TL;DR
This paper explores the quantum properties of black holes by introducing a new degree of freedom related to the horizon's opening angle, leading to insights into black hole entropy and quantum states.
Contribution
It introduces a novel conjugate variable to the horizon area and extends the Wheeler-DeWitt equation to include this degree of freedom.
Findings
The opening angle at the horizon is canonically conjugate to the horizon area.
The wave function of a black hole depends on this new degree of freedom.
Summing over horizon areas reproduces black hole entropy.
Abstract
The standard (Euclidean) action principle for the gravitational field implies that for spacetimes with black hole topology, the opening angle at the horizon and the horizon area are canonical conjugates. It is shown that the opening angle bears the same relation to the horizon area that the time separation bears to the mass at infinity. The dependence of the wave function on this new degree of freedom is governed by an extended Wheeler-DeWitt equation. Summing over all horizon areas yields the black hole entropy.
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