Quasinormal Spectrum in Six-Dimensional Thick Branes

Quasinormal modes provide a characteristic spectral description of open systems, encoding how perturbations dissipate and relax under physically relevant boundary conditions. They have attracted broad interest in gravitational wave physics. In this work, we investigate the quasinormal modes of a six-dimensional thick brane model and explore how the higher-dimensional brane geometry affects the dynamics of gravitational perturbations and other test fields. These modes can be explained as either metastable gravity wave bound states or decaying massive gravitons from different perspectives. Compared with conventional five-dimensional thick brane scenarios, the six-dimensional setup possesses a richer transverse structure, which can modify the effective perturbation potential and lead to distinctive spectral behavior. We analyze the perturbation equations in this background and compute the corresponding quasinormal spectrum. Particular attention is paid to the relation between the brane configuration, the effective potential, and the distribution of quasinormal frequencies. Our results show that the six-dimensional thick brane geometry can leave clear imprints on the quasinormal spectrum, influencing both the oscillation and damping properties of gravitational perturbations. These findings provide a dynamical spectral perspective on higher-dimensional braneworld models and may offer useful insights for future studies of braneworld holography, gravitational localization, and the stability of thick brane configurations.