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Review on Non-Relativistic Gravity
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Review on Non-Relativistic Gravity
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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, K\"unzle 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.
Forward citations
Cited by 14 Pith papers
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Spin and Quadrupole Sectors in Nonrelativistic Gravity
Derives NLO Kerr-type and Hartle-Thorne-type solutions plus NNLO mixed spin-quadrupole solutions in the Galilean branch of nonrelativistic gravity.
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Quantum Fluctuations and Newton-Cartan Geometry for Non-Relativistic de Sitter space
The one-loop partition function for non-relativistic de Sitter gravity yields a T² prefactor consistent with four symmetry generators, and the bulk admits a torsionless Newton-Cartan geometry satisfying the non-relati...
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Gravitational Memory Beyond Null Infinity through Finite-Distance Carrollian Screens
Finite-distance null screens carry a Carrollian memory whose leading tracefree large-radius part reproduces the standard Bondi displacement memory in Robinson–Trautman spacetimes.
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A unified expansion of Einstein's gravity
A unified (s,n)-parametrized expansion of the Einstein-Hilbert action yields Galilean, Carroll, Lorentzian, and string Carroll gravity, and near-horizon black hole geometries satisfy the string Carroll equations.
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Large-$N$ Carrollian Thermodynamics from AdS Black-Hole Phase-Space Contractions
Finite Carrollian limit of extended AdS first law is reinterpreted as double-scaled large-N low-temperature holographic ensemble with finite products, new boundary stress tensor, and celestial correlator representations.
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Large-$N$ Carrollian Thermodynamics from AdS Black-Hole Phase-Space Contractions
Finite Carrollian black-hole thermodynamics arises as a double-scaled low-temperature large-N ensemble in AdS/CFT, with the boundary Brown-York stress tensor reproducing the contracted bulk Hamiltonian and first law.
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Curvatures and Non-metricities in the Non-Relativistic Limit of Bosonic Supergravity
A metric-only, torsionless-connection formulation with fixed non-metricities rewrites the non-relativistic limit of bosonic supergravity covariantly and matches the vielbein string Newton-Cartan action at Lagrangian level.
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Three-dimensional non-relativistic chiral massive higher-spin gravity
A non-relativistic massive higher-spin gravity in deformed AdS₃ is constructed by Lifshitz-deforming and null-reducing chiral massless higher-spin gravity; under an assumed mass-spin relation its cubic couplings vanis...
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Worldsheet Formalism for Decoupling Limits in String Theory
Develops worldsheet sigma model for fundamental strings in critical type IIA limit showing nodal singularities and derives T-duality web unifying decoupling limits including ambitwistor and Carrollian strings.
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Carrollian bosonic supergravity at order $\alpha'$ and the universal cancellation of higher-curvature divergences
Four-derivative and higher pure-gravitational α' corrections to bosonic supergravity admit a finite Carrollian limit, with an explicit action and a universal finiteness criterion for Riem^N terms.
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Quantum Fluctuations and Newton-Cartan Geometry for Non-Relativistic de Sitter space
The one-loop partition function of the Galilean-de Sitter boundary theory is Z(β) = (2/πβ²) exp(4π²c₀/β), whose β⁻² prefactor matches the four generators of the EdS-G algebra; the matching bulk is a Newton-Cartan geom...
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Brane Symmetries Revisited: Symmetries of Tensile and Tensionless Branes in Possibly Degenerate Metrics and their Manifestations
Tensionless p-branes and branes in degenerate-metric spacetimes admit symmetry transformations built from Killing tensors of arbitrary rank, extending string W-symmetries to all brane dimensions.
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An Introduction to String Newton-Cartan Holography and Integrability
String Newton-Cartan holography, the non-relativistic limit of the AdS/CFT correspondence, is organized and reviewed around five consistency conditions, with its classical solutions, spectrum, and integrability structure.
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Aspects of Non-Relativistic Supersymmetric Theories
Discusses features of non-relativistic supersymmetric field theories from Galilean and Carrollian points of view to aid construction of electric and magnetic variants.
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