Tensor perturbations of $f(T)$-branes

TL;DR

This paper investigates the stability and graviton localization of $f(T)$-branes in AdS$_5$ spacetime, demonstrating that the brane remains stable and the zero mode can be localized for specific $f(T)$ models.

Contribution

It provides the tensor perturbation equation for $f(T)$-branes and analyzes graviton zero mode localization, extending understanding of brane stability and gravity localization in $f(T)$ gravity.

Findings

Brane stability is ensured under tensor perturbations.

Graviton zero mode can be localized on the brane for $f(T)=T+eta T^2$.

Tensor perturbation equations are derived for $f(T)$-branes.

Abstract

We explore the tensor perturbation of the $f(T)$ brane embedded in an AdS$_5$ spacetime. With the transverse-traceless condition, we get the tensor perturbation equation of the $f(T)$ brane and show that the stability of this brane system can be ensured. In addition, we take $ f(T)=T+\alpha T^2$ as an example to analyse the localization problem of the graviton zero mode. It is shown that the graviton zero mode can be localized on the brane.