Curved non-relativistic spacetimes, Newtonian gravitation and massive matter
Curved non-relativistic spacetimes, Newtonian gravitation and massive matter
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DOI：
10.1063/1.4932967
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发表时间：
2015-10-01
影响因子：
1.3
通讯作者：
Roberts, Matthew M.
中科院分区：
文献类型：
--
作者：
Geracie, Michael;Prabhu, Kartik;Roberts, Matthew M.
最近有重要的工作耦合物质的牛顿-嘉当时空的目的是调查某些凝聚态的现象。为了达到这个目的，我们需要有一个与支持大质量物质场的局部非相对论对称性相一致的完全广义时空。特别是，不能强加一个先验的几何数据的限制，如果要分析的问题响应的扰动几何。在本文中，我们构造这样一个巴格曼时空在完全的一般性，没有任何事先限制的领域指定的几何。由此产生的时空结构包括熟悉的牛顿-嘉当结构，以及与质量耦合的额外规范场。我们用几个例子来说明这个问题。我们构造的一般时空还包括作为一个特殊情况的牛顿引力的协变描述，这在以前的作品中已经得到了彻底的研究。我们还展示了巴格曼时空是如何从洛伦兹时空的合适的非相对论极限中产生的。在一篇配套论文中[M. Geracie等人，e-print arXiv：1503.02680]，我们使用这个巴格曼时空结构来研究物质耦合的细节，包括诺特-沃德恒等式，以及非相对论流体的输运现象和热力学。(C)2015 AIP Publishing LLC.
There is significant recent work on coupling matter to Newton-Cartan spacetimes with the aim of investigating certain condensed matter phenomena. To this end, one needs to have a completely general spacetime consistent with local non-relativistic symmetries which supports massive matter fields. In particular, one cannot impose a priori restrictions on the geometric data if one wants to analyze matter response to a perturbed geometry. In this paper, we construct such a Bargmann spacetime in complete generality without any prior restrictions on the fields specifying the geometry. The resulting spacetime structure includes the familiar Newton-Cartan structure with an additional gauge field which couples to mass. We illustrate the matter coupling with a few examples. The general spacetime we construct also includes as a special case the covariant description of Newtonian gravity, which has been thoroughly investigated in previous works. We also show how our Bargmann spacetimes arise from a suitable non-relativistic limit of Lorentzian spacetimes. In a companion paper [M. Geracie et al., e-print arXiv:1503.02680], we use this Bargmann spacetime structure to investigate the details of matter couplings, including the Noether-Ward identities, and transport phenomena and thermodynamics of non-relativistic fluids. (C) 2015 AIP Publishing LLC.