An impediment to torsion from spectral geometry

2024/12/27 by Arkadiusz Bochniak, Ludwik Dąbrowski, Bochniak, Arkadiusz +5 · 2 citations
Engineering · #58B34 #58J50 #83C65 #Differential Geometry (math.DG) #Elasticity and Material Modeling #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.2412.19626

openalex publication_date 2024/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Modifications of standard general relativity that bring torsion into a game have a long-standing history. However, no convincing arguments exist for or against its presence in physically acceptable gravity models. In this Letter, we provide an argument based on spectral geometry (using methods of pseudo-differential calculus) that suggests that the torsion shall be excluded from the consideration. We demonstrate that there is no well-defined functional extending to the torsion-full case of the spectral formulation of the Einstein tensor.

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• Spectral torsion of the internal noncommutative geometry of the Standard Model
• On geometric spectral functionals

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