Stable colored black holes with quartic self-interactions
Abstract
We analytically prove the linear radial stability of non-Abelian black holes with quartic self-interactions. The background, constructed from the Wu-Yang magnetic monopole ansatz, is an exact black-hole solution carrying a non-Abelian magnetic charge QNA2 controlled by a single coupling parameter χ, and admits two distinct branches. The odd sector is always stable, while in the even sector the effective potential is positive for branch~I and negative for branch~II, establishing stability and potential instability, respectively. The potential instability of branch~II is consistent with its connection to the perturbatively unstable Einstein-Yang-Mills Reissner-Nordström solution. Branch~I remains linearly stable throughout the physical domain of χ where the solutions are regular and free of naked singularities. The stability of branch~I is further confirmed through a numerical computation of the quasinormal mode spectrum using Leaver's continued fraction method and time-domain evolution supplemented with Prony method, showing no unstable modes. Our results prove the existence of the first linearly stable asymptotically flat hairy black holes in four dimensions with a minimally coupled non-Abelian Proca self-interaction.
Versions
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BibTeX
@misc{rodriguezruiz2026stable,
title = {{Stable colored black holes with quartic self-interactions}},
author = {Jose F. Rodriguez-Ruiz and Gabriel Gomez},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.16005},
eprint = {2605.16005},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.16005},
}
RIS
TY - UNPB
TI - Stable colored black holes with quartic self-interactions
AU - Jose F. Rodriguez-Ruiz
AU - Gabriel Gomez
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2605.16005
UR - https://arxiv.org/abs/2605.16005
AB - We analytically prove the linear radial stability of non-Abelian black holes with quartic self-interactions. The background, constructed from the Wu-Yang magnetic monopole ansatz, is an exact black-hole solution carrying a non-Abelian magnetic charge Q_NA^2 controlled by a single coupling parameter χ, and admits two distinct branches. The odd sector is always stable, while in the even sector the effective potential is positive for branch~I and negative for branch~II, establishing stability and potential instability, respectively. The potential instability of branch~II is consistent with its connection to the perturbatively unstable Einstein-Yang-Mills Reissner-Nordström solution. Branch~I remains linearly stable throughout the physical domain of χ where the solutions are regular and free of naked singularities. The stability of branch~I is further confirmed through a numerical computation of the quasinormal mode spectrum using Leaver's continued fraction method and time-domain evolution supplemented with Prony method, showing no unstable modes. Our results prove the existence of the first linearly stable asymptotically flat hairy black holes in four dimensions with a minimally coupled non-Abelian Proca self-interaction.
ER -