Review on Non-Relativistic Gravity

Abstract

We review the history of Newton-Cartan gravity with an emphasis on recent developments, including the covariant, off-shell large speed of light expansion of general relativity. Depending on the matter content, this expansion either leads to Newton-Cartan geometry with absolute time or to Newton-Cartan geometry with non-relativistic gravitational time dilation effects. The latter shows that non-relativistic gravity includes a strong field regime and goes beyond Newtonian gravity. We start by reviewing early developments in Newton-Cartan geometry, including the covariant description of Newtonian gravity, mainly through the works of Trautman, Dautcourt, Künzle and Ehlers. We then turn to more modern developments, such as the gauging of the Bargmann algebra, and we describe why the latter cannot be used to find an off-shell covariant description of Newtonian gravity. We review recent work on the $1/c$ expansion of general relativity and show that this leads to an alternative `type II' notion of Newton-Cartan geometry. Finally, we discuss matter couplings, solutions and odd powers in $1/c$, and we conclude with a brief summary of related topics.

arXiv comment46+10 pages, review article; v2: minor changes, reference added; v3: reference added

References in corpus (68)

• Gravity Duals of Lifshitz-like Fixed Points
• Gravitational radiation from inspiralling compact binaries completed at the third post-Newtonian order
• Celestial Mechanics, Conformal Structures, and Gravitational Waves
• Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time
• Non-Relativistic Closed String Theory
• Torsional Newton-Cartan Geometry and Lifshitz Holography
• Newtonian Gravity and the Bargmann Algebra
• Spacetime Symmetries of the Quantum Hall Effect
• Non-relativistic conformal symmetries and Newton-Cartan structures
• Non-Relativistic Strings and Limits of the AdS/CFT Correspondence
• Action Principle for Newtonian Gravity
• `Stringy' Newton-Cartan Gravity
• Null Killing Vector Dimensional Reduction and Galilean Geometrodynamics
• Generating Lie and gauge free differential (super)algebras by expanding Maurer-Cartan forms and Chern-Simons supergravity
• Lifshitz Gravity for Lifshitz Holography
• Expanding Lie (super)algebras through abelian semigroups
• Lifshitz Space-Times for Schroedinger Holography
• Schroedinger Invariance from Lifshitz Isometries in Holography and Field Theory
• On the coupling of Galilean-invariant field theories to curved spacetime
• Warped Conformal Field Theory as Lower Spin Gravity
• Perfect Fluids
• Carroll Expansion of General Relativity
• Newton-Hooke spacetimes, Hpp-waves and the cosmological constant
• String Theory and String Newton-Cartan Geometry
• Torsional Newton-Cartan gravity from the large $c$ expansion of General Relativity
• Three-Dimensional Extended Bargmann Supergravity
• Non-Relativistic Chern-Simons Theories and Three-Dimensional Horava-Lifshitz Gravity
• Connections and dynamical trajectories in generalised Newton-Cartan gravity II. An ambient perspective
• Aspects of Nonrelativistic Strings
• Connections and dynamical trajectories in generalised Newton-Cartan gravity I. An intrinsic view
• Fields and fluids on curved non-relativistic spacetimes
• Newton-Cartan (super)gravity as a non-relativistic limit
• Gravity between Newton and Einstein
• Post-Newtonian extension of the Newton-Cartan theory
• Non-Relativistic Ten-Dimensional Minimal Supergravity
• Standard and Generalized Newtonian Gravities as ``Gauge'' Theories of the Extended Galilei Group - I: The Standard Theory
• On the intrinsic torsion of spacetime structures
• On the Non-Relativistic Expansion of Closed Bosonic Strings
• Torsional Newton-Cartan Geometry from the Noether Procedure
• Non-relativistic fields from arbitrary contracting backgrounds
• The Teleparallel Equivalent of Newton-Cartan Gravity
• Extended $D=3$ Bargmann supergravity from a Lie algebra expansion
• Covariant formulation of the post-1-Newtonian approximation to General Relativity
• The Eisenhart lift: a didactical introduction of modern geometrical concepts from Hamiltonian dynamics
• Hydrodynamic Modes of Homogeneous and Isotropic Fluids
• Oddity in nonrelativistic, strong gravity
• Newton-Cartan Submanifolds and Fluid Membranes
• Eisenhart's theorem and the causal simplicity of Eisenhart's spacetime
• Carrollian and Non-relativistic Jackiw-Teitelboim Supergravity
• Lifshitz Hydrodynamics from Lifshitz Black Branes with Linear Momentum
• Galilean first-order formulation for the non-relativistic expansion of general relativity
• On the Ultrarelativistic Limit of General Relativity
• Homogeneous Nonrelativistic Geometries as Coset Spaces
• (In)finite extensions of algebras from their Inonu-Wigner contractions
• Zooming in on AdS${}_3$/CFT${}_2$ near a BPS Bound
• Symmetries of post-Galilean expansions
• Teleparallel Newton--Cartan gravity
• General theory of Galilean gravity
• Non-relativistic and Ultra-relativistic Expansions of Three-dimensional Spin-3 Gravity Theories
• Non-Relativistic and Ultra-Relativistic Scaling Limits of Multimetric Gravity
• A 3+1 formulation of the 1/c expansion of General Relativity
• Three-dimensional Newtonian gravity with cosmological constant and torsion
• Non-relativistic expansion of the Einstein-Hilbert Lagrangian
• Non-relativistic gravity theories in four spacetime dimensions
• Existence of families of spacetimes with a Newtonian limit
• Non-relativistic Geometry and the Equivalence Principle
• Lagrangians for non-relativistic gravity
• The gauging procedure and carrollian gravity

Cited by in corpus (25)

• Unification of Decoupling Limits in String and M-theory
• Worldsheet Formalism for Decoupling Limits in String Theory
• Matrix Theory Reloaded: A BPS Road to Holography
• The Non-Relativistic Geometric Trinity of Gravity
• Non-Lorentzian IIB Supergravity from a Polynomial Realization of SL(2,R)
• Longitudinal Galilean and Carrollian limits of non-relativistic strings
• A coupling prescription for post-Newtonian corrections in Quantum Mechanics
• Mixmasters in Wonderland: Chaotic dynamics from Carroll limits of gravity
• A 3+1 formulation of the 1/c expansion of General Relativity
• Uniqueness of Galilean and Carrollian limits of gravitational theories and application to higher derivative gravity
• Setting the connection free in the Galilei and Carroll expansions of gravity
• The classification of general affine connections in Newton--Cartan geometry: Towards metric-affine Newton--Cartan gravity
• Geometric post-Newtonian description of massive spin-half particles in curved spacetime
• Dynamical de Sitter black holes in a quasi-stationary expansion
• Traversable wormhole for string, but not for particle
• Gravitational Core of Double Field Theory: Lecture Notes
• Non zero Coriolis field in Ehlers' Frame Theory
• On gauge transformations in twistless-torsional Newton--Cartan geometry
• Notes on su$(1,2)\oplus$u$(1)$ Chern-Simons theory and Torsional Newton-Cartan gravity
• Conformal Mapping of Non-Lorentzian Geometries in SU(1,2) Conformal Field Theory
• Nonrelativistic expansion of type IIA NS5 brane
• On Carrollian and Galilean contractions of BMS algebra in 3 and 4 dimensions
• Universal Box Operator: $\mathbf{O}(D,D)$-Symmetry and ${\alpha }^{\prime }$-Corrections
• Group Contractions via Infinite-Dimensional Lie Theory
• Brane Symmetries Revisited: Symmetries of Tensile and Tensionless Branes in Possibly Degenerate Metrics and their Manifestations