Black Hole Entropy from complex Ashtekar variables

TL;DR

This paper demonstrates that by analytically continuing the Barbero-Immirzi parameter to complex values, the microstate count in loop quantum gravity aligns with the Bekenstein-Hawking entropy, revealing a novel feature of complex Ashtekar variables.

Contribution

It introduces a method to analytically continue the Barbero-Immirzi parameter to complex values, linking microstate counts to classical black hole entropy.

Findings

Microstate count matches Bekenstein-Hawking entropy for large area

Analytic continuation to complex parameters reveals new quantum gravity features

Supports the relevance of complex Ashtekar variables in quantum gravity

Abstract

In loop quantum gravity, the number $N_\Gamma(A,\gamma)$ of microstates of a black hole for a given discrete geometry $\Gamma$ depends on the so-called Barbero-Immirzi parameter $\gamma$. Using a suitable analytic continuation of $\gamma$ to complex values, we show that the number $N_\Gamma(A,\pm i)$ of microstates behaves as $\exp(A/(4\ell_\text{Pl}^2))$ for large area $A$ in the large spin semiclassical limit. Such a correspondence with the semiclassical Bekenstein-Hawking entropy law points towards an unanticipated and remarkable feature of the original complex Ashtekar variables for quantum gravity.