What question did this study set out to answer?

To investigate the geometric nature of gravity's weakness compared to electromagnetism and resolve the hierarchy problem.

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January 17, 2026Open Access

The Geometric Dilution of Gravity: A Topological Resolution to the Hierarchy Problem via (2,2) Split-Signature Volumetrics

Key Points

To investigate the geometric nature of gravity's weakness compared to electromagnetism and resolve the hierarchy problem.
Modeling the vacuum as a (2, 2) split-signature manifold
Analyzing the global tension of gravity on the causal horizon volume
Comparing this with the local phase space volume of topological defects
Gravity acts as global tension on causal horizon volume
Electromagnetism is confined to local phase space volume
The hierarchy ratio naturally appears as Γ = VH/Vp ∼ 10^40

Abstract

The extreme weakness of gravity relative to electromagnetism (approx. 10−40) constitutes theHierarchy Problem of the Standard Model. We propose that this disparity is not intrinsic butgeometric. By modeling the vacuum as a (2, 2) split-signature manifold, we demonstrate that gravityacts as a global tension on the entire causal horizon volume (VH), while electromagnetism is confinedto the local phase space volume of topological defects (Vp). The hierarchy ratio emerges naturallyfrom the ratio of these characteristic volumes, Γ = VH/Vp ∼ 1040, without requiring fine-tuning orsupersymmetry.

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