The Shear Threshold at the Aldred Limit: How Much Anisotropy a Spin-Torsion Bounce Can Survive

In a homogeneous but anisotropic collapse of Bianchi I type, shear acts as an additional positive energy density and competes with the negative spin-torsion term that produces the Aldred Limit bounce. This paper computes the largest shear the bounce can survive. Writing the shear as an equivalent mass density rho_sigma = sigma squared divided by (16 pi G c squared), the turnaround requires rho_sigma to stay below the maximum of rho(1 - rho/rho_A), which is rho_A/4. For neutron matter at the headline bound rho_A = 9.72e+54 g per cubic centimetre, the critical shear is sigma = 8.559e+32 per second. Set against the Planck-scale shear of 3.942e+52 per second obtained from the same formula at the Planck density, the bounce occupies only a fraction 2.171e-20 of the available shear range in amplitude, or 4.713e-40 in shear energy density. Across the published prescription band the critical shear runs from 4.279e+32 to 8.559e+32 per second. The result is a sharp, checkable statement: any simulation that claims a spin-torsion turnaround must keep its shear below the computed threshold near the turnaround density. All results are computed from stated assumptions, not measured.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-11
DOI
https://doi.org/10.5281/zenodo.24123525
Primary Topic
Cosmology and Gravitation Theories
Type
article
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article

The Shear Threshold at the Aldred Limit: How Much Anisotropy a Spin-Torsion Bounce Can Survive

William Alexander Aldred
Zenodo (CERN European Organization for Nuclear Research)
Cosmology and Gravitation Theories
article

The Shear Threshold at the Aldred Limit: How Much Anisotropy a Spin-Torsion Bounce Can Survive

William Alexander Aldred
article en

Abstract

In a homogeneous but anisotropic collapse of Bianchi I type, shear acts as an additional positive energy density and competes with the negative spin-torsion term that produces the Aldred Limit bounce. This paper computes the largest shear the bounce can survive. Writing the shear as an equivalent mass density rho_sigma = sigma squared divided by (16 pi G c squared), the turnaround requires rho_sigma to stay below the maximum of rho(1 - rho/rho_A), which is rho_A/4. For neutron matter at the headline bound rho_A = 9.72e+54 g per cubic centimetre, the critical shear is sigma = 8.559e+32 per second. Set against the Planck-scale shear of 3.942e+52 per second obtained from the same formula at the Planck density, the bounce occupies only a fraction 2.171e-20 of the available shear range in amplitude, or 4.713e-40 in shear energy density. Across the published prescription band the critical shear runs from 4.279e+32 to 8.559e+32 per second. The result is a sharp, checkable statement: any simulation that claims a spin-torsion turnaround must keep its shear below the computed threshold near the turnaround density. All results are computed from stated assumptions, not measured.

Zenodo (CERN European Organization for Nuclear Research)
Cosmology and Gravitation Theories
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