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A Hamiltonian analysis of the most general Carroll-invariant Lagrangian from the Holst action identifies its full constraint structure, gauge symmetries, and Ashtekar-like variables.

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2026-06-26 04:09 UTC pith:VP7WCTUN

load-bearing objection The paper runs a standard Hamiltonian analysis on the Carroll-invariant Holst action and introduces Ashtekar-like variables for the magnetic regime, which is useful but incremental.

arxiv 2606.26799 v1 pith:VP7WCTUN submitted 2026-06-25 gr-qc

From Holst to Carroll Gravity, a Hamiltonian point of view

J. Fernando Barbero G , Juan Margalef-Bentabol , Valle Varo , Eduardo J.S. Villase\~nor This is my paper
classification gr-qc
keywords Carroll gravityHolst actionHamiltonian analysisconstraint structuregauge symmetriesAshtekar variablesCartan geometryultrarelativistic gravity
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper performs a Hamiltonian analysis of gravity in the Carrollian regime, an ultrarelativistic limit relevant to asymptotically flat spacetimes, horizon dynamics, and condensed matter systems. It starts from the most general Carroll-invariant Lagrangian that can be derived from the Holst action and uses Cartan geometry tools to guide the work. The analysis determines the complete constraint structure, characterizes the gauge symmetries, obtains the Hamiltonian vector fields, and introduces Ashtekar-like variables in the magnetic Carrollian regime. It also examines an analog of the time gauge from the standard Holst analysis in general relativity.

Core claim

We present a comprehensive Hamiltonian analysis of the most general Carroll-invariant Lagrangian that can be derived from the Holst action. To guide the analysis, Cartan geometry tools are used. We identify the full constraint structure of the theory, characterize its gauge symmetries, obtain the explicit form of the Hamiltonian vector fields and introduce Ashtekar-like variables for the magnetic Carrollian regime. We also discuss in detail an analog of the time gauge employed in the Hamiltonian analysis of the Holst action for general relativity.

What carries the argument

The most general Carroll-invariant Lagrangian derived from the Holst action, analyzed through Cartan geometry to extract its constraint structure and symmetries.

Load-bearing premise

The most general Carroll-invariant Lagrangian derivable from the Holst action is the appropriate starting point whose Hamiltonian analysis will capture the relevant physics of the Carrollian regime.

What would settle it

An explicit calculation of the Poisson brackets among the constraints that yields a different algebra from the one obtained in the analysis would falsify the claimed constraint structure.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • The full constraint structure of the theory is identified.
  • Its gauge symmetries are characterized.
  • The explicit form of the Hamiltonian vector fields is obtained.
  • Ashtekar-like variables become available for the magnetic Carrollian regime.
  • An analog of the time gauge can be used in the same manner as in the Holst analysis of general relativity.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The identified variables and symmetries could be applied directly to models of horizon dynamics in the Carrollian limit.
  • Connections to condensed matter systems may become more explicit once the Hamiltonian vector fields are used to generate time evolution.
  • The framework could be tested by extending the analysis to include matter couplings and checking whether new constraints appear.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

0 major / 1 minor

Summary. The paper presents a Hamiltonian analysis of the most general Carroll-invariant Lagrangian derivable from the Holst action. Guided by Cartan geometry, it identifies the full constraint structure, characterizes the gauge symmetries, derives the explicit Hamiltonian vector fields, introduces Ashtekar-like variables in the magnetic Carrollian regime, and discusses an analog of the time gauge used in the standard Holst analysis of general relativity. The work targets applications to asymptotically flat spacetimes, horizon dynamics, and ultrarelativistic limits.

Significance. If the derivations hold, the manuscript supplies a canonical formulation for Carroll gravity that parallels the well-studied Holst/Ashtekar treatment of Lorentzian GR. The explicit constraint algebra, vector fields, and magnetic-regime variables could serve as a foundation for further canonical studies of Carrollian limits, including potential connections to BMS symmetries or condensed-matter analogs. The use of Cartan geometry to select the Lagrangian is a methodological strength.

minor comments (1)
  1. The abstract states that the analysis covers 'the most general Carroll-invariant Lagrangian,' but does not indicate how generality is established or whether additional assumptions (e.g., on the connection or torsion) are imposed; a brief statement in the introduction would clarify the scope.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their summary of the manuscript and for the positive significance assessment. The recommendation is listed as uncertain, yet the report contains no major comments or specific points of concern. We stand by the derivations, constraint analysis, and introduction of Ashtekar-like variables presented in the paper.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper executes a standard Hamiltonian constraint analysis on a Carroll-invariant Lagrangian obtained from the Holst action, guided by Cartan geometry and an analog of the time gauge. No load-bearing step reduces by construction to a fitted parameter, self-defined quantity, or self-citation chain; the constraint structure, gauge symmetries, vector fields, and Ashtekar-like variables are derived directly from the starting action without renaming known results or smuggling ansatze. The central claim remains a formal derivation whose validity is independent of the present paper's own outputs.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides no explicit free parameters, axioms, or invented entities; the analysis is described as deriving from the Holst action via Cartan geometry.

pith-pipeline@v0.9.1-grok · 5651 in / 1167 out tokens · 28507 ms · 2026-06-26T04:09:40.719300+00:00 · methodology

0 comments
read the original abstract

The Carrollian regime of gravity provides a useful ultrarelativistic framework for studying asymptotically flat spacetimes, horizon dynamics, and condensed matter systems. In this paper, we present a comprehensive Hamiltonian analysis of the most general Carroll-invariant Lagrangian that can be derived from the Holst action. To guide the analysis, Cartan geometry tools are used. We identify the full constraint structure of the theory, characterize its gauge symmetries, obtain the explicit form of the Hamiltonian vector fields and introduce Ashtekar-like variables for the magnetic Carrollian regime. We also discuss in detail an analog of the time gauge employed in the Hamiltonian analysis of the Holst action for general relativity.

discussion (0)

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Reference graph

Works this paper leans on

31 extracted references · 1 canonical work pages

  1. [1]

    Donnay and C

    L. Donnay and C. Marteau,Carrollian Physics at the Black Hole HorizonClass. Quan- tum Gravity 36 (2019) 165002

    2019

  2. [2]

    Duval, G

    C. Duval, G. W. Gibbons, and P.A. Horvathy,Conformal Carroll groups and BMS symmetry, Class. Quantum Gravity 31 (2014) 092001

    2014

  3. [3]

    Figueroa-O’Farrill, A

    J. Figueroa-O’Farrill, A. P´ erez, and S. Prohazka,Carroll/fracton particles and their correspondence, JHEP 06 (2023), 207

    2023

  4. [4]

    L´ evy-Leblond,Une nouvelle limite non-relativiste du groupe de Poincar´ e, An- nales de l’I.H.P

    J.-M. L´ evy-Leblond,Une nouvelle limite non-relativiste du groupe de Poincar´ e, An- nales de l’I.H.P. Physique th´ eorique 3 (1965) no. 1, 1–12

    1965

  5. [5]

    N. D. Sen Gupta,On an analogue of the Galilei group, Nuovo Cim. A 44 (1966) 512

    1966

  6. [6]

    Campoleoni, M

    A. Campoleoni, M. Henneaux, S. Pekar, A. P´ erez, and P. Salgado-Rebolledo,Magnetic Carrollian gravity from the Carroll algebra, JHEP 09 (2022) 127

    2022

  7. [7]

    March and J

    E. March and J. Read,A primer on Carroll gravity, Class. Quantum Gravity 42 (2025) 055004

    2025

  8. [8]

    Ecker, D

    F. Ecker, D. Grumiller, M. Henneaux and P. Salgado-Rebolledo,Carroll swiftons, Phys. Rev. D 110 (2024) L041901

    2024

  9. [9]

    de Boer, J

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

    2023

  10. [10]

    E. A. Bergshoeff, P. Concha, O. Fierro, E. Rodr´ ıguez and J. Rosseel,Carroll gravity from the conformal approach, PoS CORFU2024 (2025) 160

    2025

  11. [11]

    Henneaux and P

    M. Henneaux and P. Salgado-Rebolledo,Carroll contractions of Lorentz-invariant the- ories, JHEP11(2021) 180

    2021

  12. [12]

    Holst,Barbero’s Hamiltonian derived from a generalized Hilbert-Palatini action, Phys

    S. Holst,Barbero’s Hamiltonian derived from a generalized Hilbert-Palatini action, Phys. Rev. D 53 (1996) 5966

    1996

  13. [13]

    Figueroa-O’Farrill, E

    J. Figueroa-O’Farrill, E. Have, S. Prohazka, and J. Salzer,The gauging procedure and carrollian gravity, JHEP 09 (2022) 243

    2022

  14. [14]

    Bergshoeff, J

    E. Bergshoeff, J. Gomis, B. Rollier, J. Rosseel and T. ter Veldhuis,Carroll versus Galilei Gravity, JHEP 03 (2017) 165

    2017

  15. [15]

    Ashtekar,New Variables for Classical and Quantum Gravity, Phys

    A. Ashtekar,New Variables for Classical and Quantum Gravity, Phys. Rev. Lett. 57 (1986) 2244

    1986

  16. [16]

    Ashtekar,New Hamiltonian Formulation of General Relativity, Phys

    A. Ashtekar,New Hamiltonian Formulation of General Relativity, Phys. Rev. D 36 (1987) 1587

    1987

  17. [17]

    Sengupta,Hamiltonian form of Carroll gravity, Phys

    S. Sengupta,Hamiltonian form of Carroll gravity, Phys. Rev. D 107 (2023) 024010 22

    2023

  18. [18]

    Barros e S´ a,Hamiltonian analysis of general relativity with the Immirzi parameter, Int

    N. Barros e S´ a,Hamiltonian analysis of general relativity with the Immirzi parameter, Int. J. Mod. Phys. D 10 (2001) 261

    2001

  19. [19]

    DiracLectures on Quantum Mechanics(New York: Dover) 2001

    P.A.M. DiracLectures on Quantum Mechanics(New York: Dover) 2001

    2001

  20. [20]

    Gotay, J.M

    M.J. Gotay, J.M. Nester and G. Hinds,Presymplectic Manifolds and the Dirac–Bergmann Theory of Constraints, J. Math. Phys. 19 (1978) 2388

    1978

  21. [21]

    Gotay,Presymplectic Manifolds, Geometric Constraint Theory and the Dirac- Bergmann Theory of Constraints,Ph.D

    M.J. Gotay,Presymplectic Manifolds, Geometric Constraint Theory and the Dirac- Bergmann Theory of Constraints,Ph.D. thesis, Center for Theoretical Physics of the University of Maryland, 1979

    1979

  22. [22]

    Catren,Geometric foundations of Cartan gauge gravity, Int

    G. Catren,Geometric foundations of Cartan gauge gravity, Int. J. Geom. Methods Mod. Phys.12(04) 1530002

  23. [23]

    R. W. Sharpe,Differential geometry: Cartan’s generalization of Klein’s Erlangen pro- gram, vol. 166, Springer Science & Business Media, 2000

    2000

  24. [24]

    ˇCap and J

    A. ˇCap and J. Slov´ ak,Parabolic geometries I: Background and general theory, vol. 154, American Mathematical Society, 2024

    2024

  25. [25]

    J. F. Barbero G., J. Margalef-Bentabol, A. Vicente-Cano and E. J. S. Villase˜ nor, Husain-Kuchaˇ r model as the Carrollian limit of the Holst term, Class. Quantum Grav- ity 43 (2026) 105006

    2026

  26. [26]

    J. F. Barbero G.,Reality conditions and Ashtekar variables: A Different perspective, Phys. Rev. D 51 (1995) 5498–5506

    1995

  27. [27]

    J. F. Barbero G., M. Basquens y E. J. S. Villase˜ nor,Euclidean self-dual gravity: Ashtekar variables without gauge fixing, Phys. Rev. D 109 (2024) 064047

    2024

  28. [28]

    Husain and K

    V. Husain and K. Kuchaˇ r,General covariance, new variables, and dynamics without dynamics, Phys. Rev. D 42 (1990) 4070–4077

    1990

  29. [29]

    On the intrinsic torsion of spacetime structures

    J. Figueroa-O’Farrill.On the intrinsic torsion of spacetime structures, arXiv preprint. arXiv:2009.01948

    work page Pith review arXiv 2009

  30. [30]

    J. F. Barbero G., B. D´ ıaz, J. Margalef-Bentabol and E. J. S. Villase˜ nor,Hamiltonian Gotay-Nester-Hinds analysis of the parametrized unimodular extension of the Holst action, Phys. Rev. D 103 (2021) 064062

    2021

  31. [31]

    J. F. Barbero G., B. D´ ıaz, J. Margalef-Bentabol and E. J. S. Villase˜ nor,Concise symplectic formulation for tetrad gravity, Phys. Rev. D 103 (2021) 024051 23

    2021