Quasi-normal modes and black-hole quantum mechanics in 2 + 1 dimensions

We explore the relationship between classical quasi-normal mode frequencies and black-hole quantum mechanics in 2 + 1 dimensions. Following a suggestion of Hod, we identify the real part of the quasi-normal frequencies with the fundamental quanta of black-hole mass and angular momentum. We find that this identification leads to the correct quantum behaviour of the asymptotic symmetry algebra, and thus of the dual conformal field theory. Finally, we suggest a further connection between quasi-normal mode frequencies and the spectrum of a set of nearly degenerate ground states whose multiplicity may be responsible for the Bekenstein-Hawking entropy.