Black hole entropy from loop quantum gravity in higher dimensions

TL;DR

<3-5 sentence high-level summary>This work extends loop quantum gravity to higher spacetime dimensions by treating black hole horizons as boundary degrees of freedom encoded by an SO$(D{+}1)$ gauge structure. The horizon Hilbert space, built from simple representations, reduces to the well-known 3+1 dimensional counting, with a dimensionful area spectrum given by $A_H = 8\pi G\beta \sum_i \sqrt{\lambda_i(\lambda_i+D-1)}$ and a corresponding level bound $k = \lceil A_H/(8\pi G\beta)\rceil$, leading to a horizon intertwiner dimension akin to the SU$(2)$ case. Entropy is derived by tracing over bulk gauge-related states, yielding leading order $S \sim A_H/(4G)$ with universal logarithmic corrections or via an analytic continuation of the Barbero–Immirzi parameter that reproduces the expected area law. A polyhedral interpretation via Minkowski reconstruction extends the geometric picture to higher dimensions, linking simple intertwiners to higher-dimensional horizon geometries and suggesting robustness under generalizations such as Lovelock gravity.

Abstract

We propose a derivation for computing black hole entropy for spherical non-rotating isolated horizons from loop quantum gravity in four and higher dimensions. The state counting problem effectively reduces to the well studied 3+1-dimensional one based on an SU(2)-Chern-Simons theory, differing only in the precise form of the area spectrum.