Low-lying gravitational modes in the scalar sector of the global AdS ₄ black hole

We compute the quasinormal frequencies corresponding to the scalar sector of gravitational perturbations in the four-dimensional AdS-Schwarzschild black hole by using the master field formalism of [1]. We argue that the non-deformation of the boundary metric favors a Robin boundary condition on the master field over the usual Dirichlet boundary condition mostly used in the literature. Using this Robin boundary condition we find a family of low-lying modes, whose frequencies match closely with predictions from linearized hydrodynamics on the boundary. In addition to the low-lying modes, we also see the usual sequence of modes with frequencies almost following an arithmetic progression.