Entropy of generic quantum isolated horizons

Abstract. We review our recent proposal of a method to extend the quantization of spherically symmetric isolated horizons, a seminal result of loop quantum gravity, to a phase space containing horizons of arbitrary geometry. Although the details of the quantization remain formally unchanged, the physical interpretation of the results can be quite different. We highlight several such differences, with particular emphasis on the physical interpretation of black hole entropy in loop quantum gravity. The confirmation of the Bekenstein–Hawking entropy formula by Ashtekar, Baez, Corichi and Krasnov [1–3] (ABCK) is one of the triumphs of loop quantum gravity. The ABCK approach begins by quantizing a classical phase space whose points correspond to spacetimes with inner boundary at a spherically symmetric isolated horizon [4–7]. The calculation relies on spherical symmetry (just of the intrinsic geometry of the horizon itself) to make the symplectic structure on that phase space, and thus the ensuing quantization, well-defined. This paper is concerned with an apparent inconsistency in the roles played by spherical symmetry before and after quantization in the ABCK approach. Imposing spherical symmetry classically restricts the allowed bulk fields such that they induce a round metric on the horizon