Bulk Entropy in Loop Quantum Gravity

TL;DR

This paper extends boundary state counting in loop quantum gravity to bulk state counting, enabling detailed analysis of black hole entropy and its relation to boundary area, revealing a holographic regime where entropy scales with area.

Contribution

It introduces a full bulk state counting method in LQG, allowing for a detailed study of entropy-area relationship and identifying a holographic regime with tunable entropy-area factor.

Findings

Entropy scales with boundary area in the holographic regime

The entropy-area factor can be fine-tuned independently of the Immirzi parameter

Provides a new framework for bulk state counting in LQG

Abstract

In the framework of loop quantum gravity (LQG), having quantum black holes in mind, we generalize the previous boundary state counting (gr-qc/0508085) to a full bulk state counting. After a suitable gauge fixing we are able to compute the bulk entropy of a bounded region (the "black hole") with fixed boundary. This allows us to study the relationship between the entropy and the boundary area in details and we identify a holographic regime of LQG where the leading order of the entropy scales with the area. We show that in this regime we can fine tune the factor between entropy and area without changing the Immirzi parameter.