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Carroll Expansion of General Relativity
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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 22 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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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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Carrollian limit of NS-NS and Heterotic Supergravity
A finite Carrollian limit of NS-NS and heterotic supergravity is constructed by field expansion, including a gauge sector, a Green-Schwarz mechanism analysis, and a finite leading α' correction.
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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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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 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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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 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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Hamiltonian formulation of Carrollian Maxwell theory in Deformed Light-cone Kaluza-Klein-like Null reduction
Derives Carrollian Maxwell theories (magnetic and electric) plus new scalar couplings through deformed light-cone null reduction while keeping first-class Gauss constraint and gauge invariance.
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Post-Carroll Algebra, Conformal Extensions, and Field Theories
Introduces the post-Carroll algebra and its conformal extensions, including the Carroll-Schrödinger algebra, and computes two-point functions in post-Carrollian CFTs.
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Kerroll black holes
Rotating black holes are constructed in magnetic Carroll gravity, including an intrinsically Carrollian dressed solution and a Kerroll black hole from an odd-power c-expansion of GR, with conserved charges computed.
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Kerroll black holes
Rotating black holes are constructed in Carroll gravity via connection freedom and an odd-power GR expansion, yielding an intrinsically Carrollian rotating solution and the Kerroll black hole analog.
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Stationary solutions in the small-$c$ expansion of GR
Exact Lense-Thirring-type, C-metric-type, and Hartle-Thorne-type stationary vacuum solutions are constructed in the NLO and NNLO small-c expansion of GR, revealing a richer sector than magnetic Carroll gravity.
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Carroll fermions, expansions and the lightcone
Carrollian fermion actions are obtained from relativistic Dirac theory via c-expansion and connected to light-cone dynamics through co-dimension one Carroll subalgebras in the Poincaré algebra.
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Carroll hydrodynamics with spin
Carroll hydrodynamics with spin is obtained as the c→0 limit of relativistic hydrodynamics with spin, extending the description of boost-invariant flows.
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Strings near BTZ black holes: A Carrollian Chronicle
The paper classifies families of closed bosonic string solutions in the near-horizon non-extremal BTZ spacetime and identifies novel features via string-Carroll expansion.
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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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Post-Carroll Algebra, Conformal Extensions, and Field Theories
Defines post-Carroll algebra allowing central charges in higher dimensions, constructs its conformal extension and the Carroll-Schrödinger algebra matching prior theory, and derives two-point functions in post-Carroll...
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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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