Loop quantum deparametrized Schwarzschild interior and discrete black hole mass

We present the detailed analyses of a model of loop quantum Schwarzschild interior coupled to a massless scalar field and extend the results in our previous rapid communication C. Zhang, Y. Ma, S. Song, and X. Zhang, Loop quantum Schwarzschild interior and black hole remnant, Phys. Rev. D 102, 041502 (2020) to more general schemes. It is shown that the spectrum of the black hole mass is discrete and does not contain zero. This supports the existence of a black hole remnant after Hawking evaporation due to loop quantum gravity effects. Besides to show the existence of a nonvanishing minimal black hole mass in the vacuum case, the quantum dynamics for the nonvacuum case is also solved and compared with the effective one.