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Carroll Expansion of General Relativity
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We study the small speed of light expansion of general relativity, utilizing the modern perspective on non-Lorentzian geometry. This is an expansion around the ultra-local Carroll limit, in which light cones close up. To this end, we first rewrite the Einstein-Hilbert action in pre-ultra-local variables, which is closely related to the 3+1 decomposition of general relativity. At leading order in the expansion, these pre-ultra-local variables yield Carroll geometry and the resulting action describes the electric Carroll limit of general relativity. We also obtain the next-to-leading order action in terms of Carroll geometry and next-to-leading order geometric fields. The leading order theory yields constraint and evolution equations, and we can solve the evolution analytically. We furthermore construct a Carroll version of Bowen-York initial data, which has associated conserved boundary linear and angular momentum charges. The notion of mass is not present at leading order and only enters at next-to-leading order. This is illustrated by considering a particular truncation of the next-to-leading order action, corresponding to the magnetic Carroll limit, where we find a solution that describes the Carroll limit of a Schwarzschild black hole. Finally, we comment on how a cosmological constant can be incorporated in our analysis.
Forward citations
Cited by 20 Pith papers
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The Energy-Momentum-News Complex near Future Null Infinity
A Carroll-covariant energy-momentum-news complex at future null infinity yields Ward identities that generalise the Bondi loss equations, with an anomalous Carroll boost.
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Interacting Galilean and Finite-Energy Carroll Fermions
A c-dependent similarity transformation generates new Galilean and Carrollian fermion actions, including a Carrollian model with non-removable finite energy and a Galilean model with an accidental fermionic gauge symmetry.
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Carrollian limit of NS-NS and Heterotic Supergravity
Ultra-relativistic expansion plus dilaton scaling produces finite covariant Carrollian NS-NS and heterotic supergravity actions, with trivializable Green-Schwarz for the 1-form and finite leading Riem^{2} α' corrections.
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Stationary solutions in the small-$c$ expansion of GR
The NLO/NNLO small-c (Carroll) expansion of GR admits a rich stationary vacuum sector with rotating Lense-Thirring-type, C-metric-type, Hartle-Thorne-type, and higher-multipole solutions, going beyond the static magne...
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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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Scaling Symmetry and Carrollian Gravity
A single scaling-Carroll gauge-theory construction interpolates between dynamical Carroll gravity, Aristotelian gravity, and fracton gauge theories coupled to curved space.
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A conformal approach to matter coupled Aristotelian gravity
A conformal extension of the p-brane Aristotelian algebra is used to construct electric, magnetic, and electric-magnetic Aristotelian gravity actions and their matter couplings.
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Tantum Gravity
A triple-scaling limit of quantum gravity keeps black hole thermodynamics finite and reproduces the Hawking temperature.
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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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On Carrollian and Celestial Correlators in General Dimensions
Explicit two-, three-, and four-point Carrollian and celestial amplitudes for massless scalars in D dimensions, connected to the flat/Carrollian limit of AdS/CFT correlators.
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Carroll Geometry Meets De Sitter Space via Holography
The paper shows that Carroll-like geometry appears naturally at the asymptotic boundary of de Sitter space in a string-theoretic holographic construction, mirroring the Galilei-like geometry of AdS/CFT, and builds exa...
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Worldsheet CFT$_2$ and Celestial CFT$_2$ : An AdS$_3$-CFT$_2$ perspective
A near-boundary scaling limit of AdS/CFT is proposed to produce celestial CFTs, and the long-string sector of string theory on AdS3 is identified as a Lorentz-only celestial CFT2.
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Notes on su$(1,2)\oplus$u$(1)$ Chern-Simons theory and Torsional Newton-Cartan gravity
The su(1,2)⊕u(1) Chern-Simons theory is torsional Newton-Cartan gravity whose 1/c expansion reproduces the extended z=2 Schrödinger gravity and whose asymptotic symmetry is the W_3^(2)⊕u(1) algebra.
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Carrollian superstring in the flipped vacuum
The Carrollian superstring in the flipped vacuum has a non-truncated spectrum with nonzero winding in the infinite-radius limit, and its three-point graviton amplitudes match tensile superstring results up to location...
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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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The extremal Reissner-Nordstr\"om throat from non extremal near horizon expansions
String Carroll first-order data miss the RN AdS2×S2 throat; second-order (EF) or all-order radial (static) terms restore it under near-extremal scaling.
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Boundary dynamics of Maxwell-invariant three-dimensional Chern-Simons gravity
A Maxwellian extension of flat Liouville theory is derived as the boundary dual of Maxwell-invariant 2+1 Chern-Simons gravity, and is shown to match a geometric action and a Carrollian expansion of the AdS3 dual.
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Quantization of Carrollian fermions
A first interacting 4D Carrollian Yukawa theory is constructed, showing ultralocal fermion-scalar interactions and one-loop beta functions with mostly Gaussian fixed points.
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A time-like window into tensionless worldsheets
Kasner worldsheets near their null horizons reproduce the tensionless, Carrollian string physics previously found for Rindler worldsheets, with a Bogoliubov-map identification that depends on an arbitrary regularizati...
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3D Carrollian gravity from 2D Euclidean symmetry
Post-Carroll-Newtonian Chern-Simons gravities are systematically obtained by semigroup-expanding 2D Euclidean B_k algebras, recovering known Carrollian models as subcases.
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