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Fluids on null hypersurfaces and Carrollian hydrodynamics

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Emil Have

High Energy Physics - Theory · Submitted 21 Oct 2026 · 94 references

Pith's verdict: A thorough, mathematically rigorous paper that develops a geometric framework for ideal fluids on null hypersurfaces and identifies a decoupling limit that produces an autonomous thermal Carrollian fluid—the main result holds, though the Goldstone dynamics are asserted rather than fully derived.

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arXiv ID2610.30254 (version 1)
Pith ID6MAMOSYF, Pith's permanent record of this paper and its review
CitationEmil Have. "Fluids on null hypersurfaces and Carrollian hydrodynamics." arXiv:2610.30254 (2026). https://pith.science/paper/6MAMOSYF
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The paper

The paper claims

An infinite-boost limit of a timelike fluid produces an autonomous thermal Carrollian fluid on a null hypersurface, with a finite intrinsic response and an emergent boost Goldstone.

The reading

This paper develops a submanifold calculus for null hypersurfaces and classifies the ideal fluid phases that can live on them, according to whether Carroll boosts and temporal Weyl symmetry are broken. It then asks which of these phases can be realised by restricting ambient causal (timelike or null) fluids to a fixed null hypersurface. The central result is that, in a decoupling limit where the ambient fluid is infinitely boosted while its enthalpy stays finite, the induced Carrollian responses remain finite, the source terms vanish, and the subleading part of the ambient velocity becomes an independent Carroll boost Goldstone field. This proves that a finite-temperature Carrollian fluid with spontaneously broken boosts can emerge from a singular ambient limit, a scenario previously unexplored.

What carries the argument

The key machinery is a null submanifold calculus (sections 2.1–2.2) that, for a fixed embedding, decomposes the ambient metric variation into variations of the induced Carrollian data (τa, hab) and the auxiliary null vector τμ. The projected ambient energy-momentum tensor gives the Carrollian currents (energy current T^a, momentum-stress $T^{{ab}}$) plus a null traction term. The decoupling limit (Section 5.3) is defined by B = −v·U → 0 with w_T finite, so Q = w_T $B^{2}$ → 0; this makes the source term in the tangential Ward identity vanish while the Carroll boost field θ̃^a = s^a/B survives in the finite part of $T^{{ab}}$.

Extended reading notes

Core claim

The paper proves that there exists a decoupling limit of a timelike ideal fluid crossing the leaves of a null foliation that yields an autonomous (unsourced) thermal Carrollian fluid on the leaves. The limit takes the ambient fluid velocity to the null direction (infinite boost) while keeping the enthalpy finite and nonzero, which makes the ambient energy-momentum tensor diverge. However, the induced Carrollian energy-momentum and energy current stay finite because the divergent term projects onto the intrinsic ambiguity (terms proportional to vavb) of the Carrollian momentum-stress tensor. In this limit, the Carroll boost field defined from the ambient velocity becomes a genuine dynamical Goldstone field with an emergent Stueckelberg symmetry, and the intrinsic conservation laws close. The resulting Carrollian fluid is exactly the thermal phase with spontaneously broken Carroll boosts classified in Section 3.1, thus providing a concrete ambient realisation of that phase.

Load-bearing premise

The entire analysis assumes the null hypersurface embedding is fixed and non-dynamical, neglecting backreaction and transverse deformations that would be essential for physical applications like black hole horizons.

Editorial extensions

If this is right

  • The decoupling limit provides a new way to generate a finite Carrollian fluid from a singular ambient fluid, which may have applications to membrane paradigms for black hole horizons (where the horizon is a null hypersurface).
  • The construction identifies the Carroll boost Goldstone as the subleading component of an infinitely boosted timelike velocity, linking the symmetry-breaking mechanism to a simple kinematic limit.
  • The formalism of null submanifold calculus with fixed embedding can be extended to include first-order derivative corrections, which would test whether the decoupling limit reproduces the first-order Carrollian fluid derived in [20].
  • In the context of flat-space holography, the results suggest that the Bondi flux-balance laws at null infinity can be understood as sourced Carrollian Ward identities, with the decoupling limit corresponding to a regime where sources vanish.
  • The work clarifies the geometric role of the M^a vector field (introduced in [7]) as the difference between the auxiliary null vector and a reference transverse splitting, which becomes important for understanding boost-invariant objects.

Reading between the lines

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

  • The decoupling limit may have a counterpart in gravitational shockwave geometries: the infinite boost of a point particle produces a null shockwave, and the Carrollian fluid on a null surface might describe the effective degrees of freedom on the shockwave front.
  • If the embedding is taken to be dynamical, the shape equations for the null hypersurface would couple to the Carrollian fluid; the decoupling limit might then describe a late-time regime where the fluid decouples from the geometry.
  • The emergence of the Stueckelberg symmetry for the boost Goldstone in the decoupling limit suggests that similar emergent symmetries could appear in other limits of relativistic fluids, such as the non-relativistic or ultra-relativistic limits.
Original abstract

We study intrinsic ideal fluids on null hypersurfaces and their realisations by causal fluids living in the ambient spacetime. An embedded null hypersurface is equipped with an induced Carrollian structure with a temporal Weyl symmetry inherited from rescalings of the null generator, and we develop the corresponding null submanifold and variational calculus. The intrinsic fluid phases are classified according to their realisation of Carroll boosts and temporal Weyl symmetry. If we demand that an ambient fluid be confined to a null hypersurface, the ambient fluid velocity must be null, which realises an intrinsic zero-temperature Carrollian phase with unbroken Carroll boosts. In general, timelike or null ambient fluids will cross a null hypersurface and lead to an open Carrollian system. On a null foliation, the sources correspond to transport between null leaves. We then show that there exists a decoupling limit of a timelike ambient fluid which gives rise to an autonomous Carrollian fluid with spontaneously broken Carroll boosts and no source terms. This decoupling limit corresponds to an infinite boost while keeping the enthalpy finite and nonzero, which leads to a divergent ambient energy-momentum tensor. Nevertheless, the induced Carrollian responses do not see the divergent term and remain finite, and an independent Carroll boost Goldstone emerges from a subleading component of the ambient fluid velocity in this limit.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-10-23: 1 request, 6,988 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.45 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.07 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We study intrinsic ideal fluids on null hypersurfaces and their realisations by causal fluids living in the ambient spacetime. An embedded null hypersurface is equipped with an induced Carrollian structure with a temporal Weyl symmetry inherited from rescalings of the null generator, and we develop the corresponding null submanifold and variational calculus. The intrinsic fluid phases are classified according to their realisation of Carroll boosts and temporal Weyl symmetry. If we demand that an ambient fluid be confined to a null hypersurface, the ambient fluid velocity must be null, which realises an intrinsic zero-temperature Carrollian phase with unbroken Carroll boosts. In general, timelike or null ambient fluids will cross a null hypersurface and lead to an open Carrollian system. On a null foliation, the sources correspond to transport between null leaves. We then show that there exists a decoupling limit of a timelike ambient fluid which gives rise to an autonomous Carrollian fluid with spontaneously broken Carroll boosts and no source terms. This decoupling limit corresponds to an infinite boost while keeping the enthalpy finite and nonzero, which leads to a divergent ambient energy-momentum tensor. Nevertheless, the induced Carrollian responses do not see the divergent term and remain finite, and an independent Carroll boost Goldstone emerges from a subleading component of the ambient fluid velocity in this limit.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We study intrinsic ideal fluids on null hypersurfaces and their realisations by causal fluids living in the ambient spacetime. contribution 0.99 0.90 0.09 asserted 0.93
s1 An embedded null hypersurface is equipped with an induced Carrollian structure with a temporal Weyl symmetry inherited from rescalings of the null generator, and we develop the corresponding null submanifold and variational calculus. contribution 0.59 0.89 0.05 asserted 1.00
s2 The intrinsic fluid phases are classified according to their realisation of Carroll boosts and temporal Weyl symmetry. contribution 0.63 0.87 0.10 asserted 0.99
s3 If we demand that an ambient fluid be confined to a null hypersurface, the ambient fluid velocity must be null, which realises an intrinsic zero-temperature Carrollian phase with unbroken Carroll boosts. result 0.98 0.79 0.16 asserted 0.97
s4 In general, timelike or null ambient fluids will cross a null hypersurface and lead to an open Carrollian system. result 0.86 0.53 0.06 asserted 0.94
s5 On a null foliation, the sources correspond to transport between null leaves. result 0.51 0.37 0.05 asserted 0.99
s6 We then show that there exists a decoupling limit of a timelike ambient fluid which gives rise to an autonomous Carrollian fluid with spontaneously broken Carroll boosts and no source terms. result 0.83 0.93 0.39 asserted 1.00
s7 This decoupling limit corresponds to an infinite boost while keeping the enthalpy finite and nonzero, which leads to a divergent ambient energy-momentum tensor. result 0.48 0.81 0.08 asserted 1.00
s8 Nevertheless, the induced Carrollian responses do not see the divergent term and remain finite, and an independent Carroll boost Goldstone emerges from a subleading component of the ambient fluid velocity in this limit. result 0.93 0.91 0.29 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read
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not examined
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  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
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  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures
Figure 1. Intrinsic ideal Carrollian fluid phases and their realisations by ambient causal fluids. The blue boxes classify the intrinsic phases according to the realisation of Carroll boosts (rows) and temporal Weyl symmetry (columns). Spontaneously broken Carroll boosts give rise to thermal phases with a Carroll boost Goldstone, while unbroken Carroll boosts lead to zero-temperature phases with vanishing en￾thalpy. The grey box indicates the absence of a nontrivial ideal phase when there is no additional scale. In the compensated column, a compensator field Ω that is either a background…
Figure 2. Schematic representation of a null embedding X : N ,→ M. The induced metric hab is degenerate, and its kernel is spanned by v a , whose pushforward is the tangent null normal v µ . Together, the pair (v a , hab) forms the induced Carrollian structure. The tangent map is u µ a = ∂aXµ . Choosing an auxiliary null vector τ µ satisfying vµτ µ = −1 defines the intrinsic clock one-form τa = u µ a τµ. The set of all such allowed auxiliary null vectors τ µ form a parabola on the light cone at X(p), and moving along it by performing a null rotation induces a Carroll boost on N, w
Figure 3. Decomposition of the ambient null traction at a point p of a null hyper￾surface N. The null normal v µ is tangent to N, while the auxiliary null vector τ µ , satisfying vµτ µ = −1, defines the tangential projector via u µ au a ν = δ µ ν +τ µ vν. Applying this projector to the null traction −Feµ = −vνT µν gives the tangential vector −u µ aTea , where Tea = u a µFeµ is the induced energy current. Note that the figure illustrates a causal flux with Tvv := vµvνT µν > 0 so that −Feµ is future-directed for future-directed v µ , since vµ(−Feµ ) = −Tvv < 0. The dashed or
Figure 4. A null foliation as a stack of coupled Carrollian systems. The blue hypersurfaces Nu are generated by the tangent null vector v µ . The auxiliary null vector τ µ defines the transverse evolution vector R = −N τ = ∂u + ζ a∂a (cf. (5.1)), whose integral curves provide an identification between points on neighbouring leaves. The orange patches represent corresponding regions on Nu and Nu+δu which are related by transport along R, on which the tangential null traction Fea induced by the ambient fluid is evaluated. The black arrows illustrate the decomposition of R into ∂u and a…
Figure 5. The two large boost limits of a crossing timelike fluid, illustrated here for wT > 0. The two paths correspond to different scalings of the enthalpy as B → 0 in which the direction of the ambient fluid velocity approaches the null direction v µ . The grey curves are contours of wT/(4B2 ), which is the coefficient of v µ v ν in the ambient energy-momentum tensor (5.68). Along the dashed line, wT = O(B2 ), so this coefficient remains finite and the limit is a ambient null fluid. Along the solid line, wT → wT,0 ̸= 0, so the ambient energy-momentum tensor becomes singular, while th

Figures reproduced from arXiv:2610.30254 by the authors.

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