  Recently it has been proposed that a strange logarithmic expression for the
so-called Barbero-Immirzi parameter, which is one of the ingredients that are
necessary for Loop Quantum Gravity (LQG) to predict the correct black hole
entropy, is not another sign of the inconsistency of this approach to
quantization of General Relativity, but is rather a meaningful number that can
be independently justified in classical GR. The alternative justification
involves the knowledge of the real part of the frequencies of black hole
quasinormal states whose imaginary part blows up. In this paper we present an
analytical derivation of the states with frequencies approaching a large
imaginary number plus ln 3 / 8 pi M; this constant has been only known
numerically so far. We discuss the structure of the quasinormal states for
perturbations of various spin. Possible implications of these states for
thermal physics of black holes and quantum gravity are mentioned and
interpreted in a new way. A general conjecture about the asymptotic states is
stated. Although our main result lends some credibility to LQG, we also review
some of its claims in a critical fashion and speculate about its possible
future relevance for Quantum Gravity.
