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We elaborate on the Ashtekar's formalism for spherically symmetricmidisuperspaces and, for loop quantization, propound a new quantization schemewhich yields a graph-preserving Hamiltonian constraint operator and by whichone can impose the fundamental discreteness of loop quantum gravity a la thestrategy of "improved" dynamics in loop quantum cosmology (LQC). Remarkableconsequences are inferred at the heuristic level of effective dynamics: first,consistency of the constraint algebra regarding the Hamiltonian anddiffeomorphism constraints fixes the improved quantization scheme to be of theform reminiscent of the improved scheme in LQC which preserves scalinginvariance; second, consistency regarding two Hamiltonian constraints furtherdemands the inclusion of higher order holonomy corrections and fixes a ratiofactor of 2 for the improved scheme. It is suggested that the classicalsingularity is resolved and replaced by a quantum bounce which bridges aclassical solution to another classical phase. However, the constraints violatebriefly during the bouncing period, indicating that one cannot make sense ofsymmetry reduction by separating the degrees of freedom of the full theory intospherical and non-spherical ones in the vicinity of the quantum bounce,although the heuristic effective dynamics can still give a reliablesemiclassical description of large-scale physics. Particularly, for theSchwarzschild solution in accordance with the Kruskal coordinates, revealinginsights lead us to conjecture the complete quantum extension of theSchwarzschild spacetime: the black hole is evaporated via the Hawking radiationand meanwhile the quantum spacetime is largely extended from the classical onevia the quantum bounce, suggesting that the information paradox might beresolved.

Loop quantization of spherically symmetric midisuperspaces and loop quantum geometry of the maximally extended Schwarzschild spacetime