The two canonical conjugate pairs at the horizon of a D1D5 black hole

TL;DR

This paper demonstrates that a D1D5 black hole has a second canonical conjugate pair involving the opening angle at the r-y surface and a Wald-like entropy term, indicating a superposition of surfaces with different conical singularities.

Contribution

It identifies a new canonical pair at the horizon of a D1D5 black hole, extending the understanding of horizon geometry and quantum properties.

Findings

Existence of a second canonical conjugate pair involving the r-y surface.

Uncertainty in the opening angle at r-y suggests superposition of geometries.

Connection to string theory excitations of D1D5 black holes.

Abstract

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.