The scaling of black hole entropy in loop quantum gravity

TL;DR

The work addresses whether black hole entropy in loop quantum gravity can reproduce Hawking's area law without fixing the Immirzi parameter by examining entropy from the perspective of local observers near the horizon. It introduces a local area Hamiltonian and a partition function that includes both geometric and non-geometric (matter) degrees of freedom, constrained by a micro-holography bound to ensure finiteness, and derives an entropy formula with matter-induced corrections. A renormalization-group analysis shows Hawking entropy is recovered in the infrared under a specific renormalization condition on the couplings, with the puncture chemical potential vanishing at large scales and logarithmic corrections arising from matter loops. The framework connects Planck-scale discreteness to a continuum IR description and casts Hawking entropy as a renormalization condition, providing a principled way to incorporate entanglement-type corrections into the semiclassical limit of LQG.

Abstract

We discuss some general properties of black hole entropy in loop quantum gravity from the perspective of local stationary observers at distance l from the horizon. The present status of the theory indicates that black hole entropy differs from the low energy (IR) expected value A/(4G) (in natural units) in the deep Planckian regime (UV). The partition function is well defined if the number of non-geometric degrees of freedom g_M (encoding the degeneracy of the area a_p eigenvalue at a puncture p) satisfy the holographic bound g_M < exp(ap/(4G)). Our framework provides a natural renormalization mechanism such that S_UV ---> S_IR=A/(4 G) as the scale l flows.