arXiv 2406.067092024-06-25gr-qc

Carrollian Stretched Horizons的几何

Geometry of Carrollian Stretched Horizons

Laurent Freidel, Puttarak Jai-akson

备注：: 101 pages, 1 figure; v2 includes added references for conclusions and corrects the citation on page 37

AI总结：

本文提出了一个研究Carrollian stretched horizons的综合工具箱，通过引入sCarrollian structures及相关概念，统一了内禀与嵌入视角，为任意causal surface提供通用框架，并建立了引力与Carrollian流体动力学的新联系。

摘要：

在本文中，我们提出了一个用于研究Carrollian stretched horizons的综合工具箱，涵盖其几何、动力学、辛几何、对称性及相应的Noether charges。我们在任意曲面上引入了ruled stretched Carrollian structures（sCarrollian structures）的精确定义，推广了null surfaces的传统Carrollian structures，并提出了sCarrollian connection和sCarrollian stress tensor的概念。我们的方法统一了sCarrollian（内禀）和stretched horizon（嵌入）视角，为任何causal surface（无论是timelike还是null）提供了通用框架。我们用sCarrollian变量表示了Einstein equations，并讨论了sCarrollian几何的相空间辛结构。通过Noether定理，我们推导了Einstein equation和canonical charge，并计算了canonical charge沿横向（径向）方向的演化。后者可被解释为spin-2 symmetry charge。我们的框架在stretched horizons上的引力与Carrollian fluid dynamics之间建立了新颖的联系，并统一了文献中研究的各种causal surfaces，包括non-expanding和isolated horizons。我们期望这项工作能为black holes的流体动力学描述以及null surfaces的量子化提供见解。

英文摘要：

In this paper, we present a comprehensive toolbox for studying Carrollian stretched horizons, encompassing their geometry, dynamics, symplectic geometry, symmetries, and corresponding Noether charges. We introduce a precise definition of ruled stretched Carrollian structures (sCarrollian structures) on any surface, generalizing the conventional Carrollian structures of null surfaces, along with the notions of sCarrollian connection and sCarrollian stress tensor. Our approach unifies the sCarrollian (intrinsic) and stretched horizon (embedding) perspectives, providing a universal framework for any causal surface, whether timelike or null. We express the Einstein equations in sCarrollian variables and discuss the phase space symplectic structure of the sCarrollian geometry. Through Noether's theorem, we derive the Einstein equation and canonical charge and compute the evolution of the canonical charge along the transverse (radial) direction. The latter can be interpreted as a spin-2 symmetry charge. Our framework establishes a novel link between gravity on stretched horizons and Carrollian fluid dynamics and unifies various causal surfaces studied in the literature, including non-expanding and isolated horizons. We expect this work to provide insights into the hydrodynamical description of black holes and the quantization of null surfaces.

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