BF theory explanation of the entropy for rotating isolated horizons

TL;DR

This paper demonstrates that rotating isolated horizons can be described by an SO(1,1) BF theory, leading to an entropy consistent with the Bekenstein-Hawking area law, similar to nonrotating cases.

Contribution

It extends the BF theory approach to rotating isolated horizons, showing the boundary degrees of freedom and entropy are unaffected by rotation.

Findings

Boundary degrees of freedom described by SO(1,1) BF theory

Entropy matches Bekenstein-Hawking law with the same Barbero-Immirzi parameter

Symplectic form remains unchanged for rotating horizons

Abstract

In this paper, the isolated horizons with rotation are considered. It is shown that the symplectic form is the same as that in the nonrotating case. As a result, the boundary degrees of freedom can be also described by an SO$(1,1)$ BF theory. The entropy satisfies the Bekenstein-Hawking area law with the same Barbero-Immirzi parameter.