An effective model for the quantum Schwarzschild black hole

We present an effective theory to describe the quantization of spherically symmetric vacuum motivated by loop quantum gravity. We include anomaly-free holonomy corrections through a canonical transformation and a linear combination of constraints of general relativity, such that the modified constraint algebra closes. The system is then provided with a fully covariant and unambiguous geometric description, independent of the gauge choice on the phase space. The resulting spacetime corresponds to a singularity-free (black-hole/white-hole) interior and two asymptotically flat exterior regions of equal mass. The interior region contains a minimal smooth spacelike surface that replaces the Schwarzschild singularity. We find the global causal structure and the maximal analytical extension. Both Minkowski and Schwarzschild spacetimes are directly recovered as particular limits of the model. (C) 2022 The Author(s). Published by Elsevier B.V.

Automated summary

We propose an effective theory for quantizing spherically symmetric vacuum based on loop quantum gravity. By incorporating anomaly-free holonomy corrections, through a canonical transformation and a linear combination of constraints of general relativity, we ensure the closure of the modified constraint algebra. The resulting system is endowed with a fully covariant and unambiguous geometric description, independent of the gauge choice on the phase space. The obtained spacetime consists of a singularity-free (black-hole/white-hole) interior and two asymptotically flat exterior regions with equal masses. The interior region contains a minimal smooth spacelike surface that replaces the Schwarzschild singularity. We analyze the global causal structure and the maximal analytical extension, and recover both Minkowski and Schwarzschild spacetimes as particular limits of the model.