Scalar-gravitational quasinormal modes and echoes in a five dimensional thick brane

A bstract The graviscalar perturbations of thick braneworld models provide critical insights into their matter-geometry relationship, distinct from tensor modes. This work systematically investigates quasinormal modes and gravitational echoes from graviscalar perturbations in a thick brane model exhibiting internal structure and brane splitting. We find that the splitting of the brane would completely alter the structure of the quasinormal spectrum and cause the appearance of echo signals. We also find a position-dependence of echo modes within the extra dimension. Observers located on a sub-brane detect clean periodic signals, whereas those situated between sub-branes observe more complex, modulated waveforms. This effect offers a distinct signature of the brane’s internal structure. The observed echoes, along with consistent frequency- and time-domain results, advance the understanding of thick brane dynamics and open an observational window into warped extra dimensions. Moreover, the similarity between the effective potential in thick brane scenarios and that in black holes and wormholes offers valuable perspectives for studying echo-related phenomena in these gravitational systems.