Up to eleven: radiation from particles with arbitrary energy falling into higher-dimensional black holes

TL;DR

This paper analyzes gravitational radiation emitted by particles falling into higher-dimensional black holes, revealing how radiation varies with spacetime dimensions and particle energy, and suggesting a potential change in behavior beyond eleven dimensions.

Contribution

It provides the first detailed calculation of radiation from particles with arbitrary energy into higher-dimensional black holes across multiple dimensions, highlighting a possible qualitative shift at eleven dimensions.

Findings

Radiated energy increases with dimension n for particles from rest.

A local minimum in radiation occurs at a critical n for energies 1<E<=2.

Radiation predictions break down at n=11, indicating a possible change in gravitational emission behavior.

Abstract

We consider point particles with arbitrary energy per unit mass E that fall radially into a higher-dimensional, nonrotating, asymptotically flat black hole. We compute the energy and linear momentum radiated in this process as functions of E and of the spacetime dimensionality D=n+2 for n=2,...,9 (in some cases we go up to 11). We find that the total energy radiated increases with n for particles falling from rest (E=1). For fixed particle energies 1<E<=2 we show explicitly that the radiation has a local minimum at some critical value of n, and then it increases with n. We conjecture that such a minimum exists also for higher particle energies. The present point-particle calculation breaks down when n=11, because then the radiated energy becomes larger than the particle mass. Quite interestingly, for n=11 the radiated energy predicted by our calculation would also violate Hawking's area bound. This hints at a qualitative change in gravitational radiation emission for n>11. Our results are in very good agreement with numerical simulations of low-energy, unequal-mass black hole collisions in D=5 (that will be reported elsewhere) and they are a useful benchmark for future nonlinear evolutions of the higher-dimensional Einstein equations.