Entropy production in collisions of gravitational shock waves and of heavy ions

TL;DR

This paper leverages the gauge/gravity duality to bound entropy production in heavy-ion collisions by computing the area of a marginally trapped surface formed in head-on collisions of gravitational shock waves in AdS$_5$. Using a trapped-surface construction, it derives S$_{\rm trapped} \approx π (L^3/G_5)^{1/3} (2 E L)^{2/3} for large q_C, and calibrates L and E against lattice and phenomenological data to compare with RHIC results (yielding S on the order of 3×10⁴ for central collisions) and LHC predictions. The authors also discuss an O(D−2) remnant of conformal symmetry that can appear in a class of AdS shock-wave collisions, potentially realized in central heavy-ion events with D=5, and explore how halo-like broadening of the energy profile could modify the energy scaling of S_trapped to better match experimental trends. Overall, the work provides a tractable holographic framework to relate early-stage energy density to late-time entropy production, while highlighting caveats related to energy distribution, coupling, and the precise applicability of the Penrose bound in AdS. The results offer an interpretive bridge between gravitational shock dynamics and quark–gluon plasma phenomenology, with implications for LHC-era entropy scaling and possible symmetry remnants in central collisions.

Abstract

We calculate the area of a marginally trapped surface formed by a head-on collision of gravitational shock waves in AdS_D. We use this to obtain a lower bound on the entropy produced after the collision. A comparison to entropy production in heavy ion collisions is included. We also discuss an O(D-2) remnant of conformal symmetry which is present in a class of gravitational shock wave collisions in AdS_D and which might be approximately realized (with D=5) in central heavy-ion collisions.

Figures (4)

• Figure 1: A projection of the marginally trapped surface that we use onto a fixed time slice of the $\hbox{AdS}_5$ geometry. The size of the trapped surface is controlled by the energy of the massless particles that generate the shock waves. These particles are shown as dark blue dots.
• Figure 2: A plot of the total number of charged particles vs. energy. The data points were taken from table II of the PHOBOS results Back:2002wb. We show in red the region consistent with the bound (\ref{['FoundSofE']}) obtained via the gauge-string duality, using point-sourced shocks and estimates described in the text, and assuming the bound (\ref{['PenroseBound']}). The blue curve corresponds to the prediction of the Landau model Landau:1953gs.
• Figure 3: The hyperboloid whose covering space is $\hbox{AdS}_5$, with the transverse coordinates $X^1$, $X^2$, and $X^4$ suppressed. The closed green curve is the trajectory of a massive test particle. When the particle is infinitely boosted, so that $X^0=X^3$, the trajectory degenerates into the two blue lines.
• Figure 4: Left: The dependence of $\langle T_{uu} \rangle$ on transverse radius $x_T$, both for an infinitely boosted black hole in $\hbox{AdS}_5$ and for an infinitely boosted Woods-Saxon profile. $\langle T_{uu} \rangle$ is proportional to $\delta(u)$, and the quantities that we plot omit this singular factor. The normalization of the Woods-Saxon profile was chosen so that its maximum is $1$. The normalization and width of $\langle T_{uu} \rangle$ from the gravitational shock wave was chosen so that the integral and rms transverse radius match to the values extracted from the Woods-Saxon profile. Right: The area under the curves $x_T \langle T_{uu} \rangle$ obtained from Woods-Saxon and AdS profiles are the same, indicating that the total energy is the same.