  We investigate whether quasinormal modes (QNMs) can be used in the search for
signatures of extra dimensions. To address a gap in the Beyond the Standard
Model (BSM) literature, we focus here on higher dimensions characterised by
negative Ricci curvature. As a first step, we consider a product space
comprised of a four-dimensional Schwarzschild black hole space-time and a
three-dimensional nilmanifold (twisted torus); we model the black hole
perturbations as a scalar test field. We suggest that the extra-dimensional
geometry can be stylised in the QNM effective potential as a squared mass-like
term representing the Kaluza-Klein (KK) spectrum. We then compute the
corresponding QNM spectrum using three different numerical methods, and
determine a possible ``detectability bound" beyond which KK masses cannot be
detected using QNMs.
