Quasinormal modes of thick branes in $f(R)$ gravity

TL;DR

This paper explores the quasinormal modes of thick branes in $f(R)$ gravity using multiple numerical methods, revealing how model parameters influence the potential and frequency spectrum, and identifying resonance structures.

Contribution

It provides a comprehensive numerical analysis of gravitational quasinormal modes in $f(R)$ thick branes, demonstrating method consistency and the resonance nature of quasi-localized states.

Findings

Real parts of frequencies form an arithmetic progression.

Potential barrier shapes significantly affect quasinormal spectra.

Multiple numerical methods yield consistent results.

Abstract

We systematically investigate the quasinormal modes of thick branes in $f(R)$ gravity by numerically solving the Schr\"odinger-like perturbation equation of gravitational perturbations. To ensure the reliability of the results, we employ three complementary methods: the asymptotic iteration method, the direct integration of the wave equation, and the time-domain numerical evolution. We analyze how the model parameters influence the shape of the effective potential of gravitational perturbations and find that the structure of the potential barrier plays a significant role in shaping the quasinormal frequency spectrum. The results obtained from the three methods exhibit strong consistency, thereby ensuring the reliability of the calculations. In particular, the real parts of the quasinormal frequencies exhibit an approximately arithmetic progression, suggesting that the quasi-localized states can be understood as resonances between the barriers.