key assumption behind the standard derivation of the paradox. This structural reinterpretation of entanglement flow offers a new geometric route to unitarity preservation and information recovery. We examine the resulting effects on evaporation dynamics, entropy flow, and thermodynamic behavior. Our predictions are compared with those of generalized uncertainty principles (GUP), loop quantum gravity (LQG), and island-based models, and are summarized in a comparative table. Observable signatures-such as shifts in quasi-normal mode frequencies and the appearance of gravitational wave echoes from the regularized core-suggest that pseudo-complex gravity is a testable, covariant approach to resolving the paradox without invoking firewalls, holography, or exotic quantum states.