A new quantization scheme of black holes in effective loop quantum gravity

Loop quantum cosmology has achieved great successes, in which the polymerization plays a crucial role. In particular, the phase-space-variable dependent polymerization turns out to be the unique one that leads to consistent quantization of the homogeneous and isotropic universe. However, when applying the same scheme to the quantization of black holes, it meets resistances, when the Kantowski-Sachs (KS) gauge is adopted. In this paper, we continue to study the quantum effects of the polymerization near the location that a classical black hole horizon used to be, from the point of view of effective loop quantum gravity in the KS gauge. In particular, we find a phase-space-variable dependent polymerization scheme that leads to negligible quantum effects near the location of the classical black hole horizon, but significantly alters the spacetime structure near the origin, so that the classical singularity is finally replaced by a finite and regular transition surface. The final geodesically-complete spacetime consists of the regular transition surface that connects a black hole in one side and an anti-trapped region in the other side. In the anti-trapped region, no white hole horizons are found and the spacetime is extended to infinity, at which the geometric radius of the two-spheres becomes infinitely large.