An effective model for the quantum Schwarzschild black hole

TL;DR

This paper develops an effective loop quantum gravity model for Schwarzschild black holes that removes singularities, provides a covariant description, and recovers classical spacetimes as limits.

Contribution

It introduces an anomaly-free, covariant quantum model for Schwarzschild black holes with a singularity-free interior and consistent global structure.

Findings

Singularity replaced by a minimal spacelike surface

Model recovers Minkowski and Schwarzschild spacetimes as limits

Provides a consistent causal and maximal extension of the spacetime

Abstract

We present an effective theory to describe the quantization of spherically symmetric vacuum in loop quantum gravity. We include anomaly-free holonomy corrections through a canonical transformation of the Hamiltonian of general relativity, such that the modified constraint algebra closes. The system is then provided with a fully covariant and unambigous 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.