Gravitational energy loss in high energy particle collisions: ultrarelativistic plunge into a multidimensional black hole

TL;DR

This work investigates gravitational energy loss when an ultrarelativistic particle radially plunges into a $D=n+2$-dimensional Schwarzschild–Tangherlini black hole, within a brane-world motivated context. Using the Kodama–Ishibashi perturbation framework and a Green's-function integration, the authors compute scalar perturbations, extract quasinormal modes with a WKB approach, and obtain the energy spectra, total emitted energy, and angular distribution of gravitational radiation across even dimensions $D=4$–$10$. They find that the total gravitational-energy loss remains modest (roughly $7$–$13\%$ depending on $n$), with spectra shaped by a cutoff near the fundamental QNM and a strong dependence on multipole order, shifting dominance to higher $l$ as $n$ grows. The results have implications for TeV-scale black-hole production phenomenology, highlighting energy not trapped inside the horizon and guiding expectations for gravitational and non-gravitational junk in high-energy collisions.

Abstract

We investigate the gravitational energy emission of an ultrarelativistic particle radially falling into a D-dimensional black hole. We numerically integrate the equations describing black hole gravitational perturbations and obtain energy spectra, total energy and angular distribution of the emitted gravitational radiation. The black hole quasinormal modes for scalar, vector, and tensor perturbations are computed in the WKB approximation. We discuss our results in the context of black hole production at the TeV scale.