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REVIEW 5 major objections 6 minor 23 references

Doppler shifted Hawking radiation from acoustic black holes in ultra-relativistic heavy-ion collisions

T0 review · 5 major / 6 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read Ultra-relativistic heavy-ion collisions can still show acoustic Hawking radiation, because at large rapidities the quark-gluon plasma flow breaks boost invariance, giving the sonic horizon a finite Doppler redshift.

desk verdict The off-center observer point is real and worth a referee, but the LHC claim is an expectation, not a result. read the letter →

arxiv 2509.02079 v1 pith:7RD66OWE submitted 2025-09-02 hep-ph gr-qchep-thnucl-exnucl-th

Sanatan Digal , Ajit M. Srivastava This is my paper · ORCID
classification hep-phgr-qchep-thnucl-exnucl-th PACS 04.70.Dy12.38.Mh
keywords acousticblackholeHawkingradiationheavy-ioncollisionsquark-gluonplasmaBjorkenflowrapiditydistributionanaloguegravityDopplerredshift
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

An acoustic black hole forms wherever a hydrodynamic flow turns from subsonic to supersonic, and its analogue Hawking radiation should modify the momentum spectra of emitted particles. For ultra-relativistic heavy-ion collisions, the standard argument was that the boost-invariant Bjorken flow makes the sonic horizon recede at the speed of sound, infinitely red-shifting the Hawking radiation into unobservability. The paper claims this conclusion is premature: at large rapidities, the quark-gluon plasma flow necessarily deviates from boost invariance, so an observer comoving with the fluid at a non-zero rapidity sees the horizon recede more slowly than the sound speed. Using digitized flow profiles from a 200 GeV hydrodynamic simulation, the authors find recession speeds between 0.91 and 0.73 times the sound speed, redshift factors between about 1.5 and 3, and red-shifted Hawking temperatures of about 5 to 9 MeV. The predicted signature is a finite rapidity window, away from midrapidity, in which particle transverse-momentum distributions are mixed by Hawking phonons, while central rapidity remains unaffected.

What carries the argument

The acoustic (Unruh) metric for an irrotational barotropic fluid, with the horizon where the longitudinal flow velocity equals the speed of sound and Hawking temperature T=(1/2π)∂vz/∂z at the horizon. The load-bearing move is the local-observer transformation: instead of the asymptotic observer at z=0, take a fluid-comoving observer at finite rapidity η0, locate the horizon in that observer's rest frame, then track its position one small proper-time step later; the ratio of horizon displacement to time interval gives the recession velocity vhr, and the Doppler redshift factor γhr=1/√(1-(vhr/cs)^2) scales the Hawking temperature down to the observed value.

What would settle it

Compute vH/cs for a range of η0 using a full three-dimensional viscous hydrodynamic simulation at LHC energy with a lattice-QCD equation of state, without hand digitization; if vH/cs stays at or above 1 at all measurable rapidities, the finite-redshift window vanishes. Experimentally, a null result in a dedicated search for rapidity-correlated pT fluctuations in the 1–3 unit rapidity window at top LHC energies, at the predicted 5–9 MeV phonon scale, would also rule out the central claim.

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Extended reading notes

Core claim

The paper's claim: the infinite-redshift obstruction to observing acoustic Hawking radiation in ultra-relativistic heavy-ion collisions disappears once the observer sits at non-zero rapidity. In perfect Bjorken flow every observer sees the sonic horizon (vz=cs) recede at sound speed, infinitely red-shifting phonons. Real QGP flow necessarily deviates from boost invariance at large rapidities, where energy-density gradients accelerate the fluid. An observer comoving at rapidity η0 sees a horizon where vz=cs; tracking it with digitized Y(τ,η)-η curves from a 200 GeV hydrodynamic simulation gives recession speeds vH/cs ≈ 0.91–0.73, redshift factors ≈ 1.5–3, and Hawking temperatures ≈ 5–9 MeV. T

Load-bearing premise

The load-bearing premise is that the digitized, interpolated 200 GeV flow curves, extrapolated to LHC, really capture the large-rapidity deviation from boost invariance; the paper itself warns that its results are susceptible to interpolation errors (Section IV), and even a few-percent change in the recession speed could push it back to the sound speed, restoring infinite redshift.

Editorial extensions

If this is right

  • At top LHC energies, Hawking radiation should leave central-rapidity transverse-momentum distributions unchanged and produce a modified pT pattern in a finite window of non-zero rapidity.
  • The observed Hawking temperature, after redshift, is predicted to lie in the 5–9 MeV range, far below the plasma temperature but physically distinct from it; the signal is rapidity mixing, not a hot component.
  • Phonon partners on the supersonic side of the acoustic horizon are in principle measurable, implying correlated pT fluctuations across the horizon rapidity that can be searched for in two-particle correlations.
  • Effects are set in early (τ0 ~ 2 fm/c) but should persist through hadronization and freeze-out, so late-stage spectra can still carry the imprint.
  • Because larger η0 gives smaller recession speed, the redshift factor decreases toward the fragmentation region, producing a characteristic rapidity dependence of the signal strength.

Reading between the lines

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

  • A direct test: run the same horizon-tracking procedure in a modern three-dimensional viscous hydrodynamic simulation at LHC energies; the predicted vH/cs curve as a function of η0 would confirm or falsify the finite-redshift window without waiting for a dedicated measurement.
  • The same observer-dependent reasoning should apply to other analogue-gravity systems where the flow is not globally stationary; even a receding horizon can emit detectable radiation to a non-central observer whenever acceleration balances expansion.
  • If the deviation from boost invariance shrinks with collision energy, the affected rapidity window moves outward and the central unaffected region broadens, giving an energy-scaling prediction that can be checked at RHIC and LHC.
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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

5 major / 6 minor

Summary. The paper argues that in ultra-relativistic heavy-ion collisions, the acoustic black hole horizon formed where the longitudinal flow becomes supersonic need not always recede at the sound speed, because the flow deviates from Bjorken boost invariance at large rapidities. Using digitized hydrodynamic Y−η data from Bozek and Wyskiel (2009), the authors compute, for observers at several rapidities η0, the recession velocity of the acoustic horizon and the resulting Doppler-shifted Hawking temperature, obtaining T_R ~ 5–9 MeV for √s = 200 GeV Au–Au collisions. They conclude that similar or observable effects should also occur at LHC energies, with Hawking radiation affecting pT distributions only in non-central rapidity windows while leaving central rapidity unaffected.

Significance. The proposed mechanism is novel and physically motivated: for a non-boost-invariant flow, a local observer at finite rapidity can see a horizon receding at vH < cs, rendering the Hawking radiation finite rather than infinitely redshifted. This is a genuine twist on the standard conclusion that Bjorken boost invariance kills the signal. The use of an external hydro simulation avoids circularity, and the prediction of an unaffected central-rapidity region is falsifiable in principle. However, the quantitative evidence is based on a single RHIC-energy simulation with acknowledged digitization uncertainties, no LHC-specific flow input, and no end-to-end derivation of an observable momentum-space signal. The paper is therefore a proof-of-mechanism rather than a demonstrated prediction of observable effects at the level claimed in the abstract and conclusion.

major comments (5)
  1. [Table II and Conclusion] The LHC claim is an extrapolation. Table II is computed entirely from hydro for Au–Au at √s = 200 GeV (ref. [21]), where Y − η is nonzero at every η. At LHC, the boost-invariant plateau is considerably wider; for an observer at a given η0, the acoustic horizon (determined by YH = Y0 + Ys) may lie inside the plateau, where Y − η ≈ 0, so vH/cs ≈ 1 and the redshift remains infinite. The conclusion asserts that 'even at ultra-relativistic heavy-ion collisions, such as at LHC' observable effects are possible, but the paper only says 'We thus expect...' without a calculation. Please provide a computation using an LHC-appropriate flow profile (e.g., from 5.02 TeV Pb–Pb hydro), or restrict the claim to the RHIC energy used in Table II.
  2. [Eqs. (9)–(13)] The coordinate transformation for the moving observer is internally inconsistent. For a fluid element with velocity v_z0 = tanh Y0, a proper-time increment δτ changes the lab coordinates by dt = γ0 δτ and dz = γ0 v_z0 δτ. The paper instead uses z'_0 = z0 + v_z0 δτ and t'_0 = τ'_0 cosh η'_0, which is only correct when Y0 = η0. As a result, the horizon displacement δz and the observer time interval δt_obs = δτ/γ0 do not correspond to the same pair of events, so the recession velocity vhr in Eq. (13) is not a well-defined velocity. This affects all entries in Table II and the central quantitative claim.
  3. [Eqs. (15)–(17)] The velocity gradient dv/dz is evaluated from a single point at vδ = cs − 0.05, with no justification or sensitivity study. The distance between this point and the horizon is small, and the input Y(τ, η) data are hand-digitized and interpolated, with the authors acknowledging 'our results are susceptible to the errors in the interpolation procedure.' A few-percent shift in the location of vδ could move vH/cs toward 1 and erase the effect. Please provide a scan over δv and, ideally, a propagation of digitization uncertainties into T_HW and vH/cs.
  4. [Abstract vs. Conclusion] The abstract claims a 'non-trivial prediction of Hawking radiation affecting particle momentum distributions', but the paper stops at computing a horizon temperature and redshift factor. The conclusion states that 'the detailed nature of the signal remains to be worked out and we hope to present it in a future work.' Without a calculation of the resulting rapidity–pT correlations or fluctuation pattern, the observable claim is not established. Either remove the observational claim from the abstract or provide at least a quantitative estimate of the expected effect (e.g., magnitude of rapidity mixing) to justify the word 'prediction'.
  5. [Eq. (17)] The Doppler factor 1/γhr is inserted by hand. Equation (2) is the static-horizon surface-gravity result, and for a horizon receding at vH/cs ~ 0.7–0.95, the correct surface gravity in an accelerating/expanding acoustic spacetime may contain additional terms beyond a simple Lorentz factor (see refs. [19,20]). Please derive the Doppler-shifted temperature from the acoustic metric for the moving horizon, or explicitly cite the result that shows 1/γhr is the complete correction. Also note that Eq. (14) gives an imaginary factor for vH/cs > 1, as appears in Table I; this limiting case should be clarified.
minor comments (6)
  1. [Abstract] Typo: 'Bjroken' should be 'Bjorken'.
  2. [Table I] For Bjorken flow, the numerical result vH/cs = 1.03 is inconsistent with the exact expectation vH = cs; the deviation is likely a numerical artifact. Please state this explicitly, and explain why fR = ∞ rather than an undefined (imaginary) value when vH/cs > 1.
  3. [Section II (unlabeled)] The manuscript has only a numbered Introduction; other sections lack numbers. Adding section numbers would help the reader navigate the implementation and results.
  4. [Digitized data] The digitized Y(τ, η)−η data from Fig. 3 of ref. [21] should be provided as a table or ancillary file to enable reproducibility and independent error estimation.
  5. [Notation] The notation is occasionally confusing: Y0 denotes fluid rapidity at the observer's location while η0 is the space-time rapidity; v_z0 is used both as the fluid velocity and the observer's velocity. Please define these consistently at first use.
  6. [Units] In Eq. (16), the factor 200 converts fm to MeV assuming ħc ≈ 197 MeV·fm; please state this explicitly for clarity.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular reduction; the finite-redshift result is computed from external hydro input (Bozek-Wyskiel) with only background self-citations to [17,18].

full rationale

The paper's central derivation is not circular. The load-bearing input is the digitized Y(τ,η)−η curves from the external hydrodynamic simulation of Bozek-Wyskiel (ref. [21]) for √s=200 GeV Au–Au collisions. The acoustic horizon condition Y_H = Y0 + Y_s (Eq. 5) is the standard relativistic condition that the fluid rapidity at the horizon exceeds the observer's fluid rapidity by the sound-rapidity Y_s. The horizon location and recession velocity are then computed via the coordinate transformations of Eqs. (3)–(13), not fitted to the desired conclusion. Table I provides an important non-tautological check: for Bjorken flow (Y_fluid=η) the same numerical procedure returns the known infinite-redshift limit (v_H→c_s, f_R→∞), showing the algorithm does not secretly impose a finite redshift. Table II then yields finite f_R for the non-boost-invariant flow, with v_H/c_s between 0.73 and 0.95. The only self-citations are refs. [17,18], which supply the background acoustic-metric formalism and the standard Hawking-temperature formula T=κ/2π (Eq. 2); these are independently grounded in Unruh's and Visser's work and do not assume the paper's new claim about LHC observability. The paper explicitly flags its own limitations: 'Clearly, our results are susceptible to the errors in the interpolation procedure' (paragraph following the digitization description), and it notes the discretization error in choosing the lowest |Δt_obs| as 'one of the sources for various errors in the calculations'. These are correctness/fragility concerns, not circularity. The LHC conclusion is an extrapolation from a 200 GeV input and an expectation ('We thus expect...'), but extrapolation is not circular reduction. No equation is equivalent to its input by construction, and no fitted parameter is renamed as a prediction.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central finite-redshift claim depends primarily on the imported acoustic metric, the constant speed of sound, and the digitized hydro profile from ref [21]. No new entities are introduced. The main hand-set numbers are δv, δτ, and τ0; none are fitted to the claimed output, but their influence is not quantified.

free parameters (3)
  • δv = 0.05
    Step size used in Eqs.(15)-(16) to estimate the velocity gradient near the acoustic horizon; chosen by hand with no convergence study.
  • δτ = 0.01-0.1 fm/c
    Time step used in Eqs.(9)-(12) to measure horizon recession; the paper says 'typically we take it varying' but no systematic scan is reported.
  • τ0 = 2 fm/c
    Observer proper time used in Tables I and II; chosen as an early time, but the dependence of the results on this choice is not explored.
assumptions (5)
  • standard math Unruh acoustic metric applies to the QGP flow
    Metric in Eq.(1) follows from refs [1,2]; requires inviscid, irrotational, barotropic flow, stated in Section I.
  • standard math Hawking temperature formula T=κ/2π
    Eq.(2) is imported from ref [18]; the conformal factor is said not to affect the temperature.
  • domain assumption Constant speed of sound cs=1/√3
    Stated in Section II; reasonable for early central-rapidity QGP, but also used for the large-rapidity regions where the main effect is claimed.
  • domain assumption Digitized hydro simulation [21] is valid and representative
    All redshift values come from Y(τ,η)-η curves at √s=200 GeV, digitized from Fig.3 of ref [21] and extrapolated to LHC energies.
  • domain assumption Fluid acceleration is negligible over the interval δτ
    Explicitly stated in Section IV: 'the acceleration of the fluid with respect to the observer is neglected'.

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Cite this review

Pith. "Pith review of Doppler shifted Hawking radiation from acoustic black holes in ultra-relativistic heavy-ion collisions." pith.science (2026). https://pith.science/paper/7RD66OWE

@misc{pith2026250902079,
  author       = {Pith},
  title        = {Pith review of: Doppler shifted Hawking radiation from acoustic black holes in ultra-relativistic heavy-ion collisions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7RD66OWE}},
  note         = {Machine review of arXiv:2509.02079}
}
read the original abstract

In a hydrodynamic flow, with flow becoming supersonic at some point, the subsonic-supersonic boundary behaves as the horizon of a black hole. Possibility of detecting Hawking radiation from such acoustic black holes has been investigated in a variety of laboratory systems, ranging from cold atom systems, to condensed matter systems with hydrodynamic flow of electrons, to relativistic heavy-ion collisions (at relatively lower collision energies). Ultra-relativistic heavy-ion collisions, with boost-invariant longitudinal flow of the quark-gluon plasma (QGP) in a wide rapidity window has eluded this remarkable possibility because in this case the black hole horizon is dynamical, moving away from center with sound velocity, leading to infinite red shift of Hawking radiation. We show here that such a conclusion is premature. The QGP flow at very large rapidities, necessarily deviates from Bjroken boost invariant flow. Due to this, an observer close to that region sees black hole horizon with a finite redshift. It leads to non-trivial prediction of Hawking radiation affecting particle momentum distributions for a window of rapidities, leaving near central rapidity regions unaffected.

Figures

Figures reproduced from arXiv: 2509.02079 by the authors.

Figure 1
Figure 1. Schematic plot of energy density ϵ vs. rapidity η. In all the figures, the values on the ϵ and η axes are arbi￾trary, only representing qualitative aspect of the location of the acoustic horizon within the rapidity plateau region. This situation was avoided in ref.[18] by considering low energy collisions where flat rapidity region was (al￾most) absent. Energy density gradient then leads to fluid acceleration which … view at source ↗
Figure 3
Figure 3. Schematic representation of rapidity regions which [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

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