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Postcarrollian gravity

T0 review · 2 major / 6 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read The paper constructs postcarrollian gravity models in two, three, and four spacetime dimensions by expanding (A)dS Carroll gauge fields in powers of the speed of light, and claims the 2d family is the most general postcarrollian dilaton…

desk verdict A coherent postcarrollian gravity framework with real new 2d solutions and a 3d asymptotic symmetry algebra; the 'most general' 2d claim is the one piece that outruns the evidence. read the letter →

arxiv 2504.16162 v1 pith:FA7U4PGG submitted 2025-04-22 hep-th gr-qc

Florian Ecker , Daniel Grumiller , Patricio Salgado-Rebolledo This is my paper · ORCID
classification hep-thgr-qc
keywords postcarrolliangravityCarrollsymmetryLiealgebraexpansiondilatonPoisson-sigmamodelChern-SimonsMacDowell-Mansouriactionasymptotic
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper tries to establish that Carrollian gravity can be deformed one step away from the strict speed-of-light-zero limit in a controlled, algebraic way, and that the resulting postcarrollian theories are tractable in two, three, and four dimensions. Its central construction expands the (A)dS Carroll connection in powers of $c$, producing new generators that make the Carroll boost change energy ($[H,B_a]=M_a$ rather than zero). The paper claims in two dimensions that the most general postcarrollian dilaton gravity is a five-field Poisson-sigma model, solves it completely, and derives boundary actions of loop-group and Schwarzian type; in three dimensions it proposes Brown-Henneaux-like boundary conditions and derives an asymptotic symmetry algebra with central extensions; in four dimensions it writes a MacDowell-Mansouri-type action. A sympathetic reader would care because these models give a controlled handle on corrections to Carroll gravity, which underlies null boundaries, flat-space holography, and near-horizon physics.

What carries the argument

The load-bearing object is the postcarrollian Lie algebra obtained by expanding the (A)dS Carroll algebra in the parameter $c$: the fields expand as $E^0 = c\tau + c^3 l$, $E^a = e^a + c^2 m^a$, $\Omega^{0a} = c\omega^a + c^3\sigma^a$, and $\Omega^{ab} = \omega^{ab} + c^2\sigma^{ab}$, with generators split into a Carroll row $(H, P_a, B_a, J_{ab})$ and a postcarrollian row $(L, M_a, K_a, S_{ab})$. The mechanism is to expand the algebra and the connection together, inserting this expansion into BF, Chern-Simons, or MacDowell-Mansouri actions to get a leading magnetic Carroll theory plus subleading postcarrollian corrections. In 2d, the generality claim is carried by a Poisson tensor on a five-dimensional target space, with a potential depending only on Carroll-boost-invariant combinations, whose linear cases reproduce the postcarrollian JT and CGHS models.

What would settle it

Compute the deformation cohomology for the five-field Poisson-sigma target space used in section 3.1: any allowed deformation not equivalent to the Poisson tensor (3.5) with potential (3.8) would falsify the 'most general' claim. Separately, take a known 3d AdS Carroll solution, solve the postcarrollian field equations (6.15), and check whether the proposed boundary charges (6.43) are integrable and obey the algebra (6.48); a counterexample would falsify the 3d asymptotic-symmetry proposal.

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Extended reading notes

Core claim

The central discovery is that the (A)dS Carroll algebra and its gauge fields admit an expansion in powers of $c$ whose leading row is the Carroll algebra and whose subleading row is a set of postcarrollian generators $L, M_a, K_a, S_{ab}$. Applying this expansion to BF theory in 2d, Chern-Simons theory in 3d, and a MacDowell-Mansouri action in 4d produces gravitational theories whose defining feature is that Carroll boosts no longer commute with the Hamiltonian. In 2d, the paper identifies the general postcarrollian dilaton gravity action with potential $V = V(X) - (\tfrac{1}{2}X_H^2 - X_M X_P)\,U(X)$, solves all equations of motion, and finds two qualitatively different sectors separated by whether $X_M$ vanishes. In 3d, it exhibits Brown-Henneaux-like boundary conditions whose asymptotic symmetry algebra (6.48) has central extensions. In 4d, the action splits into magnetic Carroll gravity plus postcarrollian corrections, and the postcarrollian torsion constraints fix the otherwise undetermined parts of the spin connections.

Load-bearing premise

The claim that the 2d model is the most general postcarrollian dilaton gravity assumes, without proof, that the deformation-classification theorem proven for ordinary 2d dilaton gravity still applies when the two postcarrollian fields and their extra potential terms are added; if that transfer fails, the model remains consistent but is not the most general.

Editorial extensions

If this is right

  • In the strict $c\to 0$ limit the models reduce to magnetic Carroll gravity, so all postcarrollian results are direct corrections to known Carroll black-hole and Carroll JT/CGHS geometries.
  • Because $[B_a,H]=M_a\neq 0$, boosting a postcarrollian state changes its energy, giving a controlled cutoff on the spectrum of soft excitations.
  • The complete 2d solution space splits into a static sector with $X_M=0$, which reproduces Carroll black-hole-type solutions, and a cosmological sector with $X_M\neq 0$ where the dilaton is time; both are explicitly gauge-fixed.
  • Loop-group boundary conditions yield boundary actions for postcarrollian JT and CGHS; the JT boundary action reduces by inverse Higgs to a Schwarzian-type action with twisted warped transformations.
  • In 3d, Brown-Henneaux-like boundary conditions define integrable charges whose asymptotic algebra (6.48) has central extensions and contains the postcarrollian algebra as its wedge subalgebra.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the 2d generality claim survives, the same deformation-classification logic might organize all higher-order corrections in the $c^2$ expansion, giving a hierarchy of postcarrollian theories rather than an isolated first-order correction.
  • The $X_M\neq 0$ cosmological sector suggests postcarrollian corrections can turn a static Carroll dilaton into a time-dependent one; a direct test would be to track these solutions under resummation of the $c^2$ series to see whether they return to known Lorentzian cosmologies.
  • The 3d asymptotic symmetry algebra with central extensions is a natural candidate for a dual CFT/Carrolian CFT, so a Cardy-type state count of postcarrollian black holes would give a concrete holographic check.
  • One could repeat the expansion around the electric Carroll theory instead of the magnetic one; comparing the two families would show which postcarrollian features are artifacts of the magnetic starting point.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 6 minor

Summary. The paper constructs postcarrollian gravity theories in two, three, and four dimensions by expanding the (A)dS Carroll algebra and its gauge/connection fields in powers of the speed of light. In two dimensions it builds BF-type models for postcarrollian JT and CGHS gravity, then proposes a Poisson-Sigma-model formulation with a generic potential of UV type, claims this is the most general postcarrollian 2d dilaton gravity model, solves the classical equations of motion in two sectors, and derives loop-group and Schwarzian-type boundary actions. In three dimensions it writes a Chern-Simons action for the postcarrollian algebra, performs a spherical reduction to the 2d JT model, proposes Brown-Henneaux-like boundary conditions, and derives an asymptotic symmetry algebra with central terms. In four dimensions it gives a MacDowell-Mansouri-type action and discusses the second-order form and torsion constraints. The central technical inputs are a Lie-algebra expansion and a BRST deformation result imported from prior work on Lorentzian 2d dilaton gravity.

Significance. If correct, the paper provides a systematic and useful toolbox: explicit postcarrollian actions in three spacetime dimensions, a complete solution space for a natural 2d family, boundary actions, and a nontrivial asymptotic symmetry algebra in 3d. The derivations are largely self-contained after the algebraic setup, with no fitting of constants to data, and the solution classification is an explicit check of the model's consistency. The main significance is therefore conditional on the 'most general' claim in 2d and on the completeness of the asymptotic symmetry computation; both points need either proof or careful restatement before the headline claims can be taken at face value.

major comments (2)
  1. [Section 3.1, Eq. (3.5)–(3.8)] The statement 'Using BRST arguments, it can be shown along the lines of [67] that models with Poisson tensor (3.5) are the most general deformation' is load-bearing for the abstract's claim of presenting the most general postcarrollian 2d dilaton gravity model, yet no argument or proof is given. The BRST deformation result in [67] classifies deformations of the three-dimensional Lorentzian target space (X, X_H, X_P), whereas the present target space is five-dimensional, with X_M and X_Z as extra Casimir coordinates and a potential that may depend on X_M, X_Z, and X_H^2 - 2 X_P X_M. It is not automatic that the cohomology computation carries over to this enlarged, rank-two Poisson structure; additional deformation terms involving the new fields could in principle survive the master-equation/BRST-closure conditions. I request either a proof, or a precise statement of the deformation theorem and its hypotheses, or a softening of the 'most general' claim throughout the abstract and Section 3.1.
  2. [Section 6.1.2, Eq. (6.48)] The derivation of the asymptotic symmetry algebra is too compressed to verify the central-extension claim. The paper jumps from the charge formula (6.43) and on-shell conditions (6.44) to the mode algebra (6.48) via the relation δ_{ε1} Q[ε2] = {Q[ε1], Q[ε2]}, without showing the Poisson brackets among the modes. Moreover, in (6.48) every central term is proportional to the same generator L, so the statement in Section 7 that the algebra 'features two independent central extensions' is not supported as written; the displayed algebra has at most one central charge. Please provide the explicit bracket computation and clarify the number of independent central extensions.
minor comments (6)
  1. [Section 3.1] The sentence 'The fields A_I are one-forms on the base manifold and one-forms on the target space' is imprecise: A_I are one-forms on the base manifold and functions of the target-space coordinates X_I, while X_I are coordinates on the target space.
  2. [Section 3.1, Eq. (3.9)] The bulk action (3.9) omits the overall normalization k/2π that appears in the BF actions (2.12) and (2.18); please state the convention used in the PSM action.
  3. [Section 4.2] In the X_M ≠ 0 sector the paper sets X_M = -1 'without loss of generality' but does not explain the field redefinition that achieves this for a general constant Casimir value; please justify or soften this step.
  4. [Section 6.1.2] The notation in (6.47)–(6.48) uses L both for a zero-mode generator and for the central element appearing in the brackets; please distinguish the central generator from the state-dependent function a_L in the boundary connection.
  5. [Section 6.2, Eq. (6.64)] The index placement in the definition of V_ab after (6.64) appears inconsistent with the term V^{ab} e_{b\mu} in (6.64b); please check and correct the index conventions.
  6. [Section 5.2] The sentence about all possible choices of constraints leading to free-particle actions is stated without details of the investigation; a short description of the 'all such combinations we investigated' would help the reader assess the claim.

Circularity Check

1 steps flagged · score 4.0 of 10

The Sec. 3.1 'most general' claim is imported from same-author BRST result [67] without proving the five-field transfer; the rest of the construction is self-contained.

  1. uniqueness imported from authors [Section 3.1, after Eq. (3.6), for the Poisson tensor (3.5) and potential (3.6)]
    "Using BRST arguments, it can be shown along the lines of [67] that models with Poisson tensor (3.5) are the most general deformation."

    The abstract's byproduct claim that the paper presents the most general postcarrollian 2d dilaton gravity model is justified only by invoking [67], a prior paper with overlapping authorship, rather than by a derivation in this text. The present target space has five coordinates (X, XH, XP, XM, XZ) with two Casimir directions and allowed potential dependence (3.6)/(3.8), whereas the BRST uniqueness result in [67] concerns the standard Lorentzian dilaton-gravity target. No argument is supplied that the deformation cohomology is unchanged by the two added directions and the enlarged potential class, so the 'most general' wording is a load-bearing import from a self-citation, not a demonstrated consequence.

full rationale

Most of the paper's derivation chain is independent of its own outputs. The postcarrollian algebra (1.6) is computed from the explicit expansion (1.2)-(1.4); the 2d BF/PSM actions (2.12), (2.18), and (3.9) are evaluated from the algebra and their equations of motion are solved in Sec. 4; the 3d Chern-Simons action (6.13), the boundary-condition ansatz, the charge formula, and the mode algebra (6.48) are derived from the stated brackets and standard asymptotic-symmetry methods; the 4d MacDowell-Mansouri action (6.60) is likewise an algebraic construction. No parameter is fitted to data. The one place where a central advertised result reduces to a citation rather than to the paper's own computation is Sec. 3.1: the 'most general deformation' assertion is justified by 'along the lines of [67]', a same-author paper, without demonstration that the BRST cohomology result transfers from the Lorentzian three-dimensional target to the five-dimensional postcarrollian target with Casimir directions XM, XZ and potential (3.6)/(3.8). The Schwarzian boundary action (5.45) is transparently copied from [51] and is therefore an ordinary attribution, not a disguised derivation. Since the main model construction and solution space are self-contained and the circularity is confined to the imported uniqueness claim, the score is 4.

Assumptions & free parameters 4 free parameters · 3 assumptions · 2 invented entities

The central construction rests on the post-Carrollian algebra (1.6), its invariant bilinear forms, and standard BF/CS/MM technology. The general 2d model introduces arbitrary potentials V(X), U(X) and hand-chosen bilinear form normalizations. The 'most general' claim additionally assumes the BRST deformation theorem from [67] transfers to this setting, which is not demonstrated. Auxiliary fields are added to the Lorentzian action to engineer the c->0 limit.

free parameters (4)
  • Potential function V(X) = arbitrary (e.g., V=Lambda X for JT, V=X_Z for CGHS)
    Defines the general 2d dilaton gravity model (3.9)/(3.8). The paper treats it as arbitrary input; no fit.
  • Potential function U(X) = arbitrary (0 for JT/CGHS)
    Appears in the general potential V(X) - (X_H^2/2 - X_M X_P) U(X); arbitrary input model data.
  • Bilinear form coefficients (mu, nu) in 2d = mu=1 for JT; mu=1/Lambda, nu=-Lambda for CGHS
    Chosen by hand to make the invariant metric non-degenerate (eqs. (2.11), (2.17)).
  • Bilinear form coefficients rho0, rho1 in 3d/4d = rho1 != 0, rho0 arbitrary
    Chosen to define non-degenerate invariant bilinear forms (6.4), (6.50); rho0=0 in the 3d boundary analysis (section 6.1.2).
assumptions (3)
  • standard math The postcarrollian algebra (1.6) satisfies the Jacobi identities
    The commutators are asserted without proof; consistency is expected because the algebra is a Lie algebra expansion or quotient of the (A)dS Carroll algebra from [59], but the specific verification is not included.
  • standard math The invariant bilinear forms (2.11), (2.17), (6.4), (6.50) are non-degenerate and ad-invariant
    Required for the BF, Chern-Simons, and Macdowell-Mansouri actions; the paper lists the forms but does not prove ad-invariance.
  • ad hoc to paper The BRST deformation theorem of [67] extends to the postcarrollian Poisson tensor (3.5)
    Used to claim the 2d model is the most general; not proved in this paper. Quote: 'Using BRST arguments, it can be shown along the lines of [67]...' (Section 3.1).
invented entities (2)
  • Postcarrollian algebra generators L, M_a, K_a, S_ab (including 2d central generators M, Z)
    purpose: Realize subleading corrections in the speed-of-light expansion (1.2)-(1.4); they generate the postcarrollian gauge connection (1.5) and all the models.
    New algebraic elements introduced for the expansion; no empirical handle outside the paper. The 2d M and Z generators were previously studied in [51,52].
  • Auxiliary Abelian BF sectors (Phi, Psi; eta, zeta)
    purpose: Added to the Lorentzian 2d dilaton gravity action (3.14) to make the c->0 limit yield the postcarrollian action (3.20).
    These fields are an input to construct the limit, not a consequence of standard gravity.

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Cite this review

Pith. "Pith review of Postcarrollian gravity." pith.science (2026). https://pith.science/paper/FA7U4PGG

@misc{pith2026250416162,
  author       = {Pith},
  title        = {Pith review of: Postcarrollian gravity},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FA7U4PGG}},
  note         = {Machine review of arXiv:2504.16162}
}
read the original abstract

We construct postcarrollian gravity models in two, three, and four spacetime dimensions by applying algebraic expansion methods. As a byproduct, we present the most general postcarrollian 2d dilaton gravity model, construct its solutions and discuss some boundary aspects, including Schwarzian-type boundary actions. In 3d, we propose Brown-Henneaux-like boundary conditions, generalizing a corresponding Carrollian analysis, and derive the postcarrollian asymptotic symmetry algebra with its central extensions.

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Forward citations

Cited by 2 Pith papers

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Reference graph

Works this paper leans on

100 extracted references · 3 canonical work pages · cited by 2 Pith papers

  1. [67]

    Generalized dilaton gravity in 2d,

    D. Grumiller, R. Ruzziconi, and C. Zwikel, “Generalized dilaton gravity in 2d,”SciPost Phys.12(2022), no. 1, 032,2109.03266

    arXiv 2022

  2. [1]

    Une nouvelle limite non-relativiste du groupe de Poincaré,

    J.-M. Lévy-Leblond, “Une nouvelle limite non-relativiste du groupe de Poincaré,”A. Inst. Henri Poincaré III 1(1965)

    1965

  3. [2]

    On an analogue of the galilei group,

    N. D. SenGupta, “On an analogue of the galilei group,”Il Nuovo Cimento A Series 1044 (1966), no. 2, 512–517

    1966

  4. [3]

    Ondes et radiations gravitationnelles,

    J.-M. Souriau, “Ondes et radiations gravitationnelles,”Colloques Internationaux du CNRS 220 (1973) 243–256

    1973

  5. [4]

    Memory effect & Carroll symmetry, 50 years later,

    M. Elbistan, P. M. Zhang, and P. A. Horvathy, “Memory effect & Carroll symmetry, 50 years later,”Annals Phys.459 (2023) 169535,2306.14271

    arXiv 2023

  6. [5]

    Geometry of Zero Signature Space-times,

    M. Henneaux, “Geometry of Zero Signature Space-times,”Bull. Soc. Math. Belg.31 (1979) 47–63

    1979

  7. [6]

    Quantification hamiltonienne du champ de gravitation : une nouvelle approche,

    M. Henneaux, “Quantification hamiltonienne du champ de gravitation : une nouvelle approche,”Bulletin de la Classe des sciences68 (1982), no. 1, 940–971

    1982

  8. [7]

    Cosmological billiards,

    T. Damour, M. Henneaux, and H. Nicolai, “Cosmological billiards,”Class. Quant. Grav.20 (2003) R145–R200,hep-th/0212256

    arXiv 2003

Show all 100 references
  1. [8]

    Carroll Symmetry, Dark Energy and Inflation,

    J. de Boer, J. Hartong, N. A. Obers, W. Sybesma, and S. Vandoren, “Carroll Symmetry, Dark Energy and Inflation,”Front. in Phys.10(2022) 810405,2110.02319

    2022 arXiv

  2. [9]

    Tachyon condensates, Carrollian contraction of Lorentz group, and fundamental strings,

    G. Gibbons, K. Hashimoto, and P. Yi, “Tachyon condensates, Carrollian contraction of Lorentz group, and fundamental strings,”JHEP09 (2002) 061,hep-th/0209034

    2002 arXiv

  3. [10]

    Classical central extension for asymptotic symmetries at null infinity in three spacetime dimensions,

    G. Barnich and G. Compère, “Classical central extension for asymptotic symmetries at null infinity in three spacetime dimensions,”Class.Quant.Grav.24(2007) F15–F23, gr-qc/0610130

    2007 arXiv

  4. [11]

    Correspondence between Asymptotically Flat Spacetimes and Nonrelativistic Conformal Field Theories,

    A. Bagchi, “Correspondence between Asymptotically Flat Spacetimes and Nonrelativistic Conformal Field Theories,”Phys.Rev.Lett.105 (2010) 171601

    2010

  5. [12]

    Flat-Space Chiral Gravity,

    A. Bagchi, S. Detournay, and D. Grumiller, “Flat-Space Chiral Gravity,”Phys.Rev.Lett.109 (2012) 151301,1208.1658

    2012 arXiv

  6. [13]

    Holography of 3d Flat Cosmological Horizons,

    A. Bagchi, S. Detournay, R. Fareghbal, and J. Simon, “Holography of 3d Flat Cosmological Horizons,”Phys. Rev. Lett.110 (2013) 141302,1208.4372

    2013 arXiv

  7. [14]

    Entropy of three-dimensional asymptotically flat cosmological solutions,

    G. Barnich, “Entropy of three-dimensional asymptotically flat cosmological solutions,” JHEP1210 (2012) 095,1208.4371

    2012 arXiv

  8. [15]

    Dual dynamics of three dimensional asymptotically flat Einstein gravity at null infinity,

    G. Barnich and H. A. Gonzalez, “Dual dynamics of three dimensional asymptotically flat Einstein gravity at null infinity,”JHEP1305(2013) 016,1303.1075

    2013 arXiv

  9. [16]

    Conformal Carroll groups and BMS symmetry,

    C. Duval, G. W. Gibbons, and P. A. Horvathy, “Conformal Carroll groups and BMS symmetry,”Class. Quant. Grav.31(2014) 092001,1402.5894. 31 Postcarrollian gravity Daniel Grumiller

    2014 arXiv

  10. [17]

    Entanglement entropy in Galilean conformal field theories and flat holography,

    A. Bagchi, R. Basu, D. Grumiller, and M. Riegler, “Entanglement entropy in Galilean conformal field theories and flat holography,”Phys.Rev.Lett.114 (2015), no. 11, 111602, 1410.4089

    2015 arXiv

  11. [18]

    Carrollian Perspective on Celestial Holography,

    L. Donnay, A. Fiorucci, Y. Herfray, and R. Ruzziconi, “Carrollian Perspective on Celestial Holography,”Phys. Rev. Lett.129 (2022), no. 7, 071602,2202.04702

    2022 arXiv

  12. [19]

    Scattering Amplitudes: Celestial and Carrollian,

    A. Bagchi, S. Banerjee, R. Basu, and S. Dutta, “Scattering Amplitudes: Celestial and Carrollian,”Phys. Rev. Lett.128 (2022), no. 24, 241601,2202.08438

    2022 arXiv

  13. [20]

    Perfect Fluids,

    J. de Boer, J. Hartong, N. A. Obers, W. Sybesma, and S. Vandoren, “Perfect Fluids,”SciPost Phys.5 (2018), no. 1, 003,1710.04708

    2018 arXiv

  14. [21]

    Covariant Galilean versus Carrollian hydrodynamics from relativistic fluids,

    L. Ciambelli, C. Marteau, A. C. Petkou, P. M. Petropoulos, and K. Siampos, “Covariant Galilean versus Carrollian hydrodynamics from relativistic fluids,”Class. Quant. Grav.35 (2018), no. 16, 165001,1802.05286

    2018 arXiv

  15. [22]

    Near-horizon Carroll symmetry and black hole Love numbers,

    R. F. Penna, “Near-horizon Carroll symmetry and black hole Love numbers,”1812.05643

    arXiv

  16. [23]

    Carrollian Physics at the Black Hole Horizon,

    L. Donnay and C. Marteau, “Carrollian Physics at the Black Hole Horizon,”Class. Quant. Grav.36(2019), no. 16, 165002,1903.09654

    2019 arXiv

  17. [24]

    Carroll Structures, Null GeometryandConformalIsometries,

    L. Ciambelli, R. G. Leigh, C. Marteau, and P. M. Petropoulos, “Carroll Structures, Null GeometryandConformalIsometries,” Phys.Rev.D 100(2019),no.4,046010, 1905.02221

    2019 arXiv

  18. [25]

    Non-linear black hole dynamics and Carrollian fluids,

    J. Redondo-Yuste and L. Lehner, “Non-linear black hole dynamics and Carrollian fluids,” JHEP02 (2023) 240,2212.06175

    2023 arXiv

  19. [26]

    Carrollian hydrodynamics and symplectic structure on stretched horizons,

    L. Freidel and P. Jai-akson, “Carrollian hydrodynamics and symplectic structure on stretched horizons,”JHEP05 (2024) 135,2211.06415

    2024 arXiv

  20. [27]

    Carrollian motion in magnetized black hole horizons,

    F. Gray, D. Kubiznak, T. R. Perche, and J. Redondo-Yuste, “Carrollian motion in magnetized black hole horizons,”Phys. Rev. D107 (2023), no. 6, 064009,2211.13695

    2023 arXiv

  21. [28]

    Flat holography and Carrollian fluids,

    L. Ciambelli, C. Marteau, A. C. Petkou, P. M. Petropoulos, and K. Siampos, “Flat holography and Carrollian fluids,”JHEP07 (2018) 165,1802.06809

    2018 arXiv

  22. [29]

    Carrollian and celestial spaces at infinity,

    J. Figueroa-O’Farrill, E. Have, S. Prohazka, and J. Salzer, “Carrollian and celestial spaces at infinity,”JHEP 09(2022) 007,2112.03319

    2022 arXiv

  23. [30]

    Carrollian manifolds and null infinity: a view from Cartan geometry,

    Y. Herfray, “Carrollian manifolds and null infinity: a view from Cartan geometry,”Class. Quant. Grav.39(2022), no. 21, 215005,2112.09048

    2022 arXiv

  24. [31]

    Ehlers, Carroll, charges and dual charges,

    N. Mittal, P. M. Petropoulos, D. Rivera-Betancour, and M. Vilatte, “Ehlers, Carroll, charges and dual charges,”JHEP07 (2023) 065,2212.14062

    2023 arXiv

  25. [32]

    Fractons, dipole symmetries and curved spacetime,

    L. Bidussi, J. Hartong, E. Have, J. Musaeus, and S. Prohazka, “Fractons, dipole symmetries and curved spacetime,”SciPost Phys.12(2022), no. 6, 205,2111.03668. 32 Postcarrollian gravity Daniel Grumiller

    2022 arXiv

  26. [33]

    Hall effects in Carroll dynamics,

    L. Marsot, P. M. Zhang, M. Chernodub, and P. A. Horvathy, “Hall effects in Carroll dynamics,”Phys. Rept.1028(2023) 1–60,2212.02360

    2023 arXiv

  27. [34]

    Carroll/fracton particles and their correspondence,

    J. Figueroa-O’Farrill, A. Pérez, and S. Prohazka, “Carroll/fracton particles and their correspondence,”JHEP06(2023) 207,2305.06730

    2023 arXiv

  28. [35]

    Mapping relativistic to ultra/non-relativistic conformal symmetries in 2D and finite √︁ 𝑇𝑇 deformations,

    P. Rodríguez, D. Tempo, and R. Troncoso, “Mapping relativistic to ultra/non-relativistic conformal symmetries in 2D and finite √︁ 𝑇𝑇 deformations,”JHEP11 (2021) 133, 2106.09750

    2021 arXiv

  29. [36]

    Magic fermions: Carroll and flat bands,

    A. Bagchi, A. Banerjee, R. Basu, M. Islam, and S. Mondal, “Magic fermions: Carroll and flat bands,”JHEP03 (2023) 227,2211.11640

    2023 arXiv

  30. [37]

    Tensionless Strings from Worldsheet Symmetries,

    A. Bagchi, S. Chakrabortty, and P. Parekh, “Tensionless Strings from Worldsheet Symmetries,”JHEP01 (2016) 158,1507.04361

    2016 arXiv

  31. [38]

    Horizon strings as 3D black hole microstates,

    A. Bagchi, D. Grumiller, S. Sheikh-Jabbari, and M. M. Sheikh-Jabbari, “Horizon strings as 3D black hole microstates,”SciPost Phys.15(2023), no. 5, 210,2210.10794

    2023 arXiv

  32. [39]

    Strings near black holes are Carrollian,

    A. Bagchi, A. Banerjee, J. Hartong, E. Have, K. S. Kolekar, and M. Mandlik, “Strings near black holes are Carrollian,”Phys. Rev. D110 (2024), no. 8, 086009,2312.14240

    2024 arXiv

  33. [40]

    Carroll black holes,

    F. Ecker, D. Grumiller, J. Hartong, A. Pérez, S. Prohazka, and R. Troncoso, “Carroll black holes,”SciPost Phys.15(2023), no. 6, 245,2308.10947

    2023

  34. [41]

    Spacetime Subsystem Symmetries,

    S. A. Baig, J. Distler, A. Karch, A. Raz, and H.-Y. Sun, “Spacetime Subsystem Symmetries,” 2303.15590

    arXiv

  35. [42]

    Carrollian origin of spacetime subsystem symmetry,

    O. Kasikci, M. Ozkan, and Y. Pang, “Carrollian origin of spacetime subsystem symmetry,” Phys. Rev. D108 (2023), no. 4, 045020,2304.11331

    2023 arXiv

  36. [43]

    Carroll swiftons,

    F. Ecker, D. Grumiller, M. Henneaux, and P. Salgado-Rebolledo, “Carroll swiftons,”Phys. Rev. D110 (2024), no. 4, L041901,2403.00544

    2024 arXiv

  37. [44]

    Boundary Carrollian Conformal Field Theories and Open Null Strings,

    A. Bagchi, P. Chakraborty, S. Chakrabortty, S. Fredenhagen, D. Grumiller, and P. Pandit, “Boundary Carrollian Conformal Field Theories and Open Null Strings,”Phys. Rev. Lett. 134 (2025), no. 7, 071604,2409.01094

    2025 arXiv

  38. [45]

    Carroll in Shallow Water,

    A. Bagchi, A. Banerjee, S. Mondal, and S. Sarkar, “Carroll in Shallow Water,”2411.04190

    arXiv

  39. [46]

    Carroll at Phase Separation,

    S. Biswas, A. Dubey, S. Mondal, A. Banerjee, A. Kundu, and A. Bagchi, “Carroll at Phase Separation,” 2501.16426

    arXiv

  40. [47]

    Carroll stories,

    J. de Boer, J. Hartong, N. A. Obers, W. Sybesma, and S. Vandoren, “Carroll stories,”JHEP 09(2023) 148,2307.06827

    2023 arXiv

  41. [48]

    Dynamics of Carrollian scalar fields,

    L. Ciambelli, “Dynamics of Carrollian scalar fields,”Class. Quant. Grav.41(2024), no. 16, 165011, 2311.04113. 33 Postcarrollian gravity Daniel Grumiller

    2024 arXiv

  42. [49]

    A Conformal Approach to Carroll Gravity,

    E. A. Bergshoeff, P. Concha, O. Fierro, E. Rodríguez, and J. Rosseel, “A Conformal Approach to Carroll Gravity,”2412.17752

    arXiv

  43. [50]

    Gauging the Carroll Algebra and Ultra-Relativistic Gravity,

    J. Hartong, “Gauging the Carroll Algebra and Ultra-Relativistic Gravity,”JHEP08 (2015) 069, 1505.05011

    2015 arXiv

  44. [51]

    Limits of JT gravity,

    D. Grumiller, J. Hartong, S. Prohazka, and J. Salzer, “Limits of JT gravity,”JHEP02 (2021) 134, 2011.13870

    2021 arXiv

  45. [52]

    Non-relativistic and Carrollian limits of Jackiw-Teitelboim gravity,

    J. Gomis, D. Hidalgo, and P. Salgado-Rebolledo, “Non-relativistic and Carrollian limits of Jackiw-Teitelboim gravity,”JHEP05(2021) 162,2011.15053

    2021 arXiv

  46. [53]

    Electric/magnetic Newton-Hooke and Carroll Jackiw-Teitelboim gravity,

    L. Avilés, J. Gomis, D. Hidalgo, and J. Zanelli, “Electric/magnetic Newton-Hooke and Carroll Jackiw-Teitelboim gravity,”JHEP02(2023) 061,2211.03633

    2023 arXiv

  47. [54]

    Carroll Expansion of General Relativity,

    D. Hansen, N. A. Obers, G. Oling, and B. T. Søgaard, “Carroll Expansion of General Relativity,”SciPost Phys.13(2022), no. 3, 055,2112.12684

    2022 arXiv

  48. [55]

    Conformal (super)gravities with several gravitons,

    N. Boulanger, M. Henneaux, and P. van Nieuwenhuizen, “Conformal (super)gravities with several gravitons,”JHEP01(2002) 035,hep-th/0201023

    2002 arXiv

  49. [56]

    Generating Lie and gauge free differential (super)algebras by expanding Maurer-Cartan forms and Chern-Simons supergravity,

    J. A. de Azcarraga, J. M. Izquierdo, M. Picon, and O. Varela, “Generating Lie and gauge free differential (super)algebras by expanding Maurer-Cartan forms and Chern-Simons supergravity,”Nucl. Phys. B662 (2003) 185–219,hep-th/0212347

    2003 arXiv

  50. [57]

    Expanding Lie (super)algebras through Abelian semigroups,

    F. Izaurieta, E. Rodriguez, and P. Salgado, “Expanding Lie (super)algebras through Abelian semigroups,”J. Math. Phys.47 (2006) 123512,hep-th/0606215

    2006 arXiv

  51. [58]

    Lie Algebra Expansions and Actions for Non-Relativistic Gravity,

    E. Bergshoeff, J. M. Izquierdo, T. Ortín, and L. Romano, “Lie Algebra Expansions and Actions for Non-Relativistic Gravity,”JHEP08(2019) 048,1904.08304

    2019 arXiv

  52. [59]

    Newton-Hooke/Carrollian expansions of (A)dS and Chern-Simons gravity,

    J. Gomis, A. Kleinschmidt, J. Palmkvist, and P. Salgado-Rebolledo, “Newton-Hooke/Carrollian expansions of (A)dS and Chern-Simons gravity,”JHEP02 (2020) 009,1912.07564

    2020 arXiv

  53. [60]

    Possible kinematics,

    H. Bacry and J. Levy-Leblond, “Possible kinematics,”J. Math. Phys.9(1968) 1605–1614

    1968

  54. [61]

    Limits of three-dimensional gravity and metric kinematical Lie algebras in any dimension,

    J. Matulich, S. Prohazka, and J. Salzer, “Limits of three-dimensional gravity and metric kinematical Lie algebras in any dimension,”JHEP07 (2019) 118,1903.09165

    2019 arXiv

  55. [62]

    Gauge invariant formulations of lineal gravity,

    D. Cangemi and R. Jackiw, “Gauge invariant formulations of lineal gravity,”Phys. Rev. Lett. 69(1992) 233–236,hep-th/9203056

    1992 arXiv

  56. [63]

    Flat space holography and the complex Sachdev-Ye-Kitaev model,

    H. Afshar, H. A. González, D. Grumiller, and D. Vassilevich, “Flat space holography and the complex Sachdev-Ye-Kitaev model,”Phys. Rev. D101 (2020), no. 8, 086024,1911.05739

    2020 arXiv

  57. [64]

    Carroll versus Galilei Gravity,

    E. Bergshoeff, J. Gomis, B. Rollier, J. Rosseel, and T. ter Veldhuis, “Carroll versus Galilei Gravity,”JHEP03 (2017) 165,1701.06156. 34 Postcarrollian gravity Daniel Grumiller

    2017 arXiv

  58. [65]

    Magnetic Carrollian gravity from the Carroll algebra,

    A. Campoleoni, M. Henneaux, S. Pekar, A. Pérez, and P. Salgado-Rebolledo, “Magnetic Carrollian gravity from the Carroll algebra,”JHEP09(2022) 127,2207.14167

    2022 arXiv

  59. [66]

    Evanescent black holes,

    C. G. Callan, Jr., S. B. Giddings, J. A. Harvey, and A. Strominger, “Evanescent black holes,” Phys. Rev.D45 (1992) 1005–1009,hep-th/9111056

    1992 arXiv

  60. [68]

    Two-dimensional gravity and nonlinear gauge theory,

    N. Ikeda, “Two-dimensional gravity and nonlinear gauge theory,”Annals Phys.235 (1994) 435–464, hep-th/9312059

    1994 arXiv

  61. [69]

    Poisson structure induced (topological) field theories,

    P. Schaller and T. Strobl, “Poisson structure induced (topological) field theories,”Mod. Phys. Lett.A9(1994) 3129–3136,hep-th/9405110

    1994 arXiv

  62. [70]

    Dilaton gravity in two dimensions,

    D. Grumiller, W. Kummer, and D. V. Vassilevich, “Dilaton gravity in two dimensions,”Phys. Rept.369 (2002) 327–429,hep-th/0204253

    2002 arXiv

  63. [71]

    Three-dimensional Spin-3 Theories Based on General Kinematical Algebras,

    E. Bergshoeff, D. Grumiller, S. Prohazka, and J. Rosseel, “Three-dimensional Spin-3 Theories Based on General Kinematical Algebras,”JHEP 01(2017) 114,1612.02277

    2017 arXiv

  64. [72]

    Towards a bulk description of higher spin SYK,

    H. A. González, D. Grumiller, and J. Salzer, “Towards a bulk description of higher spin SYK,”JHEP05 (2018) 083,1802.01562

    2018 arXiv

  65. [73]

    Menagerie of AdS2 boundary conditions,

    D. Grumiller, R. McNees, J. Salzer, C. Valcárcel, and D. Vassilevich, “Menagerie of AdS2 boundary conditions,”JHEP 10(2017) 203,1708.08471

    2017 arXiv

  66. [74]

    Solving the Schwarzian via the Conformal Bootstrap,

    T. G. Mertens, G. J. Turiaci, and H. L. Verlinde, “Solving the Schwarzian via the Conformal Bootstrap,”JHEP08 (2017) 136,1705.08408

    2017 arXiv

  67. [75]

    The Schwarzian theory — origins,

    T. G. Mertens, “The Schwarzian theory — origins,”JHEP05(2018) 036,1801.09605

    2018 arXiv

  68. [76]

    Quantum field theory and the Jones polynomial,

    E. Witten, “Quantum field theory and the Jones polynomial,”Commun. Math. Phys.121 (1989) 351

    1989

  69. [77]

    Remarks on the Canonical Quantization of the Chern-Simons-Witten Theory,

    S. Elitzur, G. W. Moore, A. Schwimmer, and N. Seiberg, “Remarks on the Canonical Quantization of the Chern-Simons-Witten Theory,”Nucl. Phys.B326(1989) 108–134

    1989

  70. [78]

    Central Charges in the Canonical Realization of Asymptotic Symmetries: An Example from Three-Dimensional Gravity,

    J. D. Brown and M. Henneaux, “Central Charges in the Canonical Realization of Asymptotic Symmetries: An Example from Three-Dimensional Gravity,”Commun. Math. Phys.104 (1986) 207–226

    1986

  71. [79]

    The Asymptotic dynamics of three-dimensional Einstein gravity with a negative cosmological constant,

    O. Coussaert, M. Henneaux, and P. van Driel, “The Asymptotic dynamics of three-dimensional Einstein gravity with a negative cosmological constant,” Class.Quant.Grav.12(1995) 2961–2966,gr-qc/9506019

    1995 arXiv

  72. [80]

    Remarks on the Sachdev-Ye-Kitaev model,

    J. Maldacena and D. Stanford, “Remarks on the Sachdev-Ye-Kitaev model,”Phys. Rev. D94 (2016), no. 10, 106002,1604.07818. 35 Postcarrollian gravity Daniel Grumiller

    2016 arXiv

  73. [81]

    AdS2 holography and the SYK model,

    G. Sárosi, “AdS2 holography and the SYK model,”PoSModave2017(2018) 001, 1711.08482

    2018 arXiv

  74. [82]

    NotesonthecomplexSachdev-Ye-Kitaev model,

    Y.Gu, A.Kitaev, S.Sachdev, andG.Tarnopolsky, “NotesonthecomplexSachdev-Ye-Kitaev model,”JHEP02 (2020) 157,1910.14099

    2020 arXiv

  75. [83]

    Schwarzian mechanics via nonlinear realizations,

    A. Galajinsky, “Schwarzian mechanics via nonlinear realizations,”Phys. Lett. B795(2019) 277–280, 1905.01935

    2019 arXiv

  76. [84]

    Near-Horizon Geometry and Warped Conformal Symmetry,

    H. Afshar, S. Detournay, D. Grumiller, and B. Oblak, “Near-Horizon Geometry and Warped Conformal Symmetry,”JHEP03(2016) 187,1512.08233

    2016 arXiv

  77. [85]

    Warped Schwarzian theory,

    H. R. Afshar, “Warped Schwarzian theory,”JHEP 02(2020) 126,1908.08089

    2020 arXiv

  78. [86]

    Flat JT gravity and the BMS-Schwarzian,

    H. Afshar and B. Oblak, “Flat JT gravity and the BMS-Schwarzian,”JHEP 11(2022) 172, 2112.14609

    2022 arXiv

  79. [87]

    AdS Carroll Chern-Simons supergravity in 2 + 1 dimensions and its flat limit,

    L. Ravera, “AdS Carroll Chern-Simons supergravity in 2 + 1 dimensions and its flat limit,” Phys. Lett. B795 (2019) 331–338,1905.00766

    2019 arXiv

  80. [88]

    3D Carrollian gravity from 2D Euclidean symmetry,

    P. Concha, E. Rodríguez, and S. Salgado, “3D Carrollian gravity from 2D Euclidean symmetry,” 2501.00205

    arXiv

  81. [89]

    Non-Relativistic Gravity and its Coupling to Matter,

    D. Hansen, J. Hartong, and N. A. Obers, “Non-Relativistic Gravity and its Coupling to Matter,”JHEP06(2020) 145,2001.10277

    2020 arXiv

  82. [90]

    Relating black holes in two-dimensions and three- dimensions,

    A. Achucarro and M. E. Ortiz, “Relating black holes in two-dimensions and three- dimensions,”Phys. Rev.D48(1993) 3600–3605,hep-th/9304068

    1993 arXiv

  83. [91]

    Most general AdS3 boundary conditions,

    D. Grumiller and M. Riegler, “Most general AdS3 boundary conditions,”JHEP10(2016) 023, 1608.01308

    2016 arXiv

  84. [92]

    Most general flat space boundary conditions in three-dimensional Einstein gravity,

    D. Grumiller, W. Merbis, and M. Riegler, “Most general flat space boundary conditions in three-dimensional Einstein gravity,”Class. Quant. Grav.34(2017), no. 18, 184001, 1704.07419

    2017 arXiv

  85. [93]

    Sheikh-Jabbari, BlackHolePhysics: FromCollapsetoEvaporation

    D.GrumillerandM.M. Sheikh-Jabbari, BlackHolePhysics: FromCollapsetoEvaporation . Grad.Texts Math. Springer, 11, 2022

    2022

  86. [94]

    Carroll contractions of Lorentz-invariant theories,

    M. Henneaux and P. Salgado-Rebolledo, “Carroll contractions of Lorentz-invariant theories,”JHEP11(2021) 180,2109.06708

    2021 arXiv

  87. [95]

    Newtonian Gravity and the Bargmann Algebra,

    R. Andringa, E. Bergshoeff, S. Panda, and M. de Roo, “Newtonian Gravity and the Bargmann Algebra,”Class. Quant. Grav.28 (2011) 105011,1011.1145

    2011 arXiv

  88. [96]

    Asymptotic symmetries in Carrollian theories of gravity,

    A. Pérez, “Asymptotic symmetries in Carrollian theories of gravity,”JHEP 12(2021) 173, 2110.15834

    2021 arXiv

  89. [97]

    Asymptotic symmetries in Carrollian theories of gravity with a negative cosmological constant,

    A. Pérez, “Asymptotic symmetries in Carrollian theories of gravity with a negative cosmological constant,”JHEP09(2022) 044,2202.08768. 36 Postcarrollian gravity Daniel Grumiller

    2022 arXiv

  90. [98]

    AdS3 Carroll gravity: asymptotic symmetries and C-thermal configurations,

    L. Avilés, O. Fuentealba, D. Hidalgo, and P. Rodríguez, “AdS3 Carroll gravity: asymptotic symmetries and C-thermal configurations,”2503.18818

    arXiv

  91. [99]

    Tantum gravity,

    F. Ecker, A. Fiorucci, and D. Grumiller, “Tantum gravity,”Phys. Rev. D111 (2025), no. 2, L021901, 2501.00095

    2025 arXiv

  92. [100]

    Thermodynamics of black holes in two (and higher) dimensions,

    D. Grumiller and R. McNees, “Thermodynamics of black holes in two (and higher) dimensions,”JHEP04 (2007) 074,hep-th/0703230. 37

    2007 arXiv

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