Understanding quantum black holes from quantum reduced loop gravity

TL;DR

This paper analyzes a top-down loop quantum black hole model, deriving known solutions, examining quantum corrections, and revealing that the spacetime is geodesically complete without additional extensions, contrasting with bottom-up models.

Contribution

It provides a systematic study of the ABP top-down LQBH model, deriving solutions, analyzing quantum corrections, and demonstrating spacetime completeness without extensions.

Findings

Inverse volume corrections are negligible for macroscopic black holes.

The spacetime is geodesically complete without additional extensions.

Different asymptotic behaviors depend on model parameters.

Abstract

We systematically study the top-down model of loop quantum black holes (LQBHs), recently derived by Alesci, Bahrami and Pranzetti (ABP). To understand the structure of the model, we first derive several well-known LQBH solutions by taking proper limits. These include the B\"ohmer-Vandersloot and Ashtekar-Olmedo-Singh models, which were all obtained by the so-called bottom-up polymerizations within the framework of the minisuperspace quantizations. Then, we study the ABP model, and find that the inverse volume corrections become important only when the radius of the two-sphere is of the Planck size. For macroscopic black holes, the minimal radius obtained at the transition surface is always much larger than the Planck scale, and hence these corrections are always sub-leading. The transition surface divides the whole spacetime into two regions, and in one of them the spacetime is asymptotically Schwarzschild-like, while in the other region, the asymptotical behavior sensitively depends on the ratio of two spin numbers involved in the model, and can be divided into three different classes. In one class, the spacetime in the 2-planes orthogonal to the two spheres is asymptotically flat, and in the second one it is not even conformally flat, while in the third one it can be asymptotically conformally flat by properly choosing the free parameters of the model. In the latter, it is asymptotically de Sitter. However, in any of these three classes, sharply in contrast to the models obtained by the bottom-up approach, the spacetime is already geodesically complete, and no additional extensions are needed in both sides of the transition surface. In particular, identical multiple black hole and white hole structures do not exist.