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This research investigates the topological instability in Einstein-Cartan bridges and proposes a new framework for understanding cosmic evolution.

January 18, 2026Open Access

On the Topological Instability of Einstein-Cartan Bridges: From Torsion-Induced Vorticity to Spacetime Surgery and the "Decompression" Big Bang

Key Points

This research investigates the topological instability in Einstein-Cartan bridges and proposes a new framework for understanding cosmic evolution.
Analyzed the Raychaudhuri equation incorporating torsion.
Examined spin-induced torsion and its relation to geometric vorticity.
Developed a numerical proposal for testing the hypothesis via modified Ricci flow.
Demonstrated that torsion-dominated bridges are topologically unstable.
Proposed a new interpretation of the Big Bang as a response to the detachment of a child universe.
Showed conditions for causal disconnection of remnants in the parent universe.

Abstract

This paper proposes a novel cosmogenetic framework that bridges Einstein-Cartan-Sciama-Kibble (ECSK) gravity with Geometric Analysis (Ricci Flow). We challenge the standard "Big Bounce" paradigm, which typically assumes a smooth, continuous evolution of a connected spacetime (forming an eternal Einstein-Rosen bridge). Instead, we demonstrate that the interplay between spin-induced torsion and extreme curvature leads to a topological instability. By analyzing the Raychaudhuri equation with torsion, we show that spin density acts as a source of geometric vorticity (ω2), driving the gravitational collapse toward highly anisotropic, cylindrical "neck" structures rather than isotropic minima. Key contributions of this work: Torsion-Induced Instability: We provide a mechanism showing that torsion-dominated bridges are topologically unstable, analogous to the neck-pinch instability in Ricci flow and vortex tube formation in hydrodynamics. Spacetime Surgery: We hypothesize that the singularity is resolved not by a bounce, but by Perelman-style topological surgery, resulting in the detachment of a child universe (S3). The "Decompression" Big Bang: The Big Bang is reinterpreted as a dynamical response (rapid expansion) of the detached child universe to the sudden removal of external topological constraints ("liberation phase"). Topological Isolation Principle: We define the conditions under which the remnant in the parent universe remains causally disconnected, appearing as a "Frozen Star" or Black Hole protected by asymptotic time dilation and vacuum polarization. Numerical Proposal: We outline an algorithm for numerical verification using modified Ricci flow on a dynamic mesh with a surgery trigger, offering a pathway for computational validation. This model resolves the causal paradoxes of eternal wormholes and offers a concrete physical mechanism for multiverse generation without invoking a primordial singularity.

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