Curvature scaling and linear area response in charged black-hole interiors
Abstract
We identify the mechanisms and range of validity of two scaling laws reported in charged black-hole interiors. In spherical evolutions with a neutral massless scalar, mass inflation produces a large internal mass m, followed by a plateau. Small scalar and electric corrections give K≃48m2/r6, where r is the areal radius and K the Kretschmann scalar. The local exponent is near six when the mass and relative curvature correction also vary slowly with radius. The exact bound K≥28q4/(5r8), with q the charge, excludes a finite-coefficient r−6 asymptote, while a large plateau mass delays electric corrections to r∼ q2/m. For sufficiently large plateau mass, this classical regime can reach Planckian curvature before electric corrections become significant. At fixed coordinates and initial gauge, a linear response of ρ=r2 to the initial scalar amplitude A gives the half-power radius law near a simple zero. Where both mechanisms apply, K/m2∝(A*−A)−3, with A* the area zero. Full evolutions confirm the electric correction, support the half-power law at several observation times, and test the joint inverse-cube law.
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BibTeX
@misc{yang2026curvature,
title = {{Curvature scaling and linear area response in charged black-hole interiors}},
author = {Fu-Guo Yang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40043},
eprint = {2610.40043},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40043},
}
RIS
TY - UNPB
TI - Curvature scaling and linear area response in charged black-hole interiors
AU - Fu-Guo Yang
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40043
UR - https://arxiv.org/abs/2610.40043
AB - We identify the mechanisms and range of validity of two scaling laws reported in charged black-hole interiors. In spherical evolutions with a neutral massless scalar, mass inflation produces a large internal mass m, followed by a plateau. Small scalar and electric corrections give K≃48m^2/r^6, where r is the areal radius and K the Kretschmann scalar. The local exponent is near six when the mass and relative curvature correction also vary slowly with radius. The exact bound K≥28q^4/(5r^8), with q the charge, excludes a finite-coefficient r^−6 asymptote, while a large plateau mass delays electric corrections to r∼ q^2/m. For sufficiently large plateau mass, this classical regime can reach Planckian curvature before electric corrections become significant. At fixed coordinates and initial gauge, a linear response of ρ=r^2 to the initial scalar amplitude A gives the half-power radius law near a simple zero. Where both mechanisms apply, K/m^2∝(A_*−A)^−3, with A_* the area zero. Full evolutions confirm the electric correction, support the half-power law at several observation times, and test the joint inverse-cube law.
ER -