Lessons from gauge fixing and polymerization of loop quantum black holes with a cosmological constant

TL;DR

This paper investigates loop quantum black holes with a cosmological constant, revealing that fixed polymerization parameters lead to issues with positive cosmological constants, while negative ones are free of such problems.

Contribution

It demonstrates the limitations of fixed polymerization parameters in loop quantum black holes with a positive cosmological constant and compares these to known issues in cosmological models.

Findings

Large quantum effects can appear at small curvatures with positive cosmological constant.

Central singularity is resolved in all cases.

Incompatibility of Kantowski-Sachs gauge with fixed polymerization parameters for positive cosmological constant.

Abstract

Loop quantization of Schwarzschild black holes with a cosmological constant for polymerization parameters which are constant is studied in the effective spacetime description. We show that for the positive cosmological constant there can be an appearance of large quantum effects at small spacetime curvatures. These effects can manifest as an additional black hole horizon. While the central singularity is resolved in all the cases, these limitations demonstrate incompatibility of the Kantowski-Sachs gauge and schemes with fixed polymerization parameters in the presence of a positive cosmological constant. In contrast, the case of a negative cosmological constant is free of such problematic features. Noted limitations are similar to those in the $\mu_o$ scheme for the loop quantization of cosmological models.