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.We acknowledge financial support from the Basque Government Grant No. IT956-16 and from the Grant FIS2017-85076-P, funded by MCIN/AEI/10.13039/501100011033 and by “ERDF A way of making Europe”. AAB is funded by the FPI fellowship PRE2018-086516 of the Spanish MCIN