Transplanckian bremsstrahlung and black hole production

Classical gravitational bremsstrahlung in particle collisions at transplanckian energies is studied in M4×Td. The radiation efficiency ϵ≡Erad/Einitial is computed in terms of the Schwarzschild radius rS(s), the impact parameter b and the Lorentz boost factor γcm and found to be ϵ=Cd(rS/b)3d+3γcm2d+1, larger than previous estimates by several powers of γcm≫1. This means that in the ultrarelativistic case radiation loss becomes significant already for b≫rS, so radiation damping must be taken into account in estimates of black hole production at transplanckian energies. The result is reliable for impact parameters in the overlap of γνrSλC, with bc marking (for d≠0) the loss of the notion of classical trajectories and λC≡ℏ/mc being the Compton length of the scattered particles.