  We study the spectrum of the worldsheet theory of the bosonic closed string
in the massless and extremal rotating BTZ black holes. We use a hyperbolic
Wakimoto representation of the SL(2,R) currents to construct vertex operators
for the string modes on these backgrounds. We argue that there are tachyons in
the twisted sector, but these are not localised near the horizon. We study the
relation to the null orbifold in the limit of vanishing cosmological constant.
We also discuss the problem of extending this analysis to the supersymmetric
case.
