Unitarity restoring graviton radiation in the collapse regime of scattering

Abstract

We investigate graviton radiation in gravitational scattering at small impact parameters $b<R\equiv 2G\sqrt{s}$ and extreme energies $s\gg M_P^2$, a regime in which classical collapse is thought to occur, and thus radiation may be suppressed also. Here however, by analyzing the soft-based representation of radiation recently proposed in the semiclassical ACV framework, we argue that gravitons can be efficiently produced in the untrapped region $|\boldsymbol{x}|\gtrsim R>b$, so as to suggest a possible completion of the unitarity sum. In fact, such energy radiation at large distances turns out to compensate and to gradually reduce to nothing the amount of energy $E'$ being trapped at small-$b$'s, by thus avoiding the quantum tunneling suppression of the elastic scattering and suggesting a unitary evolution. We finally look at the coherent radiation sample so obtained and we find that, by energy conservation, it develops an exponential frequency damping corresponding to a "quasi-temperature" of order $\hbar/R$, which is naturally related to a Hawking radiation and is suggestive of a black-hole signal at quantum level.