近日，英国爱丁堡大学的Jørgen Musaeus及其研究团队取得一项新进展。经过不懈努力，他们对非相对论引力下的伽利略流体进行研究。相关研究成果已于2024年10月23日在国际知名学术期刊《高能物理杂志》上发表。

在本文中，研究人员推导出了非相对论引力（NRG）的非相对论AdS膜解，并证实其对应于AdS黑膜几何的1/c²展开。研究人员对非相对论AdS膜进行了伽利略变换，并推导出了相关的边界能量-动量张量。随后，研究人员证明了这是无质量伽利略流体的能量-动量张量，并解释了它是如何与边界的共形等距性联系起来的。在研究过程中，研究人员还为非相对论引力理论本身提出了几个新结果。特别是，研究人员提出了一种新的表述方式，极大地缩短并简化了NRG作用量的运动方程。

据悉，由物质适当激发的广义相对论的1/c展开可用于推导出牛顿引力的作用原理。该作用原理中的引力部分被称为非相对论引力（NRG）。可以对NRG进行不同的激发，从而构建出非牛顿引力所无法描述的解（因为它们不承认绝对时间的概念）。可以引入一个负的宇宙常数，使得NRG承认一个非相对论的AdS解。这种非相对论的AdS真空具有形成伽利略共形代数的基灵矢量，以及其边界承认一个牛顿-卡坦几何的共形类。这引发了一个问题：对于NRG，是否存在流体/引力对应关系的类似物？

附：英文原文

Title: Galilean fluids from non-relativistic gravity

Author: Hartong, Jelle, Mehra, Aditya, Musaeus, Jrgen

Issue&Volume: 2024-10-23

Abstract: The 1/c-expansion of general relativity appropriately sourced by matter can be used to derive an action principle for Newtonian gravity. The gravitational part of this action is known as non-relativistic gravity (NRG). It is possible to source NRG differently and in such a way that one can construct solutions that are not described by Newtonian gravity (as they do not admit a notion of absolute time). It is possible to include a negative cosmological constant such that NRG admits a non-relativistic AdS solution. This non-relativistic AdS vacuum has Killing vectors that form the Galilean conformal algebra and a boundary that admits a conformal class of Newton-Cartan geometries. This begs the question of whether there exists an analogue of the fluid/gravity correspondence for NRG. In this paper we derive a non-relativistic AdS brane solution of NRG and confirm that it corresponds to the 1/c²-expansion of the AdS black brane geometry. We perform a Galilean boost of the non-relativistic AdS brane and derive the associated boundary energy-momentum tensor. We then show that this is the energy-momentum tensor of a massless Galilean fluid and explain how this is linked to the conformal isometries of the boundary. Along the way, we also present several new results for the theory of non-relativistic gravity itself. In particular we present a rewriting that greatly shortens and simplifies the equations of motion of the NRG action.

DOI: 10.1007/JHEP10(2024)156

Source: https://link.springer.com/article/10.1007/JHEP10(2024)156