Curvature-driven spin transport in rank-two string-Carroll hydrodynamics
Abstract
We derive the rank-two string-Carroll limit of the canonical stress--spin Ward system for probe matter on a fixed torsion-free background. Beyond rank-one Carroll spin hydrodynamics, this retains the coupled Riemann--spin force, a second longitudinal momentum projection, and the longitudinal boost bivector allowed only by a two-dimensional longitudinal kernel. We first extract the term linear in an independent spin amplitude ς and then expand in the near-horizon parameter λ=ε2, avoiding contamination by the omitted 𝒪(ς2) thermodynamic spin feedback. For finite mixed stress and Sλμν=𝒪(ςεp), p=0 is the unique sector in which the induced stress and curvature source balance at the first generic Ward order. On the regular branch of a smooth nonextremal static spherical outer horizon, locally normalized longitudinal and transverse spin amplitudes obey the same dilution law, while the curvature force first appears at 𝒪(ςλ2). For a general barotrope, the stationary system reduces to one thermodynamic quadrature and one local inverse. For the affine constant-sound-speed family p=αℰ+Π, 0≤α<1, we obtain an explicit closed-form parametric solution, leading profiles for both spin channels, and fixed-radius, linear-spin corrections to enthalpy, pressure, and rapidity away from the sonic point. The response is governed by ℛ(L)h=(f2+3f1ψ1)/2 and the longitudinal spin flux. We prove that the stationary closed-sphere Killing flux is invariant under regular pseudo-gauge improvements. In Reissner--Nordström, the response vanishes at the radial-tidal inversion |Q|/M=2√2/3; in the Einstein--Maxwell--dilaton family, its zero is R-/R+=(1+a2)/2 for 0≤ a<1. The Frenkel limit removes this response and the longitudinal boost sector.
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BibTeX
@misc{lobos2026curvaturedriven,
title = {{Curvature-driven spin transport in rank-two string-Carroll hydrodynamics}},
author = {Nikko John Leo Lobos and Reggie Pantig},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01634},
eprint = {2609.01634},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01634},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Curvature-driven spin transport in rank-two string-Carroll hydrodynamics
AU - Nikko John Leo Lobos
AU - Reggie Pantig
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.01634
UR - https://arxiv.org/abs/2609.01634
AB - We derive the rank-two string-Carroll limit of the canonical stress--spin Ward system for probe matter on a fixed torsion-free background. Beyond rank-one Carroll spin hydrodynamics, this retains the coupled Riemann--spin force, a second longitudinal momentum projection, and the longitudinal boost bivector allowed only by a two-dimensional longitudinal kernel. We first extract the term linear in an independent spin amplitude ς and then expand in the near-horizon parameter λ=ε^2, avoiding contamination by the omitted 𝒪(ς^2) thermodynamic spin feedback. For finite mixed stress and S^λμν=𝒪(ςε^p), p=0 is the unique sector in which the induced stress and curvature source balance at the first generic Ward order. On the regular branch of a smooth nonextremal static spherical outer horizon, locally normalized longitudinal and transverse spin amplitudes obey the same dilution law, while the curvature force first appears at 𝒪(ςλ^2). For a general barotrope, the stationary system reduces to one thermodynamic quadrature and one local inverse. For the affine constant-sound-speed family p=αℰ+Π, 0≤α<1, we obtain an explicit closed-form parametric solution, leading profiles for both spin channels, and fixed-radius, linear-spin corrections to enthalpy, pressure, and rapidity away from the sonic point. The response is governed by ℛ^(L)_h=(f_2+3f_1ψ_1)/2 and the longitudinal spin flux. We prove that the stationary closed-sphere Killing flux is invariant under regular pseudo-gauge improvements. In Reissner--Nordström, the response vanishes at the radial-tidal inversion |Q|/M=2√2/3; in the Einstein--Maxwell--dilaton family, its zero is R_-/R_+=(1+a^2)/2 for 0≤ a<1. The Frenkel limit removes this response and the longitudinal boost sector.
ER -