What question did this study set out to answer?

The aim is to introduce the Spacetime Snap-back model to address black hole singularities and dark matter.

April 17, 2026Open Access

Spacetime Snap-back Theory: A Topological Resolution of Black Hole Singularities, Dark Matter, and the Stochastic Gravitational Wave Background

Key Points

The aim is to introduce the Spacetime Snap-back model to address black hole singularities and dark matter.
Developed a modified Einstein-Hilbert action incorporating Gauss-Bonnet coupling.
Derived a topological stress-energy tensor.
Calculated the Geometric Snap-back Index for different black hole geometries.
Identified dark matter abundance linked to topological remnants.
Proposed a solution to the Information Paradox using the Island Formula.
Predicted observational signatures for validation.

Abstract

Update (Version 2.0): This version includes refined mathematical derivations and updated conclusions regarding the spacetime snap-back model. propose the Spacetime Snap-back model, a modified gravity framework in which black hole evaporation terminates via a topological phase transition rather than complete evaporation. Using a modified Einstein-Hilbert action with a differentiable Gauss-Bonnet coupling, we derive the topological stress-energy tensor T00 proportional to 1/M³ and the Geometric Snap-back Index n(a) for Schwarzschild and Kerr geometries. The model predicts: 1. Dark matter abundance from Planck-scale topological remnants 2. Unitary resolution of the Information Paradox via the Island Formula 3. Three falsifiable observational signatures: - GRB spectral cutoff (Fermi-LAT) - Stochastic gravitational wave background (LISA / NANOGrav) - Planck-mass pile-up in microlensing surveys (Roman / LSST)

Spacetime Snap-back Theory: A Topological Resolution of Black Hole Singularities, Dark Matter, and the Stochastic Gravitational Wave Background

Key Points

Abstract

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