Two canonical conjugate pairs at the horizon of a D1D5 black hole

The Euclidean opening angle at the r-tE surface, Θr-tE 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, Θr-y, and a Wald-like term SWr-y. This leads to an uncertainty at Θr-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.