2017/01/22 by Eric Bergshoeff, Joaquim Gomis, Blaise Rollier +2 · 1 voice · 3 citations
Physics and Astronomy · #Connection (principal bundle) #Equations of motion #Formalism (music) #General relativity #Gravitation #Limit (mathematics) #Noncommutative and Quantum Gravity Theories #Quantum and Classical Electrodynamics #Relativity and Gravitational Theory #f(R) gravity #hep-th
paper · pdf · doi:10.1007/jhep03(2017)165
30 pages, v2:minor changes and added references
arxiv published 2017/01/22 · openalex created_date 2017/02/03 · arxiv created 2017/02/16 · arxiv updated 2017/02/16 · openalex publication_date 2017/03/01 · openalex updated_date 2026/08/05
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.