Carroll versus Galilei gravity
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Publication:1693027
DOI10.1007/JHEP03(2017)165zbMATH Open1377.83073arXiv1701.06156OpenAlexW3100127347MaRDI QIDQ1693027
Author name not available (Why is that?)
Publication date: 10 January 2018
Published in: (Search for Journal in Brave)
Abstract: We consider two distinct limits of General Relativity that in contrast to the standard non-relativistic limit can be taken at the level of the Einstein-Hilbert action instead of the equations of motion. One is a non-relativistic limit and leads to a so-called Galilei gravity theory, the other is an ultra-relativistic limit yielding a so-called Carroll gravity theory. We present both gravity theories in a first-order formalism and show that in both cases the equations of motion (i) lead to constraints on the geometry and (ii) are not sufficient to solve for all of the components of the connection fields in terms of the other fields. Using a second-order formalism we show that these independent components serve as Lagrange multipliers for the geometric constraints we found earlier. We point out a few noteworthy differences between Carroll and Galilei gravity and give some examples of matter couplings.
Full work available at URL: https://arxiv.org/abs/1701.06156
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