发表机构
School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS; National Astronomical Observatories, Chinese Academy of Sciences; CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences; Taiji Laboratory for Gravitational Wave Universe(Beijing/Hangzhou), University of Chinese Academy of Sciences（杭州高等研究院基础物理与数学学院; 中国科学院国家天文台; 中国科学院理论物理研究所; 中国科学院大学太极引力波宇宙实验室（北京/杭州））
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文对相对论性Rindler流体的对偶体度规进行Petrov分类，构造Weyl双拷贝，并推导非相对论极限，揭示了流体涡度与剪切在双拷贝中的不同编码方式。
AI 中文摘要
我们研究了在相对论梯度展开的一阶下，与$2+1$维相对论性Rindler流体对偶的四维体度规的Petrov分类和Weyl双拷贝。在施加流体方程后，领先阶的Weyl曲率由流体涡度和剪切决定。在此阶，体几何通常为Petrov II型，其中无剪切流（具有非零涡度）对应D型分支，无旋流（具有非零剪切）对应N型分支。对于D型分支，我们在固定的Rindler背景上构造了一个纯磁性的Maxwell单拷贝，并区分了具有恒定磁场的精确无源解和在一阶梯度内有效的局部微扰解。对于N型分支，我们获得了一个由$\beta$参数化的代数Weyl双拷贝族。我们推导了$\beta=0$和$\beta=1$时的显式场强和规范势，以及Maxwell方程所施加的局部Cauchy-Riemann条件。这些选择以不同方式编码流体剪切：对于$\beta=0$，剪切依赖性完全存在于零拷贝标量中，而对于$\beta=1$，它直接进入Maxwell场。最后，利用具有显式$\epsilon$计数的非相对论流体动力学展开，我们推导了D型单拷贝和两种N型选择的非相对论极限，并将所得结构与现有的非相对论构造进行了比较。
英文摘要
We study the Petrov classification and Weyl double copy of the four-dimensional bulk metric dual to a $2+1$-dimensional relativistic Rindler fluid at first order in the relativistic gradient expansion. Upon imposing the fluid equations, the leading Weyl curvature is determined by the fluid vorticity and shear. At this order, the bulk geometry is generically of Petrov type II, with a type D branch for shear-free flows with nonzero vorticity and a type N branch for irrotational flows with nonzero shear. For the type D branch, we construct a purely magnetic Maxwell single copy on a fixed Rindler background and distinguish exact source-free solutions with a constant magnetic field from local perturbative solutions valid through first order in gradients. For the type N branch, we obtain a family of algebraic Weyl double copies parametrized by $β$. We derive explicit field strengths and gauge potentials for $β=0$ and $β=1$, together with the local Cauchy-Riemann conditions imposed by Maxwell's equations. These choices encode the fluid shear differently: for $β=0$, the shear dependence resides entirely in the zeroth-copy scalar, whereas for $β=1$, it enters the Maxwell field directly. Finally, using the non-relativistic hydrodynamic expansion with explicit $ε$ counting, we derive the non-relativistic limits of the type D single copy and both type N choices, and compare the resulting structures with existing non-relativistic constructions.
Comments13 pages
