2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/52951We present a detailed analysis for the classical stability of a four dimensional Anti-de Sitter spacetime (AdS$_4$) by decomposing the first-order perturbations of a spherical symmetric gravitational field into the so called tensor harmonics which transform as irreducible representative of the rotation group (Regge-Wheeler decomposition). It is shown that there is no nontrivial stationary perturbation for the angular momentum $l < 2$. The stability analysis forces the frequency of the gravitational modes to be constrained in a way that the frequency of scalar modes are constrained.13 pages, no figureHigh Energy Physics - TheoryGeneral Relativity and Quantum CosmologyHigh Energy Physics - Phenomenologytext