Nested Apparent Horizons and Quantized Separation from Intense Hawking Backreaction

Abstract

When Hawking radiation from a rotating or non-rotating black hole becomes sufficiently intense, its own stress energy can no longer be treated as a perturbation on a fixed background. In this regime the outgoing flux may generate an additional, transient trapping surf ace exterior to the original event horizon. Using a simple spherically symmetric semi classical model we demonstrate that strong outgoing null energy can create nested apparent horizons, a feature reminiscent of the Penrose process but mediated by quantum back reaction. The effect is illustrated using a smooth Vaidya type mass profile, and conditions for bifurcation and merger of horizons are derived. We further propose that the separation between nested horizons may obey a discrete quantization rule analogous to the Bohr Sommerfeld condition,suggesting a geometric route toward quantum-gravity discreteness.