Generic isolated horizons in loop quantum gravity

TL;DR

This paper generalizes the loop quantum gravity treatment of black hole horizons to arbitrary, non-symmetric isolated horizons. By formulating a classical phase space with a new area-flux connection $ ing V$ and deriving a Chern–Simons–like horizon term, the authors show that the ABK quantization steps remain viable for the full horizon phase space, yielding the same holographic Hilbert space as in the symmetric cases. The key result is that the horizon entropy ${S}_{oldsymbol riangle} = a_{oldsymbol riangle}/(4Goldsymbol ext h)$ persists with the Barbero–Immirzi parameter $eta$ unchanged, but the microscopic interpretation shifts: horizon states now reflect different quantum shapes rather than symmetry-restricted configurations. This supports a broader, symmetry-free quantum geometry of black-hole horizons and clarifies how entropy should be understood as counting horizon shapes within the full phase space, while retaining the standard entropy value and quantization framework.

Abstract

Isolated horizons model equilibrium states of classical black holes. A detailed quantization, starting from a classical phase space restricted to spherically symmetric horizons, exists in the literature and has since been extended to axisymmetry. This paper extends the quantum theory to horizons of arbitrary shape. Surprisingly, the Hilbert space obtained by quantizing the full phase space of \textit{all} generic horizons with a fixed area is identical to that originally found in spherical symmetry. The entropy of a large horizon remains one quarter its area, with the Barbero-Immirzi parameter retaining its value from symmetric analyses. These results suggest a reinterpretation of the intrinsic quantum geometry of the horizon surface.