Grazing Collisions of Gravitational Shock Waves and Entropy Production in Heavy Ion Collision

Edward Shuryak; Shu Lin

REVIEW

Grazing Collisions of Gravitational Shock Waves and Entropy Production in Heavy Ion Collision

Shu Lin, Edward Shuryak

High Energy Physics - Theory · Submitted 9 Feb 2009 · 35 references

Pith's verdict: The non-central trapped surface in AdS5 is a real addition and the existence of a critical impact parameter looks solid, but the advertised exponent 0.37 is the least supported number in the paper.

T0 · AI review

How this review was made: An AI referee (selfhosted/deepseek-v4.1-flash) read the paper on November 11, 2026 and answered a fixed list of questions about it. T0 is the starting level every paper gets. The levels describe how deeply Pith has checked the paper, never the authors.

T0 AI review An AI read the paper and answered a fixed list of questions.
T1 Audit Automatic checks that the references and files the paper relies on exist and match.
T2 Compute The paper's code or calculations re-run with the same results.
T3 Formal statement The claims written out in a formal math language a computer can read.
T4 Proof Those claims proved, and the proof checked by computer.

How Pith checks papers →

· 5 major objections · 8 minor · Ask about this paper · The compiled record · Read the full review →

Challenge this review Comment (0) Read on arXiv ↗

Cite ▾

arXiv ID0902.1508 (version 2)

Pith ID6ECVUFKH, Pith's permanent record of this paper and its review

CitationEdward Shuryak, Shu Lin. "Grazing Collisions of Gravitational Shock Waves and Entropy Production in Heavy Ion Collision." arXiv:0902.1508 (2009). https://pith.science/paper/6ECVUFKH

Cite this reviewBibTeX for Pith's review of this paper

Claim paper

Why Pith says this

Highlight any text to comment on it.

Editor's note

read the letter

The thing to know: this is the first non-central trapped-surface computation in AdS5, and the qualitative claim — that a horizon stops forming beyond some critical impact parameter — holds up. The power law in the abstract is the part I would not lean on yet. The integral-equation reformulation is the good idea here. Turning the differential boundary-value problem of Eqs. 11-12 into a Fredholm equation on the boundary (Eqs. 34-35) is clean, the H3 Green's function is quoted correctly from Berenstein et al. and Danielsson et al., and Eq. 38 recovers Gubser-Pufu-Yarom Eq. 115 exactly. That is a real check, not a gesture. The wall-on-wall section is also better motivated than Grumiller-Romatschke: the fixed-density source in Eq. 52 gives a perturbation that decays away from z0 in both directions, and the closed-form solution with its sqrt(E1 E2) dependence is tidy. Now the soft spot, and it is the load-bearing one. Eq. 49 fits nine points from Table 1 and reports no error bar. Section 4.3 says outright that larger M is needed as the energy grows, but M is never given a value, never varied, and the residual is only 'satisfied to certain accuracy' — the accuracy is never stated. The critical point is located by watching a gradient diverge rather than by bracketing with a tolerance. A log-log slope puts most of its leverage on the highest-energy point, which is exactly the point the authors flag as hardest to resolve. None of this threatens the existence of b_c, which is robust across all nine energies and matches the flat-space Eardley-Giddings picture. It threatens the one number Fig. 2 advertises. The Kang-Nastase E^{1/6} discrepancy is waved off with 'not asymptotically large E' without showing the local slope is still drifting; that check is cheap and would settle it. Two smaller things. Abstract sentence s4's 'experimental indications' is stronger than Section 7 supports — the authors concede grazing multiplicity data do not exist and the ridge plot is suggestive only. Fine in the body, too much in the abstract. And reference [36] is offered as corroboration but is 'so far not posted', so nobody can check it. Section 6 is a genuine credit: admitting the literal Gubser tuning gives a 300 fm fireball is the right call and most authors would have buried it. Who should read it: anyone in the AdS/CFT heavy-ion program, and the gravitational-collapse people who care about the flat-space analogy. Send it out, but ask for a convergence study in M and a stated tolerance on b_c before the exponent is taken seriously.

Referee report

Significance

If the result holds, it is the AdS analogue of the Eardley–Giddings and Yoshino–Nambu critical impact parameter in flat space, and it carries a substantive physical message: black-hole formation, and hence thermalization in the dual description, switches off discontinuously as the collision becomes grazing. The methodological contribution is real and reusable — the reformulation of the trapped-surface problem as a boundary integral equation with the H3 Green's function (Eqs. 34–35) is a clean and general device, and the analytic b = 0 check against Gubser et al. (Eq. 38) is a genuine validation rather than a consistency remark. The wall-on-wall case of §5 is a welcome exactly solvable benchmark that yields a closed-form 2/3 scaling law. The paper is also candid about the limits of the heavy-ion mapping in §6, which is more than many works in this genre attempt.

Major objections (5)

[§4.3, Eq. (49), Table 1] The numerical error budget is not reported anywhere, and this is load-bearing for the paper's one quantitative result. The truncation order M in rho(theta) = sum_{n=1}^{M} a_n cos 2(n-1)theta is never given a value, never varied, and no convergence study in M or in the 199-point theta grid is presented. The convergence criterion is stated only as 'until (35) is satisfied to certain accuracy', with the accuracy never quantified and no residual Delta(theta) = B1B2 - 4 quoted at the accepted solution. Table 1 lists b_c to two decimal places with no uncertainty. For a paper whose headline number is a fitted exponent, the absence of any stated tolerance, any grid-refinement test, and any error bar on the individual b_c values makes the fit in Eq. (49) unreproducible as stated. Please report M, the achieved max|Delta|, a refinement study (e.g. M and grid size doubled at two or three energies), and uncertainties on the Table 1 entries.
[§4.3, Eq. (49), Fig. 2] The exponent 0.37 is extracted from a log-log slope over G5E/L^2 = 0.1 to 100, and the paper itself states that 'as collision energy grows, the trapped surface gets elongated in the axis of mismatch and larger M is needed to reach prescribed accuracy.' That is precisely the regime that carries the most leverage in a two-parameter log-log fit, so the least-controlled point (G5E/L^2 = 100) dominates the reported slope. Compounding this, the critical point is located by a qualitative symptom — 'the gradient diverges as Delta(theta) reduces in the iteration' — rather than by a bracketing criterion with a stated tolerance, so how close to the divergence b_c is declared is operator-dependent. Finally, the diagonal matrix elements of K are handled by least-squares extraction of ln|theta-theta'|, 1, (theta-theta')ln|theta-theta'| and (theta-theta') coefficients over an unspecified number of sample points, an uncontrolled error source concentrated where the surface curvature is largest. A fit residual or chi-squared for Eq. (49) should be quoted, and the fit should be repeated with the highest-energy point dropped to show the exponent is stable.
[Eq. (49) and the Note added in version 2] The comparison with Kang and Nastase, who report b_c ~ E^{1/6} at large E, is dismissed with 'perhaps because we are not working at asymptotically large E' without any demonstration that the two regimes are separated. Given that the present fit spans only three decades and that 0.37 and 1/6 differ by more than a factor of two, this deserves more than a parenthetical. Relatedly, the data as tabulated do not obviously discriminate 0.37 from 1/3: evaluating Eq. (49) at the endpoints gives 0.46 and 5.9 against the tabulated 0.40 and 5.30, i.e. roughly ten per cent residuals with non-monotonic sign, which is comparable to the difference between the two exponents over this range. Please state the fit residuals explicitly and give an uncertainty on beta, or soften the claim from a measured power law to an approximate trend consistent with several exponents.
[Abstract [abstract:s4] versus §7] The abstract states that 'we argue that there are experimental indications for similar critical impact parameter in real collisions', but §7 supports considerably less than this. The authors themselves note that 'the experimental multiplicity measurements for grazing collisions are not available yet', so the multiplicity panel of Fig. 5 cannot locate any b_c; the positive evidence reduces to the ridge amplitude in the right panel of Fig. 5, which is STAR data at two energies and is not shown to single out a critical impact parameter rather than a smooth centrality dependence. The abstract should be reworded to match what §7 actually establishes, for instance that the gravitational result motivates a search for a rapid change of regime at some b_c(E), with the existing data being suggestive but not decisive. I do not ask for new analysis here, only for calibration of the headline claim.
[§5, Eqs. (52)–(54)] The rejection of the Grumiller–Romatschke initial conditions is asserted rather than demonstrated. The argument that a shock amplitude growing with z is inconsistent because the background falls as 1/z^2 is plausible, but no expansion parameter is estimated and no criterion for where perturbation theory fails is given. Meanwhile the alternative source of Eq. (52), a delta function at z0, is itself a choice rather than something derived from a boundary stress tensor; Eq. (54) simply posits Tuu proportional to delta(u) with no transverse dependence. Since §5 is presented as supplying 'more reasonable initial conditions' for future work in the Grumiller–Romatschke framework, the paper owes the reader either a quantitative statement of where the two choices diverge or a retreat to the weaker claim that Eq. (52) is a convenient illustrative choice. The statement that the trapped surface 'has finite extensions in both directions' from z0 should also be shown from Eqs. (59)–(61) rather than asserted.

Minor objections (8)

[§3, Eq. (38)] The analytic b = 0 check reproducing Eq. (115) of Gubser et al. is the strongest validation in the paper and deserves to be flagged as such in the text. It would strengthen the paper further to show that the b -> 0 limit of the numerically computed area reproduces the known E^{2/3} entropy of Gubser et al., which is a check the present manuscript does not perform.
[§5, Eqs. (60)–(64)] As printed in the version I read, the dimensions of Eqs. (60), (61) and (64) do not balance: za + zb is a length while 8 pi G5 sqrt(E1 E2)/L carries different dimensions under the usual G5 ~ length^3 and E ~ energy conventions, and Eq. (64) sets 4 pi G5 E against z0. This may be a transcription issue rather than an error, but the reader cannot tell, so please verify the printed form of these equations and state the engineering dimensions of E (energy, or energy per unit transverse area) explicitly at Eq. (52).
[§4.1, sentence after Eq. (42)] The statement 'since AdS radius is a free parameter, which will not appear alone in the final result in dual field theory, we may set z0 = L without loss of generality' compresses a scaling argument into one clause. Please spell out that the dual result depends only on the dimensionless combinations G5E/L^2 and b/L, and that fixing z0 = L is a choice of units rather than a physical assumption about the nucleus size.
[Eqs. (50) and (62)] The entropy is written as S = 2A/4G5 in both places, with the factor of two attributed to the two sheets of the surface. Please state this convention once, near Eq. (50), and confirm that the same factor is used consistently in the wall-on-wall case where the geometry is different.
[Fig. 1 and Fig. 3] The axis labels of Fig. 1 are not legible in the version I read, and the caption does not state which coordinate is plotted horizontally and vertically; please label the axes explicitly and state the units. Fig. 3 shows the entropy bound only for G5E/L^2 = 100; a second energy would let the reader see how the b-dependence changes with energy, which is the paper's central theme.
[Table 1] The caption should state the fit range, the number of points, and the units of b_c/L, and should note that the entries carry no quoted uncertainty.
[References] Reference [32] duplicates reference [25] (both are Veres et al., arXiv:0806.2803); please merge them. Reference [6] (Witten) is listed but never cited in the text.
[§1, §6, §8] Several typographical errors should be corrected: 'the trapped surface seized to exist' should read 'ceased to exist' (§1); 'this growth is very compared to that predicted' is missing a word, presumably 'small' (§6); 'We also studies wall-to-wall collision' should read 'studied' (§8); and 'the it is logarithmically divergent' in §4.3 should read 'it is logarithmically divergent'.

How Pith checks papers → · Full audit of this paper →

The paper

The paper claims

Two colliding gravitational shock waves in Anti-de Sitter space only merge into a black hole if they are aimed within a critical offset, and that offset grows with collision energy.

The reading

The paper asks a sharp question about the dual-gravity picture of a heavy ion collision: when two sheets of energy pass through each other off-center, does a horizon still form? Extending a known central-collision calculation, the authors solve for the marginally trapped surface of two delta-function shock waves in five-dimensional Anti-de Sitter space at nonzero impact parameter $b$, and find that the surface exists only up to a critical value $b_c(E)$; beyond it, no horizon, and in the dual language no thermalization. The critical value is reported as a power law, $b_c/L = 1.07 (G_5 E/L^2)^{0.37}$, over the energies they simulate. They also solve a simpler wall-on-wall collision exactly, recovering the same $E^{2/3}$ entropy growth found for central point shocks. The paper closes by arguing that the literal reading of this model is wrong in detail but possibly right in spirit: the bulk scale should track parton density rather than nucleus size, and the disappearance of the horizon may correspond to the rapid change of collision regime seen in peripheral heavy ion data.

What carries the argument

The load-bearing device is a reformulation of the trapped-surface boundary value problem as a Fredholm integral equation of the first kind. The conditions $ (D - 3/L^2)(Psi_i - Phi_i) = 0 $ inside the would-be trapped region, with $Psi_i = 0$ on its boundary $C$ and the matching condition $nabla Psi_1 cdot nabla Psi_2 = 4$ on $C$, are converted by Green's identity into a surface integral over $C$ using the known Green's function of hyperbolic three-space, $G = -(1/4pi L), e^{2u}/sinh u$ with $cosh u = 1 + ((z-z')^2 + (x_perp - x_perp')^2)/(2 z z')$. The unknown boundary is parametrized as $r = rho(theta)$ with axial symmetry, the integral is discretized on 199 points in $theta$, and the shape is iterated until $B_1 B_2 = 4$ holds; the logarithmically divergent diagonal element is handled by least-squares extraction of $ln|theta-theta'|$ and constant coefficients. The critical impact parameter is then identified as the point where the gradient of the mismatch with respect to the shape diverges. A separate exactly solvable wall-on-wall case, sourced by a delta function at fixed bulk depth $z_0$, reduces to a one-dimensional problem whose solution gives $z_a + z_b = 8 pi G_5 sqrt{E_1 E_2}/L$ and an entropy per transverse area scaling as $(G_5 sqrt{E_1 E_2})^{2/3}$.

Extended reading notes

Core claim

For two shock waves of equal invariant energy $E$ colliding with transverse offset $b$ in $AdS_5$, a marginally trapped surface at the moment of collision exists only for $b$ below a critical value $b_c(E)$. The authors locate this boundary numerically for energies $G_5E/L^2$ from $0.1$ to $100$, and report that the critical impact parameter follows a power law $b_c/L = 1.07 (G_5 E/L^2)^{0.37}$ (their Eq. 49 and Fig. 2), so that $b_c$ grows with collision energy and with the size scale of the colliding object. The critical surface itself does not scale with energy in spherical coordinates; instead it becomes increasingly elongated along the axis of mismatch as the energy rises. Since the area of the trapped surface bounds the entropy produced, the disappearance of the surface at $b_c$ means entropy production switches off discontinuously rather than tapering away, which the authors present as the Anti-de Sitter counterpart of the critical impact parameter found long ago for shock collisions in flat space.

Load-bearing premise

The load-bearing premise is that a critical offset computed for infinitely thin delta-function shocks in Anti-de Sitter space, with the bulk scale set to $z_0 = L$, can be meaningfully compared with a critical centrality in a real nucleus-nucleus collision.

Editorial extensions

If this is right

In the dual description, thermalization in a grazing collision is not a gradual weakening but a threshold: below $b_c$ a horizon forms and entropy is produced, above it nothing does.
Because $b_c$ grows with energy, the same nuclear overlap that thermalizes at high collision energy can fail to thermalize at low energy, giving an energy-dependent boundary between hydrodynamical and non-hydrodynamical collisions.
The trapped-surface area still provides a lower bound on produced entropy at any impact parameter below $b_c$, so the entropy as a function of centrality can be computed once $E$ and $b$ are fixed.
The wall-on-wall solution gives a clean analytic benchmark with the same $E^{2/3}$ entropy growth as the point-shock case, useful for testing numerical schemes built for more realistic sources.

Reading between the lines

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

If the threshold is real, the experimentally cleanest signature would be an energy-dependent, not participant-number-dependent, sharpening in charged multiplicity per participant as centrality decreases; the paper notes the grazing multiplicity data needed for this do not yet exist.
The authors' own argument that the bulk scale should be tied to the saturation scale rather than the nucleus radius suggests a concrete recalibration: run the same integral-equation solver with $z_0$ set by $Q_s$ and check whether the resulting $b_c$ lands near the centrality where elliptic flow departs from hydrodynamic predictions.
The quoted exponent $0.37$ differs from an earlier estimate of $1/6$ at asymptotically large energy; a scan to much larger $G_5E/L^2$ would distinguish a genuine crossover in the exponent from a fit valid only over the simulated range.

Original abstract

AdS/CFT correspondence is now widely used for study of strongly coupled plasmas, such as produced in ultrarelativistic heavy ion collisions at RHIC. While properties of equilibrated plasma and small deviations from equilibrium are by now reasonably well understood, its initial formation and thermal equilibration is much more challenging issue which remains to be studied. In the dual gravity language, these problems are related to formation of bulk black holes, and trapped surfaces we study in this work is a way to estimate the properties (temperature and entropy) of such black hole. Extending the work by Gubser et al, we find numerically trapped surfaces for non-central collision of shock waves with different energies. We observe a critical impact parameter, beyond which the trapped surface does not exist: and we argue that there are experimental indications for similar critical impact parameter in real collisions. We also present a simple solvable example of shock wave collision: wall-on-wall collision. The applicability of this approach to heavy ion collision is critically discussed.

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-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,586 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.90 · human participants 0.02 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.17 · compares with prior results 0.77 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

AdS/CFT correspondence is now widely used for study of strongly coupled plasmas, such as produced in ultrarelativistic heavy ion collisions at RHIC. While properties of equilibrated plasma and small deviations from equilibrium are by now reasonably well understood, its initial formation and thermal equilibration is much more challenging issue which remains to be studied. In the dual gravity language, these problems are related to formation of bulk black holes, and trapped surfaces we study in this work is a way to estimate the properties (temperature and entropy) of such black hole. Extending the work by Gubser et al, we find numerically trapped surfaces for non-central collision of shock waves with different energies. We observe a critical impact parameter, beyond which the trapped surface does not exist: and we argue that there are experimental indications for similar critical impact parameter in real collisions. We also present a simple solvable example of shock wave collision: wall-on-wall collision. The applicability of this approach to heavy ion collision is critically discussed.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	AdS/CFT correspondence is now widely used for study of strongly coupled plasmas, such as produced in ultrarelativistic heavy ion collisions at RHIC.	background 1.00	0.04	0.02	asserted 1.00
s1	While properties of equilibrated plasma and small deviations from equilibrium are by now reasonably well understood, its initial formation and thermal equilibration is much more challenging issue which remains to be studied.	gap 0.97	0.04	0.02	asserted 0.99
s2	In the dual gravity language, these problems are related to formation of bulk black holes, and trapped surfaces we study in this work is a way to estimate the properties (temperature and entropy) of such black hole.	background 0.40	0.40	0.08	asserted 0.95
s3	Extending the work by Gubser et al, we find numerically trapped surfaces for non-central collision of shock waves with different energies.	contribution 0.74	0.96	0.13	asserted 1.00
s4	We observe a critical impact parameter, beyond which the trapped surface does not exist: and we argue that there are experimental indications for similar critical impact parameter in real collisions.	result 0.92	0.88	0.42	asserted 0.55
s5	We also present a simple solvable example of shock wave collision: wall-on-wall collision.	contribution 0.89	0.89	0.03	asserted 0.99
s6	The applicability of this approach to heavy ion collision is critically discussed.	limitation 0.97	0.64	0.04	asserted 0.51

What kind of paper the classifier reports this is: simulation study 0.87 · evidence from simulation or computation 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

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.** (left)The shapes of C (the trapped surface at u = v = 0) at G5E L2 = 1. The impact parameters used in the plot are 0.4L, 0.6L, 0.8L, 1.0L, 1.1L, 1.14L from the outer to the inner. The innermost shape being the critical trapped surface. (right)The shapes of C (the trapped surface at u = v = 0) at G5E L2 = 100. The impact parameters used in the plot are 1.0L, 2.0L, 3.0L, 4.0L, 5.0L, 5.3L from the outer to the inner. The innermost shape being the critical trapped surface. As collision energy grows, the trapped surface gets elongated in the axis of mismatch. Strapped = 2A 4G5 = 1 2G

**Figure 2.** The log-log plot of critical impact parameter vers

**Figure 3.** The scaled entropy 2G5S/L3 (the area of C) as a function of the impact parameter scaled b/L. The energy used is G5E L2 = 100, where L 3 G5 = 2N2 c π higher momenta (UV). First of all this is physically different from the heavy ion collisions, in which case the initial wave function have partons well localized near the so called “saturation scale”, from which the equilibration domain (trapped surface) propagates both into small z (UV) and large z (IR) directions. Second, we think it is also inconsistent: a function growing with z cannot be considered as a small perturbation to th

**Figure 4.** The scaled entropy per transverse area 2G5s L2 (the area of C per transverse area) as a function of scaled effective colliding energy G5E/L2 , where L 3 G5 = 2N2 c π . framework. However now, near the end of this work, we would like to address a wider issues of applicability limits of such approach, as well as the best strategy to use it for practical problems. Gubser et al [4] have applied the gravitational collision scenario literally, selecting initial conditions at time long before nuclei collide. More specifically, they have (i) tuned the scale L or z0 of the bulk collidi

**Figure 5.** (left) PHOBOS data [25] on integrated number of cha

Figures reproduced from arXiv:0902.1508 by the authors.

References

Works cited (35)

[36]

S. S. Gubser, S. S. Pufu and A. Yarom, “Oﬀ-center collisio ns in AdS5 with applications to multiplicity estimates in heavy-ion collisions” 25

View on Pith
[1]

E.V.Shuryak, Prog. Part. Nucl. Phys. 53, 273 (2004) [ hep-ph/0312227]. E.V.Shuryak and I. Zahed, hep-ph/0307267, Phys. Rev. C 70, 021901 (2004) Phys. Rev. D69 (2004) 014011. [ hep-th/0308073]

View on Pith Pith review arXiv 2004
[2]

J. M. Maldacena, Adv. Theor. Math. Phys. 2, 231 (1998) [Int. J. Theor. Phys. 38, 1113 (1999)] [arXiv:hep-th/9711200]

View on Pith Pith review arXiv 1998
[3]

D. Grumiller and P. Romatschke, JHEP 0808, 027 (2008) [arXiv:0803.3226 [hep-th]]

View on Pith Pith review arXiv 2008
[4]

S. S. Gubser, S. S. Pufu and A. Yarom, Phys. Rev. D 78, 066014 (2008) [arXiv:0805.1551 [hep-th]]

View on Pith Pith review arXiv 2008
[5]

J. L. Albacete, Y. V. Kovchegov and A. Taliotis, JHEP 0807, 100 (2008) [arXiv:0805.2927 [hep-th]]

View on Pith Pith review arXiv 2008
[6]

E.Witten, Adv.Theor.Math.Phys.2,235 (1998), hep-th/ 9802150

View on Pith 1998
[7]

S.S.Gubser, I.R.Klebanov and A.A. Tseytlin, Nucl. Phys . B534 (1998) 202 23

View on Pith 1998
[8]

G. Policastro, D. T. Son and A. O. Starinets, Phys. Rev. Le tt. 87 (2001) 081601

View on Pith 2001
[9]

J. Casalderrey-Solana and D. Teaney, hep-ph/0605199

View on Pith Pith review arXiv
[10]

S.-J. Sin and I. Zahed, Phys. Lett. B608 (2005) 265–273, hep-th/0407215. H. Liu, K. Rajagopal, and U. A. Wiedemann, hep-ph/0605178. C. P. Herzog, A. Karch, P. Kovtun, C. Kozcaz, and L. G. Yaﬀe, hep-th/0605158. S. S. Gubser, A. Buchel, hep-th/0605178. hep-th/0605182. S.-J. Sin and I. Zahed, hep-ph/0606049

View on Pith Pith review arXiv 2005
[11]

E. Shuryak, Prog. Part. Nucl. Phys. 62, 48 (2009) [arXiv:0807.3033 [hep-ph]]

View on Pith Pith review arXiv 2009
[12]

D. M. Eardley and S. B. Giddings, Phys. Rev. D 66, 044011 (2002) [arXiv:gr- qc/0201034]

View on Pith 2002
[13]

H. Yoshino and Y. Nambu, Phys. Rev. D 67, 024009 (2003) [arXiv:gr-qc/0209003]

View on Pith Pith review arXiv 2003
[14]

E. Kohlprath and G. Veneziano, JHEP 0206, 057 (2002) [arXiv:gr-qc/0203093]

View on Pith Pith review arXiv 2002
[15]

S. W. Hawking and R. Penrose, Proc. Roy. Soc. Lond. A 314, 529 (1970)

View on Pith 1970
[16]

D. E. Berenstein, R. Corrado, W. Fischler and J. M. Malda cena, “The operator product expansion for Wilson loops and surfaces in the large Phys. Re v. D 59, 105023 (1999) [arXiv:hep-th/9809188]

View on Pith Pith review arXiv 1999
[17]

U. H. Danielsson, E. Keski-Vakkuri and M. Kruczenski, J HEP 9901, 002 (1999) [arXiv:hep-th/9812007]

View on Pith Pith review arXiv 1999
[18]

E. Shuryak, S. J. Sin and I. Zahed, arXiv:hep-th/051119 9

View on Pith
[19]

R. A. Janik and R. Peschanski, Phys. Rev. D 73, 045013 (2006) arXiv:hep-th/0512162, arXiv:hep-th/0606149

View on Pith Pith review arXiv 2006
[20]

S. Nakamura and S. J. Sin, arXiv:hep-th/0607123. Phys. Lett. B 608, 258 (2005) [arXiv:hep-th/0310031]

View on Pith Pith review arXiv 2005
[21]

M. P. Heller, R. A. Janik and R. Peschanski, Acta Phys. Po lon. B 39, 3183 (2008) [arXiv:0811.3113 [hep-th]]

View on Pith Pith review arXiv 2008
[22]

S. Lin and E. Shuryak, Phys. Rev. D 78, 125018 (2008) [arXiv:0808.0910 [hep-th]]

View on Pith Pith review arXiv 2008
[23]

P. M. Chesler and L. G. Yaﬀe, arXiv:0812.2053 [hep-th]. 24

View on Pith Pith review arXiv
[24]

J. Polchinski and M. J. Strassler, Phys. Rev. Lett. 88, 031601 (2002) [arXiv:hep- th/0109174]

View on Pith 2002
[26]

E. V. Shuryak, Phys. Rev. C 76, 047901 (2007) [arXiv:0706.3531 [nucl-th]]

View on Pith Pith review arXiv 2007
[27]

M.Daugherity (for the STAR coll.), Anomalous centrali ty variation..., QM08, J.Phys.G.Nucl/Part.Phys. 35 (2008) 104090

View on Pith 2008
[28]

A. Dumitru, F. Gelis, L. McLerran and R. Venugopalan, Nu cl. Phys. A 810, 91 (2008) [arXiv:0804.3858 [hep-ph]]

View on Pith Pith review arXiv 2008
[29]

L. Alvarez-Gaume, C. Gomez, A. S. Vera, A. Tavanfar and M . A. Vazquez-Mozo, arXiv:0811.3969 [hep-th]

View on Pith Pith review arXiv
[30]

U. Gursoy, E. Kiritsis and F. Nitti, JHEP 0802, 019 (2008) [arXiv:0707.1349 [hep-th]]

View on Pith Pith review arXiv 2008
[31]

U. Gursoy and E. Kiritsis, JHEP 0802, 032 (2008) [arXiv:0707.1324 [hep-th]]

View on Pith Pith review arXiv 2008
[32]

G. I. Veres et al. [PHOBOS Collaboration], arXiv:0806.2803 [nucl-ex]

View on Pith Pith review arXiv
[33]

E. Shuryak, arXiv:0711.0004 [hep-ph]

View on Pith Pith review arXiv
[34]

H. Nastase, Prog. Theor. Phys. Suppl. 174, 274 (2008) [arXiv:0805.3579 [hep-th]]

View on Pith Pith review arXiv 2008
[35]

K. Kang and H. Nastase, Phys. Rev. D 72, 106003 (2005) [arXiv:hep-th/0410173]

View on Pith Pith review arXiv 2005

Forward citations

Cited by 15 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. OpenAlex reports about 97 citations worldwide. Full citation record

Holography and colliding gravitational shock waves in asymptotically AdS_5 spacetime
hep-th 2010-11 conditional novelty 7.0 of 10

A first fully nonlinear simulation of colliding planar shocks in AdS5 shows the post-collision stress tensor hydrodynamizes in about 4/mu of time, with energy density maxima receding at 0.86c.
Boost invariant flow, black hole formation, and far-from-equilibrium dynamics in N = 4 supersymmetric Yang-Mills theory
hep-th 2009-06 conditional novelty 7.0 of 10

Fully nonlinear five-dimensional gravity simulations show that strongly coupled N=4 plasma created from the vacuum reaches viscous hydrodynamics within one to two inverse temperatures.
The Maximal Entanglement Limit in Statistical and High Energy Physics
quant-ph 2026-01 unverdicted novelty 6.0 of 10

Quantum systems reach a Maximal Entanglement Limit where entanglement geometry produces thermal reduced density matrices and probabilistic behavior in statistical and high-energy physics.
Coupling constant corrections in a holographic model of heavy ion collisions
hep-th 2016-10 conditional novelty 6.0 of 10

Adding leading inverse-coupling corrections to a holographic heavy ion collision produces less stopping, more energy near the light cone, a wider initial rapidity profile, less entropy, and a 25% longer hydrodynamisat...
Non-equilibrium Condensation Process in a Holographic Superconductor
hep-th 2010-05 conditional novelty 6.0 of 10

Nonlinear time evolution of a perturbed Reissner-Nordstrom-AdS black hole below the critical temperature ends in the hairy black hole, confirming the endpoint of the holographic superconductor instability.

Show 10 more citing papers

Off-center collisions in AdS_5 with applications to multiplicity estimates in heavy-ion collisions
hep-th 2009-02 conditional novelty 6.0 of 10

An analytic formula for the trapped surface in off-center shock-wave collisions in AdS5 shows that the holographic entropy bound has too weak an impact-parameter dependence to match heavy-ion multiplicity data without...
Holographic Anisotropic Background with Confinement-Deconfinement Phase Transition
hep-th 2018-02 conditional novelty 5.0 of 10

Anisotropic black brane backgrounds in a five-dimensional dilaton-Maxwell system produce orientation-dependent confinement-deconfinement transition lines, with critical points that shift with the quark-pair orientatio...
How big are the smallest drops of quark-gluon plasma?
hep-th 2016-01 conditional novelty 5.0 of 10

Head-on and off-center collisions of localized shock waves in strongly coupled N=4 SYM produce droplets of quark-gluon plasma whose radius is about one inverse effective temperature and whose stress tensor is well des...
Holographic Thermalization with Chemical Potential
hep-th 2012-05 conditional novelty 5.0 of 10

In a holographic model of a charged strongly coupled plasma, the thermalization time is non-monotonic in the chemical potential for small probes: it decreases at small mu/T and increases at large mu/T.
Anisotropic Drag Force from 4D Kerr-AdS Black Holes
hep-th 2010-12 conditional novelty 5.0 of 10

In a rotating Kerr-AdS black hole dual to a spinning 2+1 dimensional plasma, the leading anisotropic drag force on a heavy quark equals three times the quark rest mass times the pressure gradient divided by entropy de...
Holographic Entanglement Entropy in Anisotropic Background with Confinement-Deconfinement Phase Transition
hep-th 2020-03 conditional novelty 4.0 of 10

In an anisotropic holographic model of quark-gluon plasma, the entanglement entropy of a slab-shaped region jumps at the small-to-large black hole phase transition, with jump size depending on anisotropy, chemical pot...
Heavy Ion Collisions: Achievements and Challenges
hep-ph 2014-12 conditional novelty 3.0 of 10

The angular harmonics seen in heavy-ion collisions are damped sound waves of a nearly perfect liquid, and the same collective behaviour extends down to the smallest proton-proton drops.
QCD and strongly coupled gauge theories: challenges and perspectives
hep-ph 2014-04 accept novelty 2.0 of 10

A large multi-author survey of quantum chromodynamics and strongly coupled gauge theories that catalogues the field's established results, open problems, and planned experiments as of early 2014, without reporting a n...
Heavy ions and string theory
hep-th 2013-04 accept novelty 2.0 of 10

Holographic duality gives a tractable model of the strongly coupled quark-gluon plasma, and this review catalogues where its outputs (viscosity, drag, multiplicity bounds, a critical point) land near heavy-ion data an...
Gauge/String Duality, Hot QCD and Heavy Ion Collisions
hep-th 2011-01 accept novelty 2.0 of 10

The review synthesizes a decade of work showing that strongly coupled plasma calculations from gauge/string duality give a coherent, quantitatively useful picture of hot QCD matter and heavy ion observables.

How later papers used it

54 later papers cite it

Evidence: substantial. 44 of the citing papers share no author with it, and 5 of those carry a confident label from Pith's citation classifier.

Pith read 17 of the 132 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

1 later paper by other authors is listed below: 1 used its method or tool. 1 more paper by the same authors is listed: 1 used its method or tool.

Uses its method or tool 2 of 6 papers with this label · 1 by the same authors

Followed this paper to calculate an entropy lower bound as the area of the trapped surface per unit square of the wall.

Holographic phase diagram of quark-gluon plasma formed in heavy-ions collisions (2012) · 0.99 · paraphrased: the licence does not allow quoting

By the same authors

Started with the wall shock wave model proposed in this paper.

On the critical condition in gravitational shock wave collision and heavy ion collisions (2010) (same authors) · 0.95 · paraphrased: the licence does not allow quoting

How the literature uses it

53 arXiv papers cite this in 130 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 77 sentences without a confident label

Builds on it 2 papers

Generalizations of [ref] to the case of nuclear collisions with non-zero impact parameter were presented in [ref] .

Toward Thermalization in Heavy Ion Collisions at Strong Coupling · Introduction · 0.89
In this note our aim is twofold: first to study numerically the formation of marginally closed trapped surfaces in the collision of two shock waves in AdS$_D$ space-time with a nonvanishing impact parameter in the field theory coordinates, thus extending the analysis of [ref] to $D≠5$.

Colliding AdS gravitational shock waves in various dimensions and holography · Introduction · 0.99

Uses its method or tool 6 papers

We therefore need to construct shock waves with sources in the bulk, which we will do following [ref] .

Toward Thermalization in Heavy Ion Collisions at Strong Coupling · The Problem · 0.98
We start with the wall shock wave model proposed in [ref] .

On the critical condition in gravitational shock wave collision and heavy ion collisions · Wall on wall shock wave collision · 0.95
Following [ref] we calculate entropy lower bound as "the area of the trapped surface" per an unite square of the wall[We put "area" and "trapped surface" in quotation marks since in the strict notions of the trapped surface it has to be smooth and compact.

Holographic phase diagram of quark-gluon plasma formed in heavy-ions collisions · The square trapped surface calculation · 0.99

Compares with it 3 papers

The results found in [ref] and [ref] are qualitatively similar to the corresponding situations in flat spacetime [ref] .

Colliding AdS gravitational shock waves in various dimensions and holography · Introduction · 0.98
Our estimate for the produced entropy per unit transverse area $A_⊥$ for a collision of two shock waves with the sources at $z_0$ is [ref] [equation] Using Eqs. ([ref]) and ([ref]) we obtain for $z_0 →∞$ [equation] As $μ^2 ∼s$ with $s$ the center of mass energy of the collision, we get [equation] in agreement with the result obtained in [ref] .

Toward Thermalization in Heavy Ion Collisions at Strong Coupling · Limiting Trapped Surface · 0.97
This criticality may be related to criticality found in [ref] .

Holographic phase diagram of quark-gluon plasma formed in heavy-ions collisions · Introduction · 0.95

Cites it as support 1 paper

Numerical analysis of the formation of a trapped surface in the shock wave collisions in AdS was performed in [ref] , see also [ref] for analytic results, and it supports this conclusion, see formula (3.19) in [ref] .

Energy correlations and Planckian collisions · Planckian energies · 0.99

Cites it as background 25 papers

Lately the problem of thermalization has been studied in the strong coupling framework of the Anti-de Sitter space/conformal field theory (AdS/CFT) correspondence [ref] with the goal of learning about the dynamics of the strongly-coupled QCD medium by studying the strongly coupled medium in $N =4$ super-Yang-Mills (SYM) theory [ref] .

Toward Thermalization in Heavy Ion Collisions at Strong Coupling · Introduction · 0.98
Initially this process has been considered starting from the AdS background [ref] .

Holographic Thermalization in Quark Confining Background · Introduction · 0.90
Due to the Anti-de Sitter space/conformal field theory (AdS/CFT) correspondence [ref] , the problem of two colliding gravitational shock waves, while an important problem from the standpoint of gravity theory [ref] , may also be relevant for high energy hadronic and nuclear collisions at strong coupling [ref] .

Asymmetric Collision of Two Shock Waves in AdS_5 · Introduction · 0.97

What it cites · 21 sentences without a confident label

Uses data or values from 1 paper

In Fig.[ref](left) from [ref] we show some data plotted as a function of the number of participants $N_part$.

System size, energy, centrality and pseudorapidity dependence of charged-particle density in Au+Au and Cu+Cu collisions at RHIC · Are there critical impact parameters in heavy ion collisions? · 0.98

Compares with 5 papers

It is not difficult to complete the integral in $θ$, we finally arrive at $2G_5E=√(1+ρ_0^2/L^2)ρ_0^2$, which is equivalent to (115) in [ref] .

Entropy production in collisions of gravitational shock waves and of heavy ions · Calculation of the Trapped Surface · 0.99
We find interesting critical phenomenon, analogous to shock wave collision in Minkowski background [ref] : beyond certain impact parameter, the trapped surface disappears and black hole formation does not happen.

Classical Black Hole Production in High-Energy Collisions · Introduction · 0.84
We find interesting critical phenomenon, analogous to shock wave collision in Minkowski background [ref] : beyond certain impact parameter, the trapped surface disappears and black hole formation does not happen.

Black holes from high-energy beam--beam collisions · Introduction · 0.84

Cites as background 13 papers

In $D>4$, it was solved numerically in [ref] .

Black hole formation in the grazing collision of high-energy particles · Shock Waves Collision and Trapped Surface · 0.80
Grumiller and Romatschke [ref] tried to describe the initial stage of high energy collisions, starting with the gravitational shock waves of certain type.

On the collision of two shock waves in AdS5 · Introduction · 0.97
Applications of AdS/CFT correspondence [ref] to strongly coupled QGP has generated many fundamental results [ref] , for some further results see [ref] for a recent review.

The Large N Limit of Superconformal Field Theories and Supergravity · Introduction · 0.97

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [36]

S. S. Gubser, S. S. Pufu and A. Yarom, “Oﬀ-center collisio ns in AdS5 with applications to multiplicity estimates in heavy-ion collisions” 25

View on Pith

[2] [1]

E.V.Shuryak, Prog. Part. Nucl. Phys. 53, 273 (2004) [ hep-ph/0312227]. E.V.Shuryak and I. Zahed, hep-ph/0307267, Phys. Rev. C 70, 021901 (2004) Phys. Rev. D69 (2004) 014011. [ hep-th/0308073]

View on Pith Pith review arXiv 2004

[3] [2]

J. M. Maldacena, Adv. Theor. Math. Phys. 2, 231 (1998) [Int. J. Theor. Phys. 38, 1113 (1999)] [arXiv:hep-th/9711200]

View on Pith Pith review arXiv 1998

[4] [3]

D. Grumiller and P. Romatschke, JHEP 0808, 027 (2008) [arXiv:0803.3226 [hep-th]]

View on Pith Pith review arXiv 2008

[5] [4]

S. S. Gubser, S. S. Pufu and A. Yarom, Phys. Rev. D 78, 066014 (2008) [arXiv:0805.1551 [hep-th]]

View on Pith Pith review arXiv 2008

[6] [5]

J. L. Albacete, Y. V. Kovchegov and A. Taliotis, JHEP 0807, 100 (2008) [arXiv:0805.2927 [hep-th]]

View on Pith Pith review arXiv 2008

[7] [6]

E.Witten, Adv.Theor.Math.Phys.2,235 (1998), hep-th/ 9802150

View on Pith 1998

[8] [7]

S.S.Gubser, I.R.Klebanov and A.A. Tseytlin, Nucl. Phys . B534 (1998) 202 23

View on Pith 1998

[9] [8]

G. Policastro, D. T. Son and A. O. Starinets, Phys. Rev. Le tt. 87 (2001) 081601

View on Pith 2001

[10] [9]

J. Casalderrey-Solana and D. Teaney, hep-ph/0605199

View on Pith Pith review arXiv

[11] [10]

S.-J. Sin and I. Zahed, Phys. Lett. B608 (2005) 265–273, hep-th/0407215. H. Liu, K. Rajagopal, and U. A. Wiedemann, hep-ph/0605178. C. P. Herzog, A. Karch, P. Kovtun, C. Kozcaz, and L. G. Yaﬀe, hep-th/0605158. S. S. Gubser, A. Buchel, hep-th/0605178. hep-th/0605182. S.-J. Sin and I. Zahed, hep-ph/0606049

View on Pith Pith review arXiv 2005

[12] [11]

E. Shuryak, Prog. Part. Nucl. Phys. 62, 48 (2009) [arXiv:0807.3033 [hep-ph]]

View on Pith Pith review arXiv 2009

[13] [12]

D. M. Eardley and S. B. Giddings, Phys. Rev. D 66, 044011 (2002) [arXiv:gr- qc/0201034]

View on Pith 2002

[14] [13]

H. Yoshino and Y. Nambu, Phys. Rev. D 67, 024009 (2003) [arXiv:gr-qc/0209003]

View on Pith Pith review arXiv 2003

[15] [14]

E. Kohlprath and G. Veneziano, JHEP 0206, 057 (2002) [arXiv:gr-qc/0203093]

View on Pith Pith review arXiv 2002

[16] [15]

S. W. Hawking and R. Penrose, Proc. Roy. Soc. Lond. A 314, 529 (1970)

View on Pith 1970

[17] [16]

D. E. Berenstein, R. Corrado, W. Fischler and J. M. Malda cena, “The operator product expansion for Wilson loops and surfaces in the large Phys. Re v. D 59, 105023 (1999) [arXiv:hep-th/9809188]

View on Pith Pith review arXiv 1999

[18] [17]

U. H. Danielsson, E. Keski-Vakkuri and M. Kruczenski, J HEP 9901, 002 (1999) [arXiv:hep-th/9812007]

View on Pith Pith review arXiv 1999

[19] [18]

E. Shuryak, S. J. Sin and I. Zahed, arXiv:hep-th/051119 9

View on Pith

[20] [19]

R. A. Janik and R. Peschanski, Phys. Rev. D 73, 045013 (2006) arXiv:hep-th/0512162, arXiv:hep-th/0606149

View on Pith Pith review arXiv 2006

[21] [20]

S. Nakamura and S. J. Sin, arXiv:hep-th/0607123. Phys. Lett. B 608, 258 (2005) [arXiv:hep-th/0310031]

View on Pith Pith review arXiv 2005

[22] [21]

M. P. Heller, R. A. Janik and R. Peschanski, Acta Phys. Po lon. B 39, 3183 (2008) [arXiv:0811.3113 [hep-th]]

View on Pith Pith review arXiv 2008

[23] [22]

S. Lin and E. Shuryak, Phys. Rev. D 78, 125018 (2008) [arXiv:0808.0910 [hep-th]]

View on Pith Pith review arXiv 2008

[24] [23]

P. M. Chesler and L. G. Yaﬀe, arXiv:0812.2053 [hep-th]. 24

View on Pith Pith review arXiv

[25] [24]

J. Polchinski and M. J. Strassler, Phys. Rev. Lett. 88, 031601 (2002) [arXiv:hep- th/0109174]

View on Pith 2002

[26] [26]

E. V. Shuryak, Phys. Rev. C 76, 047901 (2007) [arXiv:0706.3531 [nucl-th]]

View on Pith Pith review arXiv 2007

[27] [27]

M.Daugherity (for the STAR coll.), Anomalous centrali ty variation..., QM08, J.Phys.G.Nucl/Part.Phys. 35 (2008) 104090

View on Pith 2008

[28] [28]

A. Dumitru, F. Gelis, L. McLerran and R. Venugopalan, Nu cl. Phys. A 810, 91 (2008) [arXiv:0804.3858 [hep-ph]]

View on Pith Pith review arXiv 2008

[29] [29]

L. Alvarez-Gaume, C. Gomez, A. S. Vera, A. Tavanfar and M . A. Vazquez-Mozo, arXiv:0811.3969 [hep-th]

View on Pith Pith review arXiv

[30] [30]

U. Gursoy, E. Kiritsis and F. Nitti, JHEP 0802, 019 (2008) [arXiv:0707.1349 [hep-th]]

View on Pith Pith review arXiv 2008

[31] [31]

U. Gursoy and E. Kiritsis, JHEP 0802, 032 (2008) [arXiv:0707.1324 [hep-th]]

View on Pith Pith review arXiv 2008

[32] [32]

G. I. Veres et al. [PHOBOS Collaboration], arXiv:0806.2803 [nucl-ex]

View on Pith Pith review arXiv

[33] [33]

E. Shuryak, arXiv:0711.0004 [hep-ph]

View on Pith Pith review arXiv

[34] [34]

H. Nastase, Prog. Theor. Phys. Suppl. 174, 274 (2008) [arXiv:0805.3579 [hep-th]]

View on Pith Pith review arXiv 2008

[35] [35]

K. Kang and H. Nastase, Phys. Rev. D 72, 106003 (2005) [arXiv:hep-th/0410173]

View on Pith Pith review arXiv 2005