  The Euclidian opening angle at the $r-t_E$ surface, $\Theta_{r-t_E}$ at the
horizon of a black hole is canonically conjugate to the black hole entropy. We
prove that for a $D1D5$ black hole there exists in addition to this pair,
another canonical pair: the opening angle at the $r-y$ surface, $\Theta_{r-y}$
and a Wald like term $S_{Wr-y}$. This leads to an uncertainty at $\Theta_{r-y}$
which suggests that the surface $r-y$ is actually a superposition of surfaces
with different conical singularities. This corresponds to the same type of
singularities obtained by string theory excitations of a $D1D5$ black hole.
