Toward the AdS/CFT Gravity Dual for High Energy Collisions: II. The Stress Tensor on the Boundary

TL;DR

This work advances the AdS/CFT program for time-dependent high-energy collisions by computing the boundary stress tensor from bulk sources in AdS_5. Using a Green's-function approach to the time-dependent linearized Einstein equations, it contrasts a stationary bulk stone (zero boundary stress) with a dynamically evolving open string (nonzero, explosion-like boundary stress) and analyzes near-field, slow-motion, and multi-string scenarios. The results reveal non-hydrodynamic, non-equilibrated boundary dynamics and motivate future incorporation of backreaction and horizon formation to understand entropy production and hydrodynamization. The study thus clarifies how bulk string dynamics imprint on boundary observables and outlines a path toward modeling equilibration via a two-membrane framework.

Abstract

In this second paper of the series we calculate the stress tensor of excited matter, created by ``debris'' of high energy collisions at the boundary. We found that massive objects (``stones'') falling into the AdS center produce gravitational disturbance which however has $zero$ stress tensor at the boundary. The falling open strings, connected to receeding charges, do produce a nonzero stress tensor which we found analytically from time-dependent linearized Einstein equations in the bulk. It corresponds to exploding non-equilibrium matter: we discuss its behavior in some detail, including its internal energy density in a comoving frame and the ``freezeout surfaces''. We then discuss what happens for the ensemble of strings.

Figures (4)

• Figure 1: (color online) The contours of energy density $T^{00}$, in unit of $\frac{2\sqrt{{\lambda}}}{f_0^3\pi^2}$, in $x_1-x_2$ plane at different time. The three plots are made for $t=r$, $t=10r$ and $t=50r$ from top to bottom. Note the quark/antiquark is at $x_1=\pm vt$. In the slow moving limit, they are nearly at the origin. The magnitude of $T^{00}$ is represented by the color, with darker color corresponding to greater magnitude. As time increases, the shape of the contours gets elongated along $x_1$ axis
• Figure 2: (color online)The contours of momentum density $T^{0i}$, in unit of $\frac{2\sqrt{{\lambda}}}{f_0^3\pi^2}$, in $x_1-x_2$ plane at different time. The three plots are made for $t=r$, $t=10r$ and $t=50r$ from top to bottom. Note the quark/antiquark is at $x_1=\pm vt$. In the slow moving limit, they are nearly at the origin. The magnitude is represented by color, with darker color corresponding to greater magnitude. The direction of the momentum density is indicated by normalized arrows
• Figure 3: (color online)the profile of $\epsilon$, in unit of $\frac{2\sqrt{{\lambda}}}{f_0^3\pi^2}$, at $t=1$ with $r\approx 0.2-1$. The evolution of the shape of contour, i.e. the freezeout surface is contained in this plot. The contours with large $r$(small $\epsilon$) are nearly spherical while the contours with small $r$(large $\epsilon$) are elongated along $x_1$ axis
• Figure 4: (color online)The contours of energy density, in unit of $\frac{8\sqrt{{\lambda}}}{f_0^3\pi}$, as a function of $t$ and $x_1$. The magnitude is represented by color, with darker color corresponding to greater magnitude.