The Framework of Momentary Quantum Tunneling: A Causal Resolution for Rotating Black Holes

This work introduces the theoretical framework of Momentary Quantum Tunneling (MQT), proposing that the final state of a rotating black hole (Kerr geometry) is not a classical singularity, but rather a \emph{quantum bounce} of finite curvature, described by Loop Quantum Gravity (LQG). The classical metric function $\Delta(r)$ is regularized through \textbf{effective coupled functions of mass ($M$) and angular momentum ($a$)}, expressed as $\Delta_{q}(r) = r^2 - 2m_{\mathrm{eff}}(r)\,r + a_{\mathrm{eff}}^{2}(r)$, producing a nonsingular core. The resulting dynamics, derived from the effective Hamiltonian constraints of LQG, reveal a transient contraction–expansion cycle, in which the collapsing region undergoes a momentary tunneling into an expanding white-hole domain. Although this transition is ultrafast in internal proper time ($\tau$), it appears cosmologically long for an external observer due to extreme gravitational time dilation. This model provides a continuous gravitational evolution (collapse, bounce, and expansion), offering a semiclassical bridge between General Relativity and Quantum Mechanics. Potential astrophysical signatures and connections to cosmological bounces are discussed, suggesting a new route for resolving the black-hole information paradox.