标题： 卡罗尔流体力学与拉伸视界上的辛结构 显示英文标题

标题： Carrollian hydrodynamics and symplectic structure on stretched horizons

摘要： 膜范式展示了类时拉伸视界与零边界（如黑洞视界）之间的潜在联系，并将视界的引力动力学与流体动力学联系起来。 在本工作中，我们重新审视有限距离零边界的膜观点，并基于超曲面的rigging技术，对拉伸视界和零边界进行统一的几何处理。 这使我们能够提供零和类时超曲面的统一几何描述，解决了传统拉伸视界描述中出现的零极限奇点问题。 我们还扩展了最近被认为是最小边界正确流体图像的Carroll流体图像和零视界的几何Carroll描述，以适用于拉伸视界。 为此，我们建立了一个字典，将拉伸视界上的引力自由度与Carroll流体量相关联，并表明投影到视界的爱因斯坦方程是Carroll流体的动力学守恒定律。 最后，我们报告称，拉伸视界的引力预辛势可以表示为Carroll流体共轭变量的形式，并且从对称性中推导出Carroll守恒定律和相应的Noether电荷。 显示英文摘要

摘要： The membrane paradigm displays underlying connections between a timelike stretched horizon and a null boundary (such as a black hole horizon) and bridges the gravitational dynamics of the horizon with fluid dynamics. In this work, we revisit the membrane viewpoint of a finite distance null boundary and present a unified geometrical treatment to the stretched horizon and the null boundary based on the rigging technique of hypersurfaces. This allows us to provide a unified geometrical description of null and timelike hypersurfaces, which resolves the singularity of the null limit appearing in the conventional stretched horizon description. We also extend the Carrollian fluid picture and the geometrical Carrollian description of the null horizon, which have been recently argued to be the correct fluid picture of the null boundary, to the stretched horizon. To this end, we draw a dictionary between gravitational degrees of freedom on the stretched horizon and the Carrollian fluid quantities and show that Einstein's equations projected onto the horizon are the Carrollian hydrodynamic conservation laws. Lastly, we report that the gravitational pre-symplectic potential of the stretched horizon can be expressed in terms of conjugate variables of Carrollian fluids and also derive the Carrollian conservation laws and the corresponding Noether charges from symmetries.