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

TL;DR

This paper explores how higher-curvature and quantum corrections fundamentally change the near-singularity dynamics inside black holes, revealing new ordered oscillatory behaviors beyond classical Kasner epochs.

Contribution

It introduces a comprehensive framework showing that higher-derivative corrections lead to novel dynamical phases, including persistent oscillations and spike dynamics, inside black holes.

Findings

Identification of three distinct dynamical phases near singularities.

Demonstration that classical Kasner behavior is limited to constrained cases.

Revelation of richer, more ordered behaviors in black hole interiors with 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.