Tensor perturbations of $f(T)$-branes

Understand

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.