  We provide an explicit construction of classical strings that have endpoints
on the horizons of the 2D Lorentzian black hole. We argue that this is a dual
description of geodesics that are localized around the horizon which are the
Lorentzian counterparts of the winding strings of the Euclidean black hole (the
cigar geometry). Identifying these with the states of the black hole, we can
expect that issues of black hole information loss can be posed sharply in terms
of a fully quantizable string theory.
