Regular magnetic black holes with anti-de Sitter cores in scalar-tensor gravity: axial stability and radial instability
Abstract
We construct static, asymptotically flat regular black holes in Einstein-frame scalar--tensor gravity, sourced by a canonical scalar coupled to magnetic nonlinear electrodynamics. Prescribing the density and scalar profiles, we reconstruct the metric, the scalar--photon coupling and the potential. Regularity requires the mass function to vanish at the centre, which fixes the ADM mass, and the central r2 growth of the density to be compensated by the gradient energy of the scalar. The solutions have an anti-de Sitter core supported by a negative potential and a nearly Reissner--Nordström exterior; absence of ghosts restricts the magnetic charge to an interval that shrinks to zero at a finite core depth. Axial perturbations reduce to a symmetric two-channel master system whose positive-definite potential guarantees mode stability; spectral and time-domain quasinormal frequencies agree. Radial perturbations, by contrast, are unstable: the reconstructed potential behaves as V∝−φ5 near the asymptotic vacuum, the scalar becomes tachyonic outside the horizon, and every ghost-free black hole has a growing monopole mode with ΓM≈0.14--$0.28$. An angular Laplacian instability develops near the centre; for black holes it may lie entirely within the inner horizon, while horizonless solutions leave it uncovered and are therefore excluded.
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BibTeX
@misc{ibadov2026regular,
title = {{Regular magnetic black holes with anti-de Sitter cores in scalar-tensor gravity: axial stability and radial instability}},
author = {Rustam Ibadov and Najibullokhon Shukurullokhon},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.28670},
eprint = {2610.28670},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.28670},
}
RIS
TY - UNPB
TI - Regular magnetic black holes with anti-de Sitter cores in scalar-tensor gravity: axial stability and radial instability
AU - Rustam Ibadov
AU - Najibullokhon Shukurullokhon
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.28670
UR - https://arxiv.org/abs/2610.28670
AB - We construct static, asymptotically flat regular black holes in Einstein-frame scalar--tensor gravity, sourced by a canonical scalar coupled to magnetic nonlinear electrodynamics. Prescribing the density and scalar profiles, we reconstruct the metric, the scalar--photon coupling and the potential. Regularity requires the mass function to vanish at the centre, which fixes the ADM mass, and the central r^2 growth of the density to be compensated by the gradient energy of the scalar. The solutions have an anti-de Sitter core supported by a negative potential and a nearly Reissner--Nordström exterior; absence of ghosts restricts the magnetic charge to an interval that shrinks to zero at a finite core depth. Axial perturbations reduce to a symmetric two-channel master system whose positive-definite potential guarantees mode stability; spectral and time-domain quasinormal frequencies agree. Radial perturbations, by contrast, are unstable: the reconstructed potential behaves as V∝−φ^5 near the asymptotic vacuum, the scalar becomes tachyonic outside the horizon, and every ghost-free black hole has a growing monopole mode with ΓM≈0.14--$0.28$. An angular Laplacian instability develops near the centre; for black holes it may lie entirely within the inner horizon, while horizonless solutions leave it uncovered and are therefore excluded.
ER -