卡罗尔与牛顿和伽利略：两个对偶的非爱因斯坦时间概念

一维Carroll流体 I：Carroll-Galilei对偶性

One-dimensional Carrollian fluids I: Carroll-Galilei duality

本文利用Galilean与Carrollian代数同构，建立一维流体对偶，交换纵向与横向方向及平衡与非平衡可观测量，并研究局部提升及完整流体方程所需的几何结构。

共形Carroll群

Conformal Carroll groups

基于类似于牛顿-嘉当时空的几何性质，提出了Levy-Leblond的Carroll群的共形扩张。扩展名由整数$k$标记。这个框架包括并扩展了我们最近对Bondi-Metzner-Sachs（BMS）和Newman-Unti（NU）群的研究。关系共形Galilei群澄清。共形卡罗尔对称性是由“卡罗尔光子”来说明的。牛顿-嘉当空间和卡罗尔空间中的运动可能与巴格曼空间中的弦的运动有关。

The $κ$-Newtonian and $κ$-Carrollian algebras and their noncommutative spacetimes

We derive the non-relativistic $c\to\infty$ and ultra-relativistic $c\to 0$ limits of the $κ$-deformed symmetries and corresponding spacetime in (3+1) dimensions, with and without a cosmological constant. We apply the theory of Lie bialgebra contractions to the Poisson version of the $κ$-(A)dS quantum algebra, and quantize the resulting contracted Poisson-Hopf algebras, thus giving rise to the $κ$-deformation of the Newtonian (Newton-Hooke and Galilei) and Carrollian (Para-Poincaré, Para-Euclidean and Carroll) quantum symmetries, including their deformed quadratic Casimir operators. The corres…

Gauging the Carroll Algebra and Ultra-Relativistic Gravity

It is well known that the geometrical framework of Riemannian geometry that underlies general relativity and its torsionful extension to Riemann-Cartan geometry can be obtained from a procedure known as gauging the Poincare algebra. Recently it has been shown that gauging the centrally extended Galilei algebra, known as the Bargmann algebra, leads to a geometrical framework that when made dynamical gives rise to Horava-Lifshitz gravity. Here we consider the case where we contract the Poincare algebra by sending the speed of light to zero leading to the Carroll algebra. We show how this algebra…

三维超对称卡罗尔伽利略子

Supersymmetric Carroll Galileons in Three Dimensions

该研究提出首个含时空导数的相互作用卡罗尔超对称伽利略子类场论，通过推广二维伽利略/卡罗尔对偶至更高维并连接欧几里得超代数，构建相关多重态与张量微积分，为卡罗尔场论和超对称结构提供新见解。

引力理论的伽利略极限和卡罗尔极限的唯一性及其在高阶引力理论中的应用

Uniqueness of Galilean and Carrollian limits of gravitational theories and application to higher derivative gravity

本文研究了伽利略和卡罗尔极限的引力理论唯一性，并构建了高阶引力理论的通用展开式，提出了一种计算算法并推导了同时修正广义相对论的条件。

Gauge dependence and self-force from Galilean to Einsteinian free fall, compact stars falling into black holes, Hawking radiation and the Pisa tower at the general relativity centennial

(Short abstract). In Galilean physics, the universality of free fall implies an inertial frame, which in turns implies that the mass m of the falling body is omitted. Otherwise, an additional acceleration proportional to m/M would rise either for an observer at the centre of mass of the system, or for an observer at a fixed distance from the centre of mass of M. These elementary, but overlooked, considerations fully respect the equivalence principle and the identity of an inertial or a gravitational pull for an observer in the Einstein cabin. They value as fore-runners of the self-force and ga…

关于广义相对论的超相对论极限

On the Ultrarelativistic Limit of General Relativity

众所周知，牛顿的引力理论可以表述为四维时空理论，并遵循爱因斯坦理论的奇异极限，如果光速趋于无穷大。这里的“奇异”代表这样一个事实，即极限几何结构不同于正则黎曼时空。从几何学上讲，爱因斯坦到牛顿的转变可以被看作是光锥的“开放”。这幅图表明，爱因斯坦理论可能还有其他奇异极限：让所有光锥收缩，最终成为奇异世界线全等的一部分。极限结构可以被认为是嵌入在五维时空中的零超曲面。虽然光速在这里趋于零，但所有其他速度都趋于光速。因此，我们可以说广义相对论有一个极端相对论的极限。由此产生的理论与牛顿的引力理论一样简单，但基本的区别在于，牛顿的椭圆微分方程被本质上的常微分方程所取代，其导数与奇异同余的生成元相切。Galilei群被Lévy-Leblond引入的Carroll群所取代。我们建议研究近超相对论的情况下，从奇异结构的微扰方法，类似于后牛顿展开的$c \to \infty$的情况。