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arXiv 2006.10083hep-thgr-qc
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流体/重力对应中的Febriman-Graham规范和Bondi规范

Fefferman-Graham and Bondi Gauges in the Fluid/Gravity Correspondence

Luca Ciambelli, Charles Marteau, P. Marios Petropoulos, Romain Ruzziconi

摘要:

在三维引力中,我们讨论了Fundaman-Graham规范,Bondi规范和Eddington-Finkelstein型规范之间的关系,通常被称为导数展开,涉及流体/引力对应。从一个负的宇宙学常数出发,对每一个规范,我们导出了解空间和剩余规范同态。我们明确地构造了与各种规范相关的同构,并建立了它们的边界数据的精确匹配。我们表明,邦迪和Fundaman-Graham规是等价的,而流体/重力导数膨胀,源自部分规范固定,表现出一个额外的未指定的功能,编码的边界流体速度。邦迪规范原来描述了一个子空间的衍生扩展的解决方案空间,具有流体在一个特定的流体动力学框架。我们继续我们的分析与里奇平坦极限的邦迪规范和流体/重力导数展开。它们之间的关系在这个界限中是持续的,这个界限是明确的和非平凡的。此外,导数展开式的平坦极限映射到边界上的超相对论极限。这个过程允许解开的全息特性的邦迪规范为零的宇宙学常数,在其边界的卡罗尔对偶流体。

英文摘要:

In three-dimensional gravity, we discuss the relation between the Fefferman--Graham gauge, the Bondi gauge and the Eddington--Finkelstein type of gauge, often referred to as the derivative expansion, involved in the fluid/gravity correspondence. Starting with a negative cosmological constant, for each gauge, we derive the solution space and the residual gauge diffeomorphisms. We construct explicitly the diffeomorphisms that relate the various gauges, and establish the precise matching of their boundary data. We show that Bondi and Fefferman--Graham gauges are equivalent, while the fluid/gravity derivative expansion, originating from a partial gauge fixing, exhibits an extra unspecified function that encodes the boundary fluid velocity. The Bondi gauge turns out to describe a subspace of the derivative expansion's solution space, featuring a fluid in a specific hydrodynamic frame. We pursue our analysis with the Ricci-flat limit of the Bondi gauge and of the fluid/gravity derivative expansion. The relations between them persist in this limit, which is well-defined and non-trivial. Moreover, the flat limit of the derivative expansion maps to the ultra-relativistic limit on the boundary. This procedure allows to unravel the holographic properties of the Bondi gauge for vanishing cosmological constant, in terms of its boundary Carrollian dual fluid.

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