  According to a recent proposal, the so-called Barbero-Immirzi parameter of
Loop Quantum Gravity can be fixed, using Bohr's correspondence principle, from
a knowledge of highly-damped black hole oscillation frequencies. Such
frequencies are rather difficult to compute, even for Schwarzschild black
holes. However, it is now quite likely that they may provide a fundamental link
between classical general relativity and quantum theories of gravity. Here we
carry out the first numerical computation of very highly damped quasinormal
modes (QNM's) for charged and rotating black holes. In the Reissner-Nordstr\"om
case QNM frequencies and damping times show an oscillatory behaviour as a
function of charge. The oscillations become faster as the mode order increases.
At fixed mode order, QNM's describe spirals in the complex plane as the charge
is increased, tending towards a well defined limit as the hole becomes
extremal. Kerr QNM's have a similar oscillatory behaviour when the angular
index $m=0$. For $l=m=2$ the real part of Kerr QNM frequencies tends to
$2\Omega$, $\Omega$ being the angular velocity of the black hole horizon, while
the asymptotic spacing of the imaginary parts is given by $2\pi T_H$.
