Black holes from high-energy beam--beam collisions

TL;DR

This work extends the Eardley-Giddings framework to determine black-hole formation in high-energy collisions of two finite-front shock waves (massless beams) in $D \ge 4$ by constructing marginally trapped surfaces (MCTS) and, where applicable, closed trapped surfaces (CTS). It analyzes both homogeneous and axisymmetric non-homogeneous beam profiles across dimensions and impact parameters, deriving explicit collapse criteria such as $R_2 \ge 2\sqrt{f_1 f_2}$ in $D=4$ and $R_2 > 2f$ in $D>4$, as well as a universal axisymmetric energy-distribution condition $1=\frac{1}{\Omega_{D-2} r_c^{D-3}}\sqrt{E_1(r_c)E_2(r_c)}$ for finite-radius beams. The findings show that black-hole formation is robust under broad beam configurations, including fractal profiles, and provide a framework to re-evaluate BH-production cross-sections in models with large extra dimensions, while also connecting to string-cosmology scenarios where generic collapse can arise without Planck-scale tuning. Overall, the paper delivers concrete criteria for collapse in trans-Planckian beam collisions and highlights the relevance of geometric, dimensionless parameters over fundamental length scales in predicting black-hole formation and its implications for collider physics and cosmology.

Abstract

Using a recent technique, proposed by Eardley and Giddings, we extend their results to the high-energy collision of two beams of massless particles, i.e. of two finite-front shock waves. Closed (marginally) trapped surfaces can be determined analytically in several cases even for collisions at non-vanishing impact parameter in D\ge 4 space-time dimensions. We are able to confirm and extend earlier conjectures by Yurtsever, and to deal with arbitrary axisymmetric profiles, including an amusing case of ``fractal'' beams. We finally discuss some implications of our results in high-energy experiments and in cosmology.

Figures (1)

• Figure 1: Null geodesics in the metric (\ref{['barmetric']}) for homogeneous beams with $f_1=f_2=f=\frac{R}{2}$ (from Ref.FPV) and the hypersurface $S_1\subset S$. The geodesics come in from the left, parallel to the $z$-axes, then jump according to the dotted lines and reappear on the circle $(\frac{z}{f}+1)^2 +(\frac{x}{f})^2=1$. All the geodesics hitting the wave at $t=z=0$ converge in $-f$ at the same time, the outermost coming in at 90 degrees. The bold line is the hypersurface $S_1:\ z=t=\frac{x^2}{4f}-f$. The dashed-dotted line is the hypersurface $z=-\frac{x^2}{4f}$.