arxiv: 2605.12291 · v1 · submitted 2026-05-12 · ✦ hep-th · nucl-th

Recognition: no theorem link

Necessary conditions for causality from linearized stability at ultra-high boosts

Shuvayu Roy , Sukanya Mitra , Rajeev Singh

Authors on Pith no claims yet

Pith reviewed 2026-05-13 04:32 UTC · model grok-4.3

classification ✦ hep-th nucl-th

keywords relativistic hydrodynamicscausalitylinear stabilityLorentz boostMuller-Israel-Stewartdispersion relationhydrodynamic validity

0 comments

The pith

Linear stability at near-luminal boosts determines full causality conditions in relativistic hydrodynamics

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

This paper establishes that in relativistic hydrodynamic systems, the linear stability criteria evaluated only at the spatially homogeneous limit become sufficient to identify the necessary conditions for causality across all momenta when the system is boosted to near-luminal speeds. The key enabler is a gamma-suppression effect in the dispersion relation, where higher-order wavenumber terms are suppressed at large Lorentz factors. This approach allows constraining the causal parameter space without leaving the low-energy hydrodynamic regime. It is demonstrated in the conformal Muller-Israel-Stewart theory as an efficient alternative to full momentum-dependent analysis.

Core claim

The central discovery is that the Lorentz-invariant stability property of causal theories leads to gamma-suppression in boosted frames, making stability at zero wavenumber adequate for ensuring causality conditions even at non-zero momenta at ultra-high boosts.

What carries the argument

Gamma-suppression of higher-order terms in the dispersion relation at large Lorentz boosts, arising from the Lorentz-invariant stability of causal theories.

If this is right

The method provides an efficient derivation of necessary causality conditions in conformal MIS theory.
It operates entirely within the regime of hydrodynamic validity.
Generalizes to any relativistic hydrodynamic system satisfying the stability property.

Where Pith is reading between the lines

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

This technique could reduce computational effort in scanning parameter spaces for causal hydrodynamic models used in heavy ion collision simulations.
Future work might apply it to non-conformal or viscous fluids beyond MIS.
Direct numerical checks of dispersion relations at intermediate boosts could confirm the suppression onset.

Load-bearing premise

Causal theories exhibit Lorentz-invariant stability that produces gamma-suppression of higher terms in the dispersion relation at large boosts.

What would settle it

Finding a causal relativistic hydrodynamic theory whose dispersion relation does not exhibit gamma-suppression at high boosts, or one that passes homogeneous stability but violates causality at finite momentum, would falsify the approach.

Figures

Figures reproduced from arXiv: 2605.12291 by Rajeev Singh, Shuvayu Roy, Sukanya Mitra.

**Figure 2.** Figure 2: FIG. 2: Parameter space satisfying Im( [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3: Parameter space satisfying Im( [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4: Parameter space satisfying Im( [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5: Parameter space satisfying Im( [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗

**Figure 6.** Figure 6: FIG. 6: Parameter space satisfying Im( [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗

**Figure 7.** Figure 7: FIG. 7: Parameter space satisfying Im( [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗

**Figure 8.** Figure 8: FIG. 8: Parameter space satisfying Im( [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗

**Figure 9.** Figure 9: FIG. 9 [PITH_FULL_IMAGE:figures/full_fig_p009_9.png] view at source ↗

**Figure 10.** Figure 10: FIG. 10 [PITH_FULL_IMAGE:figures/full_fig_p010_10.png] view at source ↗

**Figure 11.** Figure 11: FIG. 11: Parameter space satisfying Im( [PITH_FULL_IMAGE:figures/full_fig_p010_11.png] view at source ↗

**Figure 12.** Figure 12: FIG. 12: Parameter space satisfying Im( [PITH_FULL_IMAGE:figures/full_fig_p010_12.png] view at source ↗

**Figure 13.** Figure 13: FIG. 13: Parameter space satisfying Im( [PITH_FULL_IMAGE:figures/full_fig_p012_13.png] view at source ↗

**Figure 14.** Figure 14: FIG. 14: Parameter space satisfying Im( [PITH_FULL_IMAGE:figures/full_fig_p012_14.png] view at source ↗

read the original abstract

In this work, we provide a novel method to constrain the causal parameter space of a relativistic hydrodynamic system exclusively from its linear stability analysis at non-zero momenta. Our approach exploits the Lorentz-invariant stability property of causal theories. In boosted frames, the dispersion relation exhibits a feature that we call ``$\gamma$-suppression,'' whereby the higher-order terms in the wavenumber expansion are increasingly suppressed beyond leading order at large boosts. As a consequence, at near-luminal values of Lorentz boost, stability criteria at the spatially homogeneous limit are sufficient to identify the region of the parameter space that satisfies the necessary conditions of causality, even at non-zero momenta. After presenting the general hydrodynamic framework, we test the method in conformal M\"uller-Israel-Stewart theory and show that it provides an efficient way of deriving the necessary conditions of causality while remaining within the low-energy regime of hydrodynamic validity.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Ultra-high boosts let you pull necessary causality conditions from zero-momentum stability alone in relativistic hydro, but only if the gamma suppression really kills all relevant corrections near the boundary.

read the letter

The paper's main point is that Lorentz invariance plus a large boost suppresses higher-order terms in the dispersion relation, so the sign of Im(omega) at k=0 in the boosted frame already tells you the necessary causality region for finite momenta. They lay this out for general relativistic hydro and then run it on conformal Müller-Israel-Stewart theory, recovering the expected bounds while staying inside the hydrodynamic regime. That reduction is the actual novelty; most prior stability analyses still had to scan finite k explicitly, and this shortcut looks cleaner for parameter scans in nuclear or astrophysical applications. The execution is straightforward and the test case is a good sanity check. The soft spot is exactly the one the stress-test note flags. Near the causality boundary the leading term is small by definition, so any subleading coefficient that does not fall off at least as fast as 1/gamma could still flip the sign at small but nonzero k'. The abstract claims the suppression works, but without seeing the explicit next-order expansion and its gamma scaling when the leading coefficient approaches zero, it is not obvious the homogeneous limit captures everything. If the paper only demonstrates the leading term and asserts the rest follows, that leaves a modest but real gap in the argument. The logic itself is not circular and the citations track the relevant hydro literature. This is useful reading for anyone who builds or constrains causal hydrodynamic models. I would bring it to a reading group focused on foundations of relativistic hydro or effective field theory. I would not cite it in my own work in the next year unless I were doing similar causality scans. It deserves peer review; the idea is concrete enough and the potential payoff for model building is clear, even if the suppression proof needs tightening.

Referee Report

2 major / 2 minor

Summary. The paper presents a method to constrain the causal parameter space of relativistic hydrodynamic theories using only linearized stability analysis at the spatially homogeneous limit (k'=0) in ultra-high-boost frames. It exploits the Lorentz-invariant stability of causal theories, which induces a γ-suppression of higher-order terms in the boosted-frame dispersion relation at large Lorentz factors. Consequently, stability criteria evaluated at k'=0 become sufficient to identify the full region of parameter space satisfying necessary causality conditions, even for non-zero momenta. The approach is illustrated in conformal Müller-Israel-Stewart theory, where it yields the known causality bounds while remaining within the hydrodynamic regime.

Significance. If the central claim holds, the method offers a practical shortcut for deriving necessary causality constraints in higher-order hydrodynamics without exhaustive momentum-space scans, which is valuable given the growing complexity of transport coefficients in modern formulations. The explicit demonstration in conformal MIS theory and the emphasis on staying within low-energy validity are strengths. However, the result's utility depends on whether γ-suppression is robust enough near causality boundaries to preclude finite-k' instabilities.

major comments (2)

[Abstract and general framework] Abstract and the general framework section: The assertion that γ-suppression renders stability at k'=0 sufficient for all momenta rests on the leading term dominating the sign of Im(ω') uniformly. Near the causality boundary, subleading O(k'^2) and higher coefficients could grow with γ or with hydrodynamic transport coefficients, potentially allowing instabilities at small but finite k' that are missed by the homogeneous limit. This requires an explicit bound showing that the suppression factor outpaces any growth in the coefficients.
[Conformal MIS test] Conformal MIS test section: The derivation of the boosted dispersion relation and the explicit verification of γ-suppression for the O(k'^2) term should be provided, including the scaling with γ and the transport coefficients. Without this, it is unclear whether the method recovers the full necessary causality conditions or only a subset.

minor comments (2)

[General framework] Clarify the precise definition of 'near-luminal' boosts (e.g., a minimum γ value) and the regime of validity for the hydrodynamic approximation at those boosts.
[Conformal MIS test] Add a brief comparison table or plot showing the parameter-space region obtained via the new method versus the full causality analysis at finite k.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We appreciate the opportunity to address the concerns regarding the robustness of the γ-suppression argument and the explicitness of the conformal MIS demonstration. We respond to each major comment below and will revise the manuscript to incorporate the requested clarifications and bounds.

read point-by-point responses

Referee: [Abstract and general framework] Abstract and the general framework section: The assertion that γ-suppression renders stability at k'=0 sufficient for all momenta rests on the leading term dominating the sign of Im(ω') uniformly. Near the causality boundary, subleading O(k'^2) and higher coefficients could grow with γ or with hydrodynamic transport coefficients, potentially allowing instabilities at small but finite k' that are missed by the homogeneous limit. This requires an explicit bound showing that the suppression factor outpaces any growth in the coefficients.

Authors: We acknowledge the referee's valid concern that near causality boundaries the subleading coefficients might grow sufficiently to undermine the dominance of the leading term. In the general framework we establish that the leading contribution to Im(ω') scales as 1/γ while higher-order terms acquire additional 1/γ factors from the Lorentz transformation of the wave vector. To make this rigorous, the revised manuscript will include an explicit bound on the remainder terms, demonstrating that for boosts large enough to remain inside the hydrodynamic regime the leading term controls the sign of Im(ω') uniformly, even when transport coefficients approach their causality limits. revision: yes
Referee: [Conformal MIS test] Conformal MIS test section: The derivation of the boosted dispersion relation and the explicit verification of γ-suppression for the O(k'^2) term should be provided, including the scaling with γ and the transport coefficients. Without this, it is unclear whether the method recovers the full necessary causality conditions or only a subset.

Authors: We agree that the conformal MIS section would benefit from a more detailed expansion. The manuscript already obtains the boosted-frame dispersion relation by Lorentz-transforming the rest-frame quadratic equation and then takes the large-γ limit at k'=0. In the revision we will insert the intermediate steps of this transformation, followed by the explicit O(k'^2) expansion of Im(ω'). The coefficients will be written out in terms of the shear relaxation time τ_π and the conformal equation of state, making the γ-suppression factors manifest and confirming that the resulting stability condition at k'=0 reproduces the complete known causality bounds for conformal MIS theory. revision: yes

Circularity Check

0 steps flagged

No circularity; derivation uses external stability property and explicit verification in MIS theory

full rationale

The paper's central method exploits the Lorentz-invariant stability property of causal theories to identify γ-suppression of higher-order terms in the boosted-frame dispersion relation. Stability criteria at k'=0 are then shown to suffice for necessary causality conditions at finite momenta near luminal boosts. This is tested by direct substitution into the conformal Müller-Israel-Stewart hydrodynamic equations and dispersion relation, without any parameter fitting, self-referential definition, or load-bearing self-citation that reduces the result to its inputs. The derivation chain remains independent of the target causality region and is externally falsifiable via the explicit MIS calculation.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the domain assumption that causal theories possess Lorentz-invariant stability and that the dispersion relation exhibits gamma-suppression at large boosts; no free parameters or invented entities are introduced in the abstract.

axioms (2)

domain assumption Causal relativistic hydrodynamic theories possess Lorentz-invariant linear stability properties.
Invoked to justify analyzing stability in boosted frames as equivalent to causality constraints.
domain assumption The dispersion relation in boosted frames exhibits gamma-suppression of higher-order wavenumber terms.
Core mechanism allowing reduction to homogeneous-limit stability criteria.

pith-pipeline@v0.9.0 · 5446 in / 1250 out tokens · 67314 ms · 2026-05-13T04:32:43.606419+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

59 extracted references · 59 canonical work pages

[1]

In the boosted frame, the mode frequencyωis ob- tained not merely in a power series ofk, but rather in a series of (k/γ), i.e., expanded in an infinite se- ries of the wavenumber suppressed by the Lorentz factorγ

work page
[2]

γ-suppression

For the non-hydrodynamic modes in (8), each co- efficientα ∗ n is itself an infinite series in (va 0). The coefficients of this nested series include the LRF coefficientsa n ranging fromn= 0 to∞, i.e., the knowledge of the LRF modes to their entirety. IV. BOOSTED DISPERSION MODES OF THE MIS THEOR Y The dispersion spectra of any given theory in the LRF can...

work page
[3]

MIS-Shear: Non-hydro-mode The non-hydrodynamic coefficientsα ∗ n for the MIS shear-channel tilln= 6 are: α∗ 0 = i λv2 −τ π , α ∗ 1 = 2λv λv2 −τ π , α ∗ 2 =i λ , α ∗ 3 = 2λ2v , α ∗ 4 =−iλ 2 5λv2 −τ π , α∗ 5 = 2λ3v 3τπ −7λv 2 , α ∗ 6 = 2iλ3 τ 2 π + 21λ2v4 −14λτ πv2 . (A2)

work page
[4]

MIS-Shear: Hydro-mode The hydrodynamic coefficients ˜an for the MIS shear-channel tilln= 6 are: ˜a1 =−v ,˜a 2 =− iλ γ2 ,˜a 3 =− 2λ2v γ2 ,˜a 4 = iλ2 5λv2 −τ π γ2 ˜a5 = 2λ3v 7λv2 −3τ π γ2 ,˜a 6 =− 2iλ3 τ 2 π + 21λ2v4 −14λτ πv2 γ2 . (A3)

work page
[5]

MIS-Sound: Non-hydro-mode The non-hydrodynamic coefficientsα ∗ n for the MIS sound-channel tilln= 6 are: α∗ 0 =− i v2 −3 v2(4λ+τ π)−3τ π , α ∗ 1 =− 24λv (v2 −3) (v 2(4λ+τ π)−3τ π) , α ∗ 2 =− 36iλ v2 + 1 (v2 −3) 3 , α∗ 3 =− 48λv τπ v4 −9 + 2λ 2v4 + 15v2 + 9 (v2 −3) 5 , α∗ 4 = 12iλ (v2 −3) 7 h 81τπ(τπ −4λ) + 5v 8(4λ+τ π)2 + 420λv6(4λ+τ π) + 126v4(4λ−τ π)(10...

work page
[6]

MIS-Sound: Hydro-modes The hydrodynamic coefficients ˜an for the MIS sound-channel frequenciesω ± tilln= 6 are: ˜a1 = 2v v2 −3 ∓ √ 3 γ2 (v2 −3) ,˜a 2 = 18iλ v2 + 1 γ2 (v2 −3) 3 ± 2i √ 3λv v2 + 9 γ2 (v2 −3) 3 , ˜a3 = 24λv γ2 (v2 −3) 5 h τπ v4 −9 + 2λ 2v4 + 15v2 + 9 i ± 2 √ 3λ γ2 (v2 −3) 5 h τπ v2 −3 v4 + 18v2 + 9 + 3λ v6 + 35v4 + 75v2 + 9 i , ˜a4 =− 6iλ γ2...

work page
[7]

(B2) is approximated as (ω−vk){i+γτ π(ω−vk)}= 0.(B3) The first parenthesis of Eq

MIS shear channel For the MIS shear channel, the dispersion relation reads γ τπ −λ 2 ω2 +{i−2γvk(τ π −λ)}ω+ −ivk+γk 2 τπv2 −λ = 0,(B1) which can be expressed as (ω−vk){i+γτ π(ω−vk)} −γλ(ωv−k) 2 = 0.(B2) At the limit,λ→0, Eq. (B2) is approximated as (ω−vk){i+γτ π(ω−vk)}= 0.(B3) The first parenthesis of Eq. (B3) provides only hydrodynamic modes with the exa...

work page
[8]

(B6) as γτπI1 +γ 4 3 λI2 +iI 3 = 0,(B8) where I1 = (ω−vk) (ω−vk) 2 − 1 3(ωv−k) 2 , I 2 =−(ω−vk) (ωv−k) 2 , I 3 = (ω−vk) 2 − 1 3 (ωv−k) 2 .(B9) This allows Eq

MIS sound channel For the MIS sound channel, the dispersion relation reads A0 3ω3 + A0 2 +A 1 2k ω2 + A1 1k+A 2 1k2 ω+ A2 0k2 +A 3 0k3 = 0,(B6) where A0 3 =τ π − 4λ 3 + τπ 3 v2 , A 0 2 =i 1 γ 1− v2 3 , A 1 2 = 8λ 3 − 7τπ 3 v+ 4λ 3 + τπ 3 v3 , A 1 1 =−i 1 γ 4 3 v , A2 1 =− 4λ 3 + τπ 3 + 7τπ 3 − 8λ 3 v2 , A 2 0 =i 1 γ v2 − 1 3 , A 3 0 =−τ πv3 + 4λ 3 + τπ 3 ...

work page
[9]

Fluid mechanics: Volume 6 (course of theoretical physics),

L. D. Landau and E. M. Lifshitz, “Fluid mechanics: Volume 6 (course of theoretical physics),” Elsevier Science : Amsterdam (1987)

work page 1987
[10]

Relativistic viscous hydrodynamics, conformal invariance, and holography,

R. Baier, P. Romatschke, D. T. Son, A. O. Starinets, and M. A. Stephanov, “Relativistic viscous hydrodynamics, conformal invariance, and holography,” JHEP04(2008) 100,arXiv:0712.2451 [hep-th]

work page arXiv 2008
[11]

Hydrodynamic Models for Heavy Ion Collisions,

P. Huovinen and P. V. Ruuskanen, “Hydrodynamic Models for Heavy Ion Collisions,” Ann. Rev. Nucl. Part. Sci.56(2006) 163–206,arXiv:nucl-th/0605008

work page arXiv 2006
[12]

Collective flow and viscosity in relativistic heavy-ion collisions

U. Heinz and R. Snellings, “Collective flow and viscosity in relativistic heavy-ion collisions,” Ann. Rev. Nucl. Part. Sci.63(2013) 123–151,arXiv:1301.2826 [nucl-th]

work page Pith review arXiv 2013
[13]

Hydrodynamic Modeling of Heavy-Ion Collisions

C. Gale, S. Jeon, and B. Schenke, “Hydrodynamic Modeling of Heavy-Ion Collisions,” Int. J. Mod. Phys. A 28(2013) 1340011,arXiv:1301.5893 [nucl-th]

work page Pith review arXiv 2013
[14]

Properties of hot and dense matter from relativistic heavy ion collisions,

P. Braun-Munzinger, V. Koch, T. Sch¨ afer, and J. Stachel, “Properties of hot and dense matter from relativistic heavy ion collisions,” Phys. Rept.621 (2016) 76–126,arXiv:1510.00442 [nucl-th]

work page arXiv 2016
[15]

Relativistic fluid dynamics: physics for many different scales,

N. Andersson and G. L. Comer, “Relativistic fluid dynamics: physics for many different scales,” Living Rev. Rel.24no. 1, (2021) 3,arXiv:2008.12069 [gr-qc]

work page arXiv 2021
[16]

Hydrodynamics of galactic dark matter,

L. G. Cabral-Rosetti, T. Matos, D. Nunez, and R. A. Sussman, “Hydrodynamics of galactic dark matter,” Class. Quant. Grav.19(2002) 3603–3616, arXiv:gr-qc/0112044

work page arXiv 2002
[17]

Causality and the Dispersion Relation: Logical Foundations,

J. S. Toll, “Causality and the Dispersion Relation: Logical Foundations,” Phys. Rev.104(1956) 1760–1770

work page 1956
[18]

Stability and causality in dissipative relativistic fluids,

W. A. Hiscock and L. Lindblom, “Stability and causality in dissipative relativistic fluids,” Annals Phys. 151(1983) 466–496

work page 1983
[19]

Generic instabilities in first-order dissipative relativistic fluid theories,

W. A. Hiscock and L. Lindblom, “Generic instabilities in first-order dissipative relativistic fluid theories,” Phys. Rev. D31(1985) 725–733

work page 1985
[20]

Stability and causality in the Israel-Stewart energy frame theory,

T. S. Olson, “Stability and causality in the Israel-Stewart energy frame theory,” Annals Phys.199 (1990) 18

work page 1990
[21]

New Developments in Relativistic Viscous Hydrodynamics,

P. Romatschke, “New Developments in Relativistic Viscous Hydrodynamics,” Int. J. Mod. Phys. E19 (2010) 1–53,arXiv:0902.3663 [hep-ph]

work page arXiv 2010
[22]

Lectures on hydrodynamic fluctuations in relativistic theories,

P. Kovtun, “Lectures on hydrodynamic fluctuations in relativistic theories,” J. Phys. A45(2012) 473001, arXiv:1205.5040 [hep-th]

work page arXiv 2012
[23]

Linear plane waves in dissipative relativistic fluids,

W. A. Hiscock and L. Lindblom, “Linear plane waves in dissipative relativistic fluids,” Phys. Rev. D35(1987) 3723–3732

work page 1987
[24]

Causality and existence of solutions of relativistic viscous fluid dynamics with gravity,

F. S. Bemfica, M. M. Disconzi, and J. Noronha, “Causality and existence of solutions of relativistic viscous fluid dynamics with gravity,” Phys. Rev. D98 no. 10, (2018) 104064,arXiv:1708.06255 [gr-qc]

work page arXiv 2018
[25]

Stability and Causality in relativistic dissipative hydrodynamics,

G. S. Denicol, T. Kodama, T. Koide, and P. Mota, “Stability and Causality in relativistic dissipative hydrodynamics,” J. Phys. G35(2008) 115102, arXiv:0807.3120 [hep-ph]

work page arXiv 2008
[26]

Does stability of relativistic dissipative fluid dynamics imply causality?,

S. Pu, T. Koide, and D. H. Rischke, “Does stability of relativistic dissipative fluid dynamics imply causality?,” Phys. Rev. D81(2010) 114039,arXiv:0907.3906 [hep-ph]

work page arXiv 2010
[27]

Linear stability of Israel-Stewart theory in the presence of net-charge diffusion,

C. V. Brito and G. S. Denicol, “Linear stability of Israel-Stewart theory in the presence of net-charge diffusion,” Phys. Rev. D102no. 11, (2020) 116009, arXiv:2007.16141 [nucl-th]

work page arXiv 2020
[28]

Nonlinear Causality of General First-Order Relativistic Viscous Hydrodynamics,

F. S. Bemfica, M. M. Disconzi, M. M. Disconzi, J. Noronha, and J. Noronha, “Nonlinear Causality of General First-Order Relativistic Viscous Hydrodynamics,” Phys. Rev. D100no. 10, (2019) 104020,arXiv:1907.12695 [gr-qc]. [Erratum: Phys.Rev.D 105, 069902 (2022)]

work page arXiv 2019
[29]

First-Order General-Relativistic Viscous Fluid Dynamics,

F. S. Bemfica, M. M. Disconzi, and J. Noronha, “First-Order General-Relativistic Viscous Fluid Dynamics,” Phys. Rev. X12no. 2, (2022) 021044, arXiv:2009.11388 [gr-qc]

work page arXiv 2022
[30]

First-order relativistic hydrodynamics is stable,

P. Kovtun, “First-order relativistic hydrodynamics is stable,” JHEP10(2019) 034,arXiv:1907.08191 [hep-th]

work page arXiv 2019
[31]

Stable and causal relativistic Navier-Stokes equations,

R. E. Hoult and P. Kovtun, “Stable and causal relativistic Navier-Stokes equations,” JHEP06(2020) 067,arXiv:2004.04102 [hep-th]

work page arXiv 2020
[32]

Is first-order relativistic hydrodynamics in a general frame stable and causal for arbitrary interactions?,

R. Biswas, S. Mitra, and V. Roy, “Is first-order relativistic hydrodynamics in a general frame stable and causal for arbitrary interactions?,” Phys. Rev. D106 no. 1, (2022) L011501,arXiv:2202.08685 [nucl-th]. 18

work page arXiv 2022
[33]

An expedition to the islands of stability in the first-order causal hydrodynamics,

R. Biswas, S. Mitra, and V. Roy, “An expedition to the islands of stability in the first-order causal hydrodynamics,” Phys. Lett. B838(2023) 137725, arXiv:2211.11358 [nucl-th]

work page arXiv 2023
[34]

Rigorous Bounds on Transport from Causality,

M. P. Heller, A. Serantes, M. Spali´ nski, and B. Withers, “Rigorous Bounds on Transport from Causality,” Phys. Rev. Lett.130no. 26, (2023) 261601, arXiv:2212.07434 [hep-th]

work page arXiv 2023
[35]

Can We Make Sense of Dissipation without Causality?,

L. Gavassino, “Can We Make Sense of Dissipation without Causality?,” Phys. Rev. X12no. 4, (2022) 041001,arXiv:2111.05254 [gr-qc]

work page arXiv 2022
[36]

Bounds on transport from hydrodynamic stability,

L. Gavassino, “Bounds on transport from hydrodynamic stability,” Phys. Lett. B840(2023) 137854, arXiv:2301.06651 [hep-th]

work page arXiv 2023
[37]

Dispersion Relations Alone Cannot Guarantee Causality,

L. Gavassino, M. M. Disconzi, and J. Noronha, “Dispersion Relations Alone Cannot Guarantee Causality,” Phys. Rev. Lett.132no. 16, (2024) 162301, arXiv:2307.05987 [hep-th]

work page arXiv 2024
[38]

Thermodynamic Stability Implies Causality,

L. Gavassino, M. Antonelli, and B. Haskell, “Thermodynamic Stability Implies Causality,” Phys. Rev. Lett.128no. 1, (2022) 010606,arXiv:2105.14621 [gr-qc]

work page arXiv 2022
[39]

Stability and causality criteria in linear mode analysis: Stability means causality,

D.-L. Wang and S. Pu, “Stability and causality criteria in linear mode analysis: Stability means causality,” Phys. Rev. D109no. 3, (2024) L031504, arXiv:2309.11708 [hep-th]

work page arXiv 2024
[40]

Causality and classical dispersion relations,

R. E. Hoult and P. Kovtun, “Causality and classical dispersion relations,” Phys. Rev. D109no. 4, (2024) 046018,arXiv:2309.11703 [hep-th]

work page arXiv 2024
[41]

Causal and stable superfluid hydrodynamics,

R. E. Hoult and A. Shukla, “Causal and stable superfluid hydrodynamics,” JHEP04(2025) 172, arXiv:2410.22855 [hep-th]

work page arXiv 2025
[42]

Do faster-than-light group velocities imply violation of causality?,

R. Fox, C. G. Kuper, and S. G. Lipson, “Do faster-than-light group velocities imply violation of causality?,” Nature223(1969) 597

work page 1969
[43]

Causality criteria,

E. Krotscheck and W. Kundt, “Causality criteria,” Communications in Mathematical Physics60(1978) 171–180

work page 1978
[44]

Relativistic Fluid Dynamics In and Out of Equilibrium -- Ten Years of Progress in Theory and Numerical Simulations of Nuclear Collisions

P. Romatschke and U. Romatschke, Relativistic Fluid Dynamics In and Out of Equilibrium. Cambridge Monographs on Mathematical Physics. Cambridge University Press, 5, 2019. arXiv:1712.05815 [nucl-th]

work page Pith review arXiv 2019
[45]

Hydrodynamic Gradient Expansion in Gauge Theory Plasmas,

M. P. Heller, R. A. Janik, and P. Witaszczyk, “Hydrodynamic Gradient Expansion in Gauge Theory Plasmas,” Phys. Rev. Lett.110no. 21, (2013) 211602, arXiv:1302.0697 [hep-th]

work page arXiv 2013
[46]

Hydrodynamics Beyond the Gradient Expansion: Resurgence and Resummation

M. P. Heller and M. Spalinski, “Hydrodynamics Beyond the Gradient Expansion: Resurgence and Resummation,” Phys. Rev. Lett.115no. 7, (2015) 072501,arXiv:1503.07514 [hep-th]

work page Pith review arXiv 2015
[47]

Field redefinition and its impact in relativistic hydrodynamics,

S. Bhattacharyya, S. Mitra, S. Roy, and R. Singh, “Field redefinition and its impact in relativistic hydrodynamics,” Phys. Rev. D111no. 1, (2025) 014034,arXiv:2409.15387 [nucl-th]

work page arXiv 2025
[48]

Stochastic relativistic advection diffusion equation from the Metropolis algorithm,

G. Ba¸ sar, J. Bhambure, R. Singh, and D. Teaney, “Stochastic relativistic advection diffusion equation from the Metropolis algorithm,” Phys. Rev. C 110no. 4, (2024) 044903,arXiv:2403.04185 [nucl-th]

work page arXiv 2024
[49]

Relativistic viscous hydrodynamics in the density frame: Numerical tests and comparisons,

J. Bhambure, A. Mazeliauskas, J.-F. Paquet, R. Singh, M. Singh, D. Teaney, and F. Zhou, “Relativistic viscous hydrodynamics in the density frame: Numerical tests and comparisons,” Phys. Rev. C111no. 6, (2025) 064910,arXiv:2412.10303 [nucl-th]

work page arXiv 2025
[50]

Noncovariant parabolic theories of relativistic diffusion,

L. Gavassino, “Noncovariant parabolic theories of relativistic diffusion,” Phys. Rev. D112no. 3, (2025) 034026,arXiv:2505.18815 [gr-qc]

work page arXiv 2025
[51]

Causality criteria from stability analysis at ultrahigh boost,

S. Roy and S. Mitra, “Causality criteria from stability analysis at ultrahigh boost,” Phys. Rev. D110no. 1, (2024) 016012,arXiv:2306.07564 [hep-th]

work page arXiv 2024
[52]

Relativistic Dispersion Spectra across Lorentz boosted frames: Spurious modes and the enigma of causality,

S. Bhattacharyya, S. Mitra, S. Roy, and R. Singh, “Relativistic Dispersion Spectra across Lorentz boosted frames: Spurious modes and the enigma of causality,” (12, 2025) ,arXiv:2512.12450 [hep-th]

work page arXiv 2025
[53]

Nonstationary irreversible thermodynamics: A Causal relativistic theory,

W. Israel, “Nonstationary irreversible thermodynamics: A Causal relativistic theory,” Annals Phys.100(1976) 310–331

work page 1976
[54]

Transient relativistic thermodynamics and kinetic theory,

W. Israel and J. M. Stewart, “Transient relativistic thermodynamics and kinetic theory,” Annals Phys.118 (1979) 341–372

work page 1979
[55]

Zum Paradoxon der Warmeleitungstheorie,

I. Muller, “Zum Paradoxon der Warmeleitungstheorie,” Z. Phys.198(1967) 329–344

work page 1967
[56]

Causality, Analyticity and an IR Obstruction to UV Completion

A. Adams, N. Arkani-Hamed, S. Dubovsky, A. Nicolis, and R. Rattazzi, “Causality, analyticity and an IR obstruction to UV completion,” JHEP10(2006) 014, arXiv:hep-th/0602178

work page Pith review arXiv 2006
[57]

Causality in curved spacetimes: The speed of light and gravity,

C. de Rham and A. J. Tolley, “Causality in curved spacetimes: The speed of light and gravity,” Phys. Rev. D102no. 8, (2020) 084048,arXiv:2007.01847 [hep-th]

work page arXiv 2020
[58]

Causal effective field theories,

M. Carrillo Gonzalez, C. de Rham, V. Pozsgay, and A. J. Tolley, “Causal effective field theories,” Phys. Rev. D106no. 10, (2022) 105018,arXiv:2207.03491 [hep-th]

work page arXiv 2022
[59]

Serra, J

F. Serra, J. Serra, E. Trincherini, and L. G. Trombetta, “Causality constraints on black holes beyond GR,” JHEP08(2022) 157,arXiv:2205.08551 [hep-th]

work page arXiv 2022