Non-relativistic limits and three-dimensional coadjoint Poincaré gravity
Eric Bergshoeff, Joaquim Gomis, Patricio Salgado-Rebolledo
2020Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences16 citationsDOIOpen Access PDF
Abstract
We show that a recently proposed action for three-dimensional non-relativistic gravity can be obtained by taking the limit of a relativistic Lagrangian that involves the coadjoint Poincaré algebra. We point out the similarity of our construction with the way that three-dimensional Galilei gravity and extended Bargmann gravity can be obtained by taking the limit of a relativistic Lagrangian that involves the Poincaré algebra. We extend our results to the anti-de Sitter case and we will see that there is a chiral decomposition at both the relativistic and non-relativistic level. We comment on possible further generalizations.
Topics & Concepts
Poincaré conjectureLagrangianLimit (mathematics)PhysicsAction (physics)Mathematical physicsRelativistic quantum chemistryRelativistic particlePoint (geometry)Classical mechanicsAlgebra over a fieldMathematicsPure mathematicsQuantum mechanicsMathematical analysisGeometryElectronBlack Holes and Theoretical PhysicsCosmology and Gravitation TheoriesNoncommutative and Quantum Gravity Theories