发表机构
University of Santo Tomas; Mapúa University（圣多马大学; 马普阿大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究推导了二阶弦-卡罗尔流体动力学的自旋输运方程，分析了曲率与自旋的耦合效应，得到了定常解及不同引力模型下的响应特征，拓展了卡罗尔流体动力学的理论框架。
AI 中文摘要
我们推导了固定无挠背景下探测物质的正则应力-自旋Ward系统的二阶弦-卡罗尔极限。与一阶卡罗尔自旋流体动力学不同，该极限保留了耦合的黎曼-自旋力、第二个纵向动量投影，以及仅由二维纵向核允许的纵向boost双向量。我们首先提取独立自旋振幅$\varsigma$的线性项，随后在近视界参数$\lambda=\varepsilon^2$下展开，避免被省略的$\mathcal{O}(\varsigma^2)$热力学自旋反馈所干扰。对于有限的混合应力以及$S^{\lambda\mu\nu}=\mathcal{O}(\varsigma\varepsilon^p)$，$p=0$是诱导应力与曲率源在首个通用Ward阶次下达到平衡的唯一扇区。在光滑非极端静态球对称外视界的正则分支上，局域归一化的纵向和横向自旋振幅遵循相同的稀释定律，而曲率力首次出现在$\mathcal{O}(\varsigma\lambda^2)$阶。对于一般正压流体，定常系统可简化为一个热力学积分和一个局域逆运算。对于仿射常声速族$p=\alpha\mathcal E+\Pi$（$0\leq\alpha<1$），我们得到了显式闭合形式的参数解，给出了两个自旋通道的分布轮廓，以及在声点以外对焓、压强和快度的固定半径线性自旋修正。该响应由$\mathcal R^{(L)}_h=(f_2+3f_1\psi_1)/2$和纵向自旋通量主导。我们证明了定常闭球Killing通量在正则伪规范改进下保持不变。在Reissner–Nordström时空中，该响应在径向潮汐反转点$|Q|/M=2\sqrt{2}/3$处消失；在Einstein–Maxwell–伸缩子族中，其零点满足$R_-/R_+=(1+a^2)/2$（$0\leq a<1$）。Frenkel极限会消除该响应以及纵向boost扇区。
英文摘要
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 $\mathcal{O}(ς^2)$ thermodynamic spin feedback. For finite mixed stress and $S^{λμν}=\mathcal{O}(ςε^p)$, $p=0$ 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 $\mathcal{O}(ςλ^2)$. For a general barotrope, the stationary system reduces to one thermodynamic quadrature and one local inverse. For the affine constant-sound-speed family $p=α\mathcal E+Π$, $0\leqα<1$, 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 $\mathcal R^{(L)}_h=(f_2+3f_1ψ_1)/2$ 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 $|Q|/M=2\sqrt{2}/3$; in the Einstein--Maxwell--dilaton family, its zero is $R_-/R_+=(1+a^2)/2$ for $0\leq a<1$. The Frenkel limit removes this response and the longitudinal boost sector.
Comments26 pages
