Unified Dynamics of Black-Hole Interiors: From Geometric to Scalar-Kinetic Dominance

Abstract

We identify a unified dynamical picture connecting small-amplitude scalar input at the event horizon to scalar--Kasner interiors. Within boundary-supported stationary families, area contraction drives the transition from geometric to scalar kinetic dominance. For the Schwarzschild-like branch, contraction suppresses the relative curvature contribution, so the scalar kinetic term becomes dominant while the gradient remains small. For the Kerr--Newman-like branch, the scalar gradient is strongly amplified as area contraction carries the solution toward the would-be Cauchy-horizon zero, followed by a narrow transition to scalar kinetic dominance. Cancellation between the kinetic and geometric terms produces a positive minimum of a metric diagnostic, explaining inner-horizon loss dynamically. Fully coupled numerical solutions for the Schwarzschild-like branch and four-dimensional stationary axisymmetric Kerr--Newman interiors, including the Reissner--Nordström and Kerr limits, support this picture. Area contraction provides the common physical mechanism, while the would-be Cauchy-horizon zero determines the strength of gradient amplification and the localization of the transition.