  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.
