Transplanckian bremsstrahlung and black hole production

Abstract

Classical gravitational bremsstrahlung in particle collisions at transplanckian energies is studied in M4 ×T d . The radiation efficiency ǫ ≡ E rad /E initial is computed in terms of the Schwarzschild radius rS( √ s), the impact parameter b and the Lorentz factor γcm and found to be ǫ = C d (rS/b) 3d+3 γ 2d+1 cm , larger than previous estimates by many powers of γcm ≫ 1. This means that in the ultrarelativistic case radiation loss becomes significant 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 γ ν rS < b < bc, ν = 1/2(d + 1), and b > λC , with bc marking (for d = 0) the loss of the notion of classical trajectories and λC ≡ /mc the Compton length of the scattered particles.Black hole (BH) production in LHC, predicted [1] in models with TeV-scale gravity and large extra dimensions [2-4] about ten years ago, has been the subject of intense theoretical study and numerical simulations (for a review see [5]). The prediction is based on the assumption that for impact parameters of the order of the horizon radius corresponding to the CM collision energy 2E = √ s(1) an event horizon should form due to the non-linear nature of gravity. Thewhere R is the large compactification radius. This classical, essentially, picture of BH formation is justified for transplanckian energies Indeed [6], in this case the D-dimensional Planck length l * = G D /c 3 1/(d+2) = /M * c and the de Broglie length of the collision λ B = c/ √ s satisfy the classicality condition λ B ≪ l * ≪ r S . Furthermore, gravity is believed to be the dominant force in the transplanckian region. Thus, for BH masses large compared to M * , the use of classical Einstein theory is well justified. Moreover, it seems that formation of BHs in four dimensions is predicted by string theory [7]. Thus, in spite of the fact that there are issues which require further study [8], a consensus has been reached that the prediction of BHs in ultra-high energy collisions is robust and is summarized in the widely accepted four-stage process of formation and evaporation of BHs in colliders [1,9], namely (i) formation of a closed trapped surface (CTS) in the collision of shock waves modeling the head-on particle collision, (ii) the balding phase, during which the BH emits gravitational waves and relaxes to the Myers-Perry BH, (iii) Hawking evaporation and superradiance phase in *

Radiation from particles with arbitrary energy falling into higher-dimensional black holes

“…This surprising agreement is at least consistent with the observation that radiation is weak, and therefore nonlinear effects are small. However, as D grows the amount of radiation emission also grows (a similar effect was observed recently in other settings [43,44]). The extrapolation of perturbative results to finite mass ratio must eventually break down, for the following reason.…”

Branestrahlung: Radiation in the particle-brane collision

“…Finally, we would like to draw attention to one peculiarity of the radiation amplitude: it exhibits the backward destructive interference between the local and nonlocal contributions, contrary to the forward destructive interference of the particle-particle bremsstrahlung [38,39] and synchrotron radiation [32,40]. In an attempt to explain the difference, one can observe that i) the brane gravity is repulsive, and ii) the source of radiation is the brane, which moves in the particle rest frame in the backward direction.…”

Gravitational radiation in massless-particle collisions

“…Apart from its obvious relevance in the context of TeV-scale gravity models with large extra dimensions [2], it is very important in relation to the structure of string…”