{"id":"77a6a259-3339-40a3-851b-1db43bb59978","arxiv_id":"2505.04701","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"Equal-time vacuum correlations of a test quantum field on a dynamically collapsing, horizon-forming spacetime develop non-local peaks across the apparent horizon, and the outside peak moves away from the horizon over time.","lead":"This paper simulates a test quantum field on a spacetime that collapses into a black hole, and follows how its vacuum correlations evolve. It finds correlated peaks appearing across the horizon, with the exterior peak moving outward, which it interprets as the entangled Hawking pair and outgoing Hawking flux.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Initial Minkowski modes are imposed on a curved t=0 slice, so observed correlations may be quench artifacts rather than Hawking partners.","rationale":"The most load-bearing condition for the central claim is not merely resolution but state preparation: the simulation must be computing the response of the physical 'in' vacuum to the collapse. Because the initial modes (Eq. 33) are flat-space solutions while the initial metric (Eq. 25) is already curved by an O(1) Gaussian scalar profile (A=5, D=1), the initial state contains spurious excitations. The subcritical evolution's time-dependent correlations underline that the state is not the stationary vacuum of the evolving geometry. This is a correctness risk in the physical interpretation, more fundamental than truncation artifacts: even with perfect convergence, the peaks could be quench radiation. The concrete eigenvalue-initialization check isolates the Hawking contribution cleanly. The reader's weakest assumption was numerical robustness; the possible lack of convergence is real, but the state-preparation issue is the sharper threat to the 'entangled Hawking partners' claim. I therefore keep the conditional verdict but add this explicit condition.","tokens_in":21514,"tokens_out":14487,"duration_ms":170940,"concrete_test":"Repeat the supercritical run with adiabatic initial data: at t=0, numerically solve the spatial eigenvalue problem for the test-field operator defined by Eq. (32) with the actual A(r), B=1, alpha=1, choose the vacuum as the lowest-energy (positive-frequency) eigenstate, and evolve with the same grid, N_k=N_l=50, kmin=pi/15, and m1=1. Compare the equal-time correlation profile C(t,r; r'=0.7) and the exterior peak trajectory with Fig. 5; if the nonlocal peak and outward motion survive with comparable amplitude, the quench interpretation is excluded, while if they weaken or disappear, the reported Hawking-partner correlations are dominated by the initial state mismatch.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section II.B initializes the test-field modes as flat-space Bessel functions (Eq. 33) at t=0, but for the supercritical profile f(r)=5 exp(-r^2), Eq. (25) makes the initial spatial metric A(r) deviate substantially from 1. These flat modes are not positive-frequency eigenmodes of the actual initial-slice Hamiltonian, so the state is not the vacuum of the initial geometry. The Conclusion's statement that this gives 'the in-state (which is equivalent to the Unruh vacuum)' is therefore unsupported: the physical in-vacuum for a collapse should be the vacuum of the asymptotic past, not a flat-space mode basis imposed on a strongly curved Cauchy surface. The mismatch acts as an instantaneous quantum quench. Consistent with this, the subcritical run (Fig. 4) already shows a moving/reflected diagonal peak and outward-traveling oscillatory tails even though no horizon forms; these are not features of a stationary vacuum in flat space. Unless the quench contribution is removed, the across-horizon peaks and the outward-moving exterior peak in Fig. 5 cannot be uniquely attributed to Hawking pair creation, so the central claim is not yet established.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript studies the equal-time vacuum correlations of a test quantum scalar field on a dynamical, spherically symmetric spacetime undergoing gravitational collapse sourced by a classical massless scalar field. The test field is quantized on the evolving background and regularized with Pauli-Villars fields, and its mode functions are initialized as flat-space spherical Bessel functions and evolved with a modified version of the Berczi et al. code. For a supercritical Gaussian profile, the authors find that after an apparent horizon forms, non-local positive correlation peaks appear with one member inside and one outside the horizon, and the exterior peak moves outward during the stationary-horizon phase; these features are interpreted as entangled Hawking partners and as evidence for a quantum atmosphere. A subcritical profile is used as a control, and correlations of both the field and its conjugate momentum are presented.","tokens_in":21750,"tokens_out":5949,"duration_ms":57605,"significance":"If the reported across-horizon correlations were robust, the paper would provide a useful first-principles dynamical demonstration of pair-correlation structure in a collapsing geometry, with direct connections to the quantum-atmosphere proposal and to analogue black-hole experiments. The authors give a detailed account of the numerical implementation, report small Hamiltonian-constraint violations (L2 norm at most 0.02), and state that the qualitative features persist for a second initial profile, which are genuine strengths. However, the central physical interpretation is not yet established because the initial state is imposed as a flat-space vacuum on a curved slice, no convergence or truncation study is presented for the correlation observables, and the subcritical control already shows non-trivial moving oscillatory structure in flat spacetime.","major_comments":[{"comment":"The in-vacuum is not the vacuum of the initial hypersurface. Eq. (33) sets the mode functions to flat-space spherical Bessel functions at t=0, but for the supercritical Gaussian amplitude A=5 the Hamiltonian constraint, Eq. (25), gives an initial metric function A(r) that differs substantially from unity, so the initial slice carries nontrivial curvature. The Conclusion's assertion that the Minkowski-mode vacuum is 'equivalent to the Unruh vacuum' is therefore unsupported; the state is better described as a quench from a flat-mode basis on a curved slice. Since the subcritical run in Fig. 4 already shows a moving, reflected diagonal peak and outward-propagating oscillatory tails, the across-horizon peaks in Fig. 5 cannot be uniquely attributed to Hawking pair creation without isolating the quench contribution. A concrete test would be to evolve the same initial modes on an exactly flat background and subtract the resulting correlations, or to initialize with an adiabatic vacuum adapted to the initial A(r).","section":"II.B and V, Eq. (33)"},{"comment":"No convergence or robustness study is given for the correlation observables. The simulation fixes N_k=N_l=50, kmin=pi/15, dr=0.025, the box size, the Kreiss-Oliger coefficients, and the Pauli-Villars mass m1=1, and the text itself notes that high-l modes develop instabilities and that the parameter domain is limited. The central claim that the peak structure and its outward motion are physical rather than numerical artifacts requires a resolution study, a mode-truncation study, and sensitivity checks with respect to kmin and m1; none is reported.","section":"II.C"},{"comment":"The subcritical control does not quantitatively isolate the effect of horizon formation. Both the subcritical and supercritical runs show a local diagonal peak that moves and develops oscillatory tails; in the supercritical case the fork and outward-moving peaks appear after the horizon forms, but no comparison of the same observables at matched times, and no subtraction of the subcritical or flat-background correlation, is provided. The claim that the non-local features are specifically correlated with horizon formation needs such a comparison.","section":"IV, Figs. 4 and 5"},{"comment":"The identification of the outward-moving exterior peak with outgoing Hawking flux rests on the coordinate r and the chosen 1+log slicing. Because the apparent-horizon location and the lapse behavior are gauge-dependent, the outward motion of the peak should be checked in an invariant way, for example by computing the peak position in proper distance along the slice or by repeating the run in a different gauge, before it is interpreted as physical outgoing flux.","section":"IV and V"}],"minor_comments":[{"comment":"There are typographical artifacts in Eqs. (27) and (28): '\\hat dk' should be 'dk' and '\\hat X_l' should be a summation symbol.","section":"II.B, Eqs. (27)-(28)"},{"comment":"The regularized momentum correlation in Eq. (31) is not labeled with a 'reg' subscript, unlike Eq. (30); please make the notation uniform.","section":"II.B, Eq. (31)"},{"comment":"The value of the width D used for the A=5 and A=1 runs is not stated explicitly; please give the full parameter set for both runs.","section":"II.C"},{"comment":"The color scale changes from row to row in Figs. 5-7, making it difficult to compare amplitudes quantitatively; a common scale or normalized color map would help.","section":"Figures 5-7"},{"comment":"Reference [96] points to a GitHub repository; please consider citing an archived version or a published companion paper for reproducibility.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"This is an interesting numerical study that fits the journal's scope. My main concern is not the numerics per se but the interpretation: the missing initial-state control and convergence study are feasible additions, so I recommend major revision rather than rejection. The authors should also be asked to make the code and full parameter choices available for reproducibility."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know about arXiv:2505.04701. First, the numerical observation is genuinely new: equal-time vacuum correlations of a test field on a collapsing spherically symmetric background show off-diagonal peaks straddling the apparent horizon, with the exterior member moving outward as the horizon settles. That has not been seen in a gravitational (non-analogue) collapse simulation before. Second, the paper's interpretation of those peaks as Hawking partners is not yet supported, because the initial state is an instantaneous quench, not the vacuum of the initial geometry.\n\nThe authors evolve massless test-field modes with Pauli-Villars regularization on a collapsing background, adapting the Berczi et al. code. The background runs look credible—the Hamiltonian constraint stays below about 0.02 in the supercritical case, and they are transparent about high-l instabilities. The result also has natural contrasts: static Schwarzschild shows no across-horizon correlations, and the sourcing-field correlations in Berczi et al. clump inside the horizon, so the structure here is distinct. For that, credit is due.\n\nThe soft spot is load-bearing. Equation (33) sets the initial modes to flat-space spherical Bessel functions in coordinate r. For the supercritical profile, Eq. (25) makes A(r) deviate substantially from 1, so these are not eigenmodes of the slice Hamiltonian. The state is therefore not the vacuum of the initial geometry, and the claim that this is \"equivalent to the Unruh vacuum\" is unjustified—the Unruh vacuum is defined by past-null-infinity modes, not flat-space modes plunked onto a curved slice. The subcritical run (Fig. 4) sharpens the worry: even without a horizon, correlations develop a moving/reflected peak and oscillatory tails. At least part of what the authors attribute to Hawking physics may be quench or scattering artifacts. I do not see a control that separates those contributions, and the stress-test note appears to land.\n\nSecond, there is no convergence or robustness study accompanying the two-point functions. The mode sums are cut at N_k=N_l=50 with kmin=pi/15, the ghost mass is fixed at m1=1, and the box is fixed; there is no resolution scan, regulator-mass scan, or box-size check. Given the acknowledged instability domain, one would want at least a few off-default runs to show that the peak structure and its outward motion are stable.\n\nThird, the information-paradox discussion at the end is speculative. The paper does not compute entanglement entropy or a reduced density matrix; calling the correlations \"not so subtle\" and capable of restoring unitarity is a leap the actual results do not support.\n\nBottom line: this is a paper for the numerical-relativity-meets-QFT crowd, and it deserves a serious referee. The referee should demand a proper in-state construction, or at least a careful discussion of the quench, plus convergence checks, before the central claim is accepted. My own verdict is skeptical-but-fair: the observation is likely real as a numerical phenomenon, but \"Hawking pairs\" has not been earned yet.","headline":"A genuinely new numerical observation of across-horizon correlation peaks in a dynamical collapse, but the initial state is a quench, so the Hawking-pair attribution is not yet established.","tokens_in":22281,"tokens_out":4921,"would_cite":true,"duration_ms":48214,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"In a dynamical collapse to a black hole, the vacuum correlations of a test quantum field develop non-local peaks that join points inside the horizon to points outside, and the exterior peak travels outward as the spacetime settles toward…","keywords":["Hawking radiation","quantum correlations","gravitational collapse","test quantum field","black hole horizon","quantum atmosphere","numerical relativity","Pauli-Villars regularization"],"falsifier":"Repeat the same collapse with doubled mode counts ($N_k=N_l=100$), a halved infrared cutoff ($k_{\\min}=\\pi/30$), a smaller grid spacing, and at least two regulator masses ($m_1=0.5$ and $2$), and check whether the across-horizon peak's position, sign, and outward speed survive within a few percent; if the peak shifts, shrinks, or vanishes under any change, the claimed non-local correlations are numerical artifacts rather than Hawking-pair structure.","tokens_in":21271,"feed_emoji":"🕳️","tokens_out":10279,"duration_ms":90866,"temperature":0.7,"pith_summary":"The paper tries to establish that Hawking pair creation is visible in the equal-time vacuum correlations of a quantum field during gravitational collapse itself, not just in the late-time flux. It evolves a test scalar field on a spherically symmetric background that collapses past the critical threshold to form a black hole, and finds that once the apparent horizon appears, the correlation function develops peaks connecting an interior point to an exterior point. The exterior member of each correlated pair moves away from the horizon during the stationary regime, which the authors read as the outgoing Hawking partner heading toward an asymptotic observer. The same non-local structure appears for the field's conjugate momentum, with fringes perpendicular to the diagonal. A sympathetic reader would care because this supplies a fully dynamical, gravitational counterpart to the across-horizon correlations that have been predicted in toy models and seen in Bose-Einstein-condensate analogue black holes.","feed_headline":"Collapsing spacetime shows Hawking pairs as moving correlation peaks","feed_subtitle":"Across-horizon peaks in a test field's vacuum correlations appear as the black hole forms and drift outward.","key_machinery":"The load-bearing object is the regularized equal-time two-point function of the test field, expressed as a mode sum over spherical-harmonic modes, $$\\langle 0|\\hat\\Phi_q(t,r)\\hat\\Phi_q(t,r')|0\\rangle_{\\rm reg} = \\frac{\\hbar $c^{2}$}{4\\pi}\\sum_{l}(2l+1)\\int dk \\sum_{n=0}^{5}(-1)^n \\tilde u_{k,l;n}(t,r')\\tilde u^*_{k,l;n}(t,r),$$ with a parallel expression for the conjugate momentum $\\hat\\Pi_q$. The $\\tilde u_{k,l;n}$ are rescaled mode functions, initialized as Minkowski modes and evolved together with the Einstein-Klein-Gordon system for the collapsing background. The numerical core is a tenth-order finite-difference evolution with Kreiss-Oliger dissipation on a uniform grid, with the mode sums truncated at $N_k=N_l=50$ and infrared cutoff $k_{\\min}=\\pi/15$. The argument runs through the correlation maps this mode sum produces at successive times: the evolving lapse freezes dynamics inside the horizon, while the off-diagonal structure outside builds up and moves outward. The Pauli-Villars subtraction with five auxiliary fields makes the correlation finite on the lattice, and the particular grid choices define the domain on which the claim is made.","core_discovery":"On the paper's own terms, the central discovery is that the regularized equal-time correlators $\\langle 0|\\hat\\Phi_q(t,r)\\hat\\Phi_q(t,r')|0\\rangle_{\\rm reg}$ and the corresponding momentum correlator acquire off-diagonal structure once the collapsing matter forms an apparent horizon. For a supercritical Gaussian profile, a valley of negative correlation develops just inside the apparent-horizon radius while a positive peak appears outside, and the outside peak's location increases with time, with amplitude of the same order as the local peak. The authors interpret the inside-outside pair as an entangled Hawking partner pair, in the terminology of a toy model with an event horizon, and the outward motion as outgoing Hawking flux. They emphasize that the exterior peak first appears at a macroscopic distance from the apparent horizon, which they take as evidence for a quantum atmosphere rather than emission at the horizon. In a subcritical collapse that disperses without forming a horizon, no such non-local across-horizon peaks develop, so the effect is tied to horizon formation.","pith_inferences":["Tracking the exterior peak's location as a function of time during the stationary phase and comparing its growth rate with the surface gravity $\\kappa$ of the apparent horizon would turn the reported outward motion into a quantitative test of the Hawking-flux prediction.","A natural next step, not taken in the paper, is to compute the entanglement entropy after tracing out the interior degrees of freedom and check whether its growth follows a Page-curve-like pattern.","Varying the initial Gaussian amplitude across the critical threshold and recording the peak amplitude or onset time could connect the correlation signal to the scaling laws of critical collapse.","Applying the same correlation diagnostic to the field that sources the collapse would separate features generic to horizon formation from features caused by backreaction between the field and geometry."],"forward_implications":["Equal-time vacuum correlations can carry the Hawking-pair signal during collapse itself, so the phenomenon is not confined to asymptotic late-time fluxes.","The first exterior peak appears a macroscopic distance outside the apparent horizon, supporting the quantum-atmosphere picture over emission at the horizon.","The gravitational correlation maps reproduce the qualitative shape of the analogue black hole density correlations, giving a common language between gravitational and condensed-matter Hawking experiments.","The off-diagonal correlations reach the same order as the local diagonal peak, illustrating how the neglected cross terms in the reduced density matrix could matter for information recovery.","The momentum correlator shows fringes perpendicular to the diagonal outside the horizon, offering a second observable with the same partner structure."],"supporting_citations":[{"why":"Supplies the toy-model event-horizon calculation whose 'entangled Hawking partner' terminology the paper uses to name the across-horizon correlation peaks.","marker":"[28]"},{"why":"Shows that equal-time correlations in static Schwarzschild spacetime lack such non-local across-horizon peaks, the contrast that motivates attributing the new peaks to collapse dynamics.","marker":"[29]"},{"why":"Derives the non-local density-density correlation signature for Bose-Einstein-condensate analogue black holes that the paper compares with its gravitational correlation maps.","marker":"[70]"},{"why":"Provides the numerical relativity formalism and discretization framework for evolving a quantum scalar field through critical collapse, which this paper adapts to a test field.","marker":"[97]"},{"why":"Introduces the Pauli-Villars regularization of the quantum field's expectation values on the lattice that the paper uses to define its finite correlation functions.","marker":"[98]"},{"why":"Gives the recent collapse simulation of correlations of the sourcing quantum field, whose interior clumping the paper contrasts with the test-field correlations reported here.","marker":"[100]"},{"why":"Supplies the Kreiss-Oliger dissipation scheme whose parameter choices control the stability domain in which the correlation results are obtained.","marker":"[105]"}],"fun_headline_variants":["Hawking pair peaks drift outward as black hole forms","Collapse study links correlation peaks to Hawking pairs","Across-horizon peaks reveal Hawking pair in collapse","Gravitational collapse shows moving Hawking correlation peaks"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the non-local correlation peaks and their outward motion are properties of the quantum state on the collapsing spacetime, not artifacts of the finite grid, the truncation to fifty $k$- and $l$-modes, the infrared cutoff, or the Pauli-Villars ghost mass.","fun_headline_variants_meta":{"raw":{"variants":["Hawking pair peaks drift outward as black hole forms","Collapse study links correlation peaks to Hawking pairs","Across-horizon peaks reveal Hawking pair in collapse","Gravitational collapse shows moving Hawking correlation peaks"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000142,"raw_usage":{"total_tokens":1132,"prompt_tokens":870,"completion_tokens":262,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":486,"completion_tokens_details":{"reasoning_tokens":198}},"tokens_in":486,"tokens_out":262,"duration_ms":3105,"temperature":1.0,"reasoning_tokens":198,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T23:23:49.990195+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Repeat the same collapse with doubled mode counts ($N_k=N_l=100$), a halved infrared cutoff ($k_{\\min}=\\pi/30$), a smaller grid spacing, and at least two regulator masses ($m_1=0.5$ and $2$), and check whether the across-horizon peak's position, sign, and outward speed survive within a few percent; if the peak shifts, shrinks, or vanishes under any change, the claimed non-local correlations are numerical artifacts rather than Hawking-pair structure.","supporting_citations":[{"cited_title":"On the origin of the particles in black hole evaporation","cited_arxiv_id":"0804.1686","evidence_quote":"Supplies the toy-model event-horizon calculation whose 'entangled Hawking partner' terminology the paper uses to name the across-horizon correlation peaks."},{"cited_title":"Gravitational collapse of quantum fields and Choptuik scaling,","cited_arxiv_id":null,"evidence_quote":"Provides the numerical relativity formalism and discretization framework for evolving a quantum scalar field through critical collapse, which this paper adapts to a test field."},{"cited_title":"Berczi, P","cited_arxiv_id":null,"evidence_quote":"Introduces the Pauli-Villars regularization of the quantum field's expectation values on the lattice that the paper uses to define its finite correlation functions."}],"review_version":1}