We study the stability of static spherically symmetric exact solutions of Einstein equations coupled with nonlinear electrodynamics, in the magnetic sector. These solutions satisfy the heuristic model proposed by Ashtekar, Corichi, and Sudarsky for hairy black holes, meaning that the horizon mass is related to their Arnowitt-Deser-Misner (ADM) mass and to the corresponding particlelike solution. We test the unstability conjecture that emerges for hairy black holes and it turned out that it becomes confirmed except for the Einstein-Born-Infeld solutions.
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Nora Bretón (2005) studied this question.
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