Gravity-induced spontaneous radiation (GISR) treats black holes as general quantum systems with multiple levels and high degeneracy. As results, the intermediate state ofan evaporating black hole is a superposition of various black hole and radiation product combinations with different mass ratios. Since the classical description of a black hole follows from partially tracing out indices of this superposition, the entanglement entropy between the black hole and its radiation products exhibits the first increasing then decreasing feature, aligning with the prediction of Page curve, This work provides a concise introduction to the concept ofGISR, and calculates the entropy variation curve for an initially eight-fold degenerate black hole, demonstrating that the late-time Rabi oscillations are significantly suppressed comparing with its first cycle's increasing-decreasing behaviour.

The question of one-dimensional oscillation driven by inverse square forces arises in two important scenarios in physics: the classical orbital interpretation of hydrogen atom electron wave functions and the Newtonian mechanical description of self-gravitating collapsing spheres. The popular viewpoint suggests that these two scenarios involve issues of “unrealistic orbital concepts” and “inapplicability of Newtonian mechanics” respectively, leading to a lack of in-depth exploration of this problem. This paper argues that the classical orbits of hydrogen atom electrons are not only real but also crucial in fundamentally understanding the area law featured entropy of black holes and their nontrivial internal structures. Depending on the classical interpretation of quantized wave functions, this internal structure can be understood as oscillatory modes of black hole matter contents over crossing the central point, or as oscillatory modes of those matters across the horizon surface itself with the inner space cut out completely.