Massive scalar field perturbations in Weyl black holes

In this work we consider the propagation of massive scalar fields in the background of Weyl black holes, and we study the effect of the scalar field mass in the spectrum of the quasinormal frequencies (QNFs) via the Wentzel-Kramers-Brillouin (WKB) method and the pseudo-spectral Chebyshev method. The spectrum of QNFs is described by two families of modes: the photon sphere and the de Sitter modes. Essentially, we show via the WKB method that the photon sphere modes exhibit an anomalous behaviour of the decay rate of the QNFs; that is, the longest-lived modes are the ones with higher angular numbers, and there is a critical value of the scalar field mass beyond which the anomalous behaviour is inverted. We also analyse the effect of the scalar field mass on each family of modes and on their dominance, and we give an estimated value of the scalar field mass where the interchange in the dominant family occurs.