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.
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BibTeX
@misc{yang2026unified,
title = {{Unified Dynamics of Black-Hole Interiors: From Geometric to Scalar-Kinetic Dominance}},
author = {Fu-Guo Yang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36129},
eprint = {2610.36129},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36129},
}
RIS
TY - UNPB
TI - Unified Dynamics of Black-Hole Interiors: From Geometric to Scalar-Kinetic Dominance
AU - Fu-Guo Yang
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.36129
UR - https://arxiv.org/abs/2610.36129
AB - 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.
ER -