Exploring an S-matrix for gravitational collapse

TL;DR

The paper extends the ACV S-matrix framework to axisymmetric collisions of extended sources, showing CTS-based bounds align with the onset of critical behavior in the S-matrix singularities. By reducing to a 1D evolution for $\rho(t)$, the authors solve the axisymmetric equations of motion and map out critical lines across diverse source profiles. Near criticality, the on-shell action and graviton multiplicity display universal, fractional-power scaling reminiscent of Choptuik critical collapse, with implications for estimating black-hole formation and energy absorption. The results validate the axisymmetric case as a robust laboratory for connecting CTS criteria, S-matrix structure, and possible Choptuik-like exponents, while outlining the need for momentum-space analyses to fully capture inelastic dynamics and beyond-critical behavior.

Abstract

We analyze further a recently proposed S-matrix description of transplanckian scattering in the specific case of axisymmetric collisions of extended sources, where some of the original approximations are not necessary. We confirm the claim that such an approximate description appears to capture the essential features of (the quantum counterpart of) classical gravitational collapse. More specifically, the S-matrix develops singularities whose location in the sources' parameter space are consistent with (and numerically close to) the bounds coming from closed-trapped-surface collapse criteria. In the vicinity of the critical "lines" the phase of the elastic S-matrix exhibits a universal fractional-power behaviour reminiscent of Choptuik's scaling near critical collapse.

Figures (6)

• Figure 1: Looking for the maximal solution of Eqs.(\ref{['firstorder']}), $\sigma(1) = 1$, as a function of the initial value $\sigma(0)=\sigma_0$ (in the specific case $d=1$, $R/L=0.46$)
• Figure 2: The critical (solid) line in the $(R,d)$ plane having set $L=1$. We also show (dashed line) the upper bound on $R_c$ from the CTS criterion (\ref{['KVcrit']}). The BH phase is above the solid line.
• Figure 3: Two gaussian sources around the origin. The BH phase lies below the critical (solid) line in the $(L_1,L_2)$ plane. We also show (dashed line) the lower bound on the curve from the CTS criterion (\ref{['KVcrit']}).
• Figure 4: The maximal solution, in the dispersive phase, also for $t>1$ (two identical sources, eq. (\ref{['acv']}), with $d=1$, $R/L=0.44$).
• Figure 5: The total multiplicity of emitted gravitons (points) and the best fit: $0.138-0.46(R_c-R)^{0.523}$. A fit with the fixed power $1/2$ is marginally worse.