Transplanckian bremsstrahlung and black hole production

Abstract

Classical gravitational bremsstrahlung in particle collisions at transplanckian energies is studied in ${\mathcal{M}}_4\times {\mathcal{T}}^d$. The radiation efficiency $ϵ\equiv E_{\mathrm{rad}}/E_{\mathrm{initial}}$ is computed in terms of the Schwarzschild radius $r_S(\sqrt{s})$, the impact parameter $b$ and the Lorentz factor ${\gamma }_{\mathrm{cm}}$ and found to be $ϵ=C_d(r_S/b{)}^{3d+3}{\gamma }_{\mathrm{cm}}^{2d+1}$, larger than previous estimates by many powers of ${\gamma }_{\mathrm{cm}}\gg 1$. The result is reliable for impact parameters in the overlap of $r_S<b<b_c\mathrm{and}b>{\lambda }_C$, with $b_c$ marking (for $d\ne 0$) the loss of the notion of classical trajectories and ${\lambda }_C\equiv \hslash /mc$ the Compton length of the scattered particles. The condition on $s$ and $m$ for extreme radiation damping and (presumably) no black hole production is also derived.

Comments: 4 pages, revtex 4. The discussion section is changed to better clarify the region of validity of our calculation. The physical conclusions and the abstract are modified accordingly. A few more references added. We just added the preprint number CCTP-2010-18