On the horizon area of effective loop quantum black holes

TL;DR

This paper analyzes an effective loop quantum gravity model of black holes, demonstrating that quantum corrections are small at the horizon and that the model can describe Planck-scale black holes with classical-like exterior metrics.

Contribution

It solves the dynamical equations of the ABBV model, derives the scaling of the polymerisation parameter, and shows the quantum corrections are minimal even at Planck scales.

Findings

Quantum corrections at the horizon are small even for Planck-scale black holes.

The exterior metric remains similar to classical Schwarzschild, with a screened central mass.

The horizon area remains unchanged from classical theory.

Abstract

Effective models of quantum black holes inspired by Loop Quantum Gravity (LQG) have had success in resolving the classical singularity with polymerisation procedures and by imposing the LQG area gap as a minimum area. The singularity is replaced by a hypersurface of transition from black to white holes, and a recent example is the Ashtekar, Olmedo and Singh (AOS) model for a Schwarzschild black hole. More recently, a one-parameter model, with equal masses for the black and white solutions, was suggested by Alonso-Bardaji, Brizuela and Vera (ABBV). An interesting feature of their quantisation is that the angular part of the metric retains its classical form and the horizon area is therefore the same as in the classical theory. In the present contribution we solve the dynamical equations derived from the ABBV effective Hamiltonian and, by applying the AOS minimal area condition, we obtain the scaling of the polymerisation parameter with the black hole mass. We then show that this effective model can also describe Planck scale black holes, and that the curvature and quantum corrections at the horizon are small even at this scale. By generating the exterior metric through a phase rotation in the dynamical variables, we also show that, for an asymptotic observer, the Kretschmann scalar is the same as in the classical Schwarzschild solution, but with a central mass screened by the quantum fluctuations.