Beyond Kasner Epochs: Ordered Oscillations and Spike Dynamics Inside Black Holes with Higher-Derivative Corrections

Abstract: Building upon the long-standing paradigm that dynamics near a spacelike singularity are governed by a sequence of Kasner epochs, we demonstrate that this picture is fundamentally altered when higher-curvature or quantum gravitational corrections are included. By incorporating such terms alongside a minimally coupled scalar field, we discover three distinct dynamical phases near the singularity: modified Kasner eons, persistent periodic oscillations, and oscillatory spike dynamics with growing amplitude. In particular, the Kasner-like geometry persisting only in highly constrained situations. The latter two regimes represent a clean departure from classical Kasner phenomenology, revealing a richer and more ordered landscape of behaviors in the deep interior of black holes beyond Einstein gravity. This work establishes a comprehensive approach for understanding the gravitational nonlinearity in the most extreme gravitational environment.