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

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 greater than or similar to 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.