2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/50776We work on the relation between the local thermodynamic instability and the dynamical instability of large black holes in four-dimensional anti-de Sitter space proposed by Gubser and Mitra. We find that all perturbations suppressing the metric fluctuations at linear order become dynamically unstable when black holes lose the local thermodynamic stability. We discuss how dynamical instabilities can be explained by the Second Law of Thermodynamics.Latex, 10 pages, no figures, Corrected contentHigh Energy Physics - TheoryGeneral Relativity and Quantum Cosmologytext