论文标题
审查非权利主义重力
Review on Non-Relativistic Gravity
论文作者
论文摘要
我们回顾了牛顿 - 卡丹重力的历史，重点是最近的发展，包括协变量，脱落的大速度的一般相对性的速度。根据物质的含量，这种扩展要么导致具有绝对时间的牛顿 - 卡丹几何形状，要么导致具有非相关引力时间扩张效应的牛顿 - 卡丹几何几何形状。后者表明，非权利主义重力包括强大的野外状态，超越了牛顿重力。我们首先回顾了牛顿 - 卡丹几何形状的早期发展，包括对牛顿重力的协变描述，主要是通过Trautman，Dautcourt，Künzle和Ehlers的作品。然后，我们转向更现代的发展，例如对Bargmann代数的测量，我们描述了为什么不能使用后者来找到对牛顿重力的脱壳协变的描述。我们回顾了有关$ 1/c $一般相对论的最新工作，并表明这导致了牛顿 - 卡丹几何学的另一种“ II型”概念。最后，我们以$ 1/c $的价格讨论了物质耦合，解决方案和奇数权力，并以相关主题的简要摘要得出结论。
We review the history of Newton-Cartan gravity with an emphasis on recent developments, including the covariant, off-shell large speed of light expansion of general relativity. Depending on the matter content, this expansion either leads to Newton-Cartan geometry with absolute time or to Newton-Cartan geometry with non-relativistic gravitational time dilation effects. The latter shows that non-relativistic gravity includes a strong field regime and goes beyond Newtonian gravity. We start by reviewing early developments in Newton-Cartan geometry, including the covariant description of Newtonian gravity, mainly through the works of Trautman, Dautcourt, Künzle and Ehlers. We then turn to more modern developments, such as the gauging of the Bargmann algebra, and we describe why the latter cannot be used to find an off-shell covariant description of Newtonian gravity. We review recent work on the $1/c$ expansion of general relativity and show that this leads to an alternative `type II' notion of Newton-Cartan geometry. Finally, we discuss matter couplings, solutions and odd powers in $1/c$, and we conclude with a brief summary of related topics.
