In this work, we investigate the gravitational resonances in various f(T)-brane models with the warp factor $$\text {e}^{A(y)}=\tanh \big (k(y+b)\big )-\tanh \big (k(y-b)\big )$$
e
A
(
y
)
=
tanh
(
k
(
y
+
b
)
)
-
tanh
(
k
(
y
-
b
)
)
, where f(T) is an arbitrary function of the torsion scalar T. For three kinds of f(T), we give the solutions to the system. Besides, we consider the tensor perturbation of the vielbein and obtain the effective potentials by the Kaluza–Klein (KK) decomposition. Then we analyze what kind of effective potential can produce the gravitational resonances. The effects of different parameters on the gravitational resonances are analyzed. The lifetimes of the resonances could be long enough as regards the age of our universe in some ranges of the parameters. This indicates that the gravitational resonances might be considered as one of the candidates for dark matter. Combining the current experimental observations, we constrain the parameters for these brane models.
Based on the five-dimensional Einstein–Maxwell theory, Bah et al. constructed a singularity-free topology star/black hole [Phys. Rev. Lett. 126, 151101 (2021)]. After performing the Kaluza–Klein reduction, i.e., integrating the extra space dimension, it can obtain an effective four-dimensional spherically static charged black hole with scalar hair. In this paper, we study the quasinormal modes (QNMs) of the scalar, electromagnetic, and gravitational fields in the background of this effective four-dimensional charged black hole. The radial parts of the perturbed fields all satisfy a Schrödinger-like equation. Using the asymptotic iteration method, we obtain the QNM frequencies semianalytically. For low-overtone QNMs, the results obtained using both the asymptotic iteration method and the Wentzel–Kramers–Brillouin approximation method agree well. In the null coordinates, the evolution of a Gaussian package is also studied. The QNM frequencies obtained by fitting the evolution data also agree well with the results obtained using the asymptotic iteration method.
In this work, we investigate the numerical evolution of massive Kaluza–Klein (KK) modes of a scalar field in a thick brane. We derive the Klein–Gordon equation in five-dimensional spacetime, and obtain the evolution equation and the Schrödinger-like equation. With the resonances of the scalar KK modes as the initial data, the scalar field is evolved with the maximally dissipative boundary condition. The results show that there are scalar KK resonant particles with long life on the brane, which indicates that these resonances might be regarded as a candidate for dark matter.
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