Entropy of Self-Gravitating Systems from Holst's Lagrangian

TL;DR

This paper demonstrates that conservation laws derived from Holst's Lagrangian, used in Loop Quantum Gravity, align with those in standard General Relativity on solutions, supporting the classical entropy calculations of black holes.

Contribution

It shows that Holst's Lagrangian yields the same classical conserved quantities and entropy as standard GR, validating its use in black hole entropy computations.

Findings

Conservation laws from Holst's Lagrangian agree with GR on solutions.

Holst's Lagrangian reproduces the standard entropy law S=A/4.

Supports the classical validity of LQG black hole entropy calculations.

Abstract

We shall prove here that conservation laws from Holst's Lagrangian, often used in LQG, do not agree with the corresponding conservation laws in standard GR. Nevertheless, these differences vanish on-shell, i.e. along solutions, so that they eventually define the same classical conserved quantities. Accordingly, they define in particular the same entropy of solutions, and the standard law S=A/4 is reproduced for systems described by Holst's Lagragian. This provides the classical support to the computation usually done in LQG for the entropy of black holes which is in turn used to fix the Barbero-Immirzi parameter.