Carroll versus Galilei gravity

  • Eric Bergshoeff
  • Joaquim Gomis
  • Blaise Rollier
  • Jan Rosseel
  • Tonnis ter Veldhuis
Open Access
Regular Article - Theoretical Physics


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.


Space-Time Symmetries Classical Theories of Gravity 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2017

Authors and Affiliations

  • Eric Bergshoeff
    • 1
  • Joaquim Gomis
    • 2
  • Blaise Rollier
    • 1
  • Jan Rosseel
    • 3
  • Tonnis ter Veldhuis
    • 1
  1. 1.Centre for Theoretical PhysicsUniversity of GroningenGroningenThe Netherlands
  2. 2.Departament de Física Cuàntica i Astrofísica and Institut de Ciències del CosmosUniversitat de BarcelonaBarcelonaSpain
  3. 3.Faculty of PhysicsUniversity of ViennaViennaAustria

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