Characteristic Modes of Non-minimally Coupled Thick Branes

Abstract

Characteristic modes provide important information about the intrinsic properties and dynamical response of gravitational systems. In this work, we investigate characteristic modes of thick branes with a non-minimally coupled bulk scalar field. Two representative thick brane solutions are considered, corresponding to a single-kink scalar configuration and a deformed kink configuration with internal structure, respectively. By analyzing the tensor perturbation equations, we first examine the localization of the graviton zero mode in the two brane models. For both brane models, the graviton zero mode is localized on the brane. No pronounced resonant Kaluza--Klein (KK) modes are found for the single-kink brane at $ξ=1/7$. For the deformed brane, we investigate the resonant KK modes at $ξ=0.99$, finding that increasing the deformation parameter $k$ leads to more resonant modes and a longer-lived first resonance. We then calculate the quasinormal modes (QNMs) of both brane models independently in the frequency and time domains. The quasinormal frequencies (QNFs) obtained by the independent methods agree well for the low overtones. The masses and decay rates of the resonant KK modes agree closely with the real parts and the magnitudes of the imaginary parts of the corresponding QNFs, respectively.