We apply the mimetic f (T ) theory into the thick brane model. We take the Lagrange multiplier formulation of the action and get the corresponding field equations of motion. Considering the mimetic field as a single-kink or a double-kink, we find solutions for different kinds of f (T ). Besides, we investigate the stability of the mimetic f (T ) brane by considering the tensor perturbations of the vielbein. Localization problem is also studied and it is shown that the four-dimensional gravity can be recovered for all the solutions. The effects of the torsion show that for the polynomial form of f (T ), the zero mode has a split compared with that of f (T ) = T , but the situations for the exponential form of f (T ) are similar to that of f (T ) = T .

In this paper we investigate the innermost stable circular orbit (ISCO) for a classical spinning test particle in the background of Kerr-Newman black hole. It is shown that the orbit of the spinning particle is related to the spin of the test particle. The motion of the spinning test particle will be superluminal if its spin is too large. We give an additional condition by considering the superluminal constraint for the ISCO in the black hole backgrounds. We obtain numerically the relations between the ISCO and the properties of the black holes and the test particle. It is found that the radius of the ISCO for a spinning test particle is smaller than that of a non-spinning test particle in the black hole backgrounds.

It is known that a five-dimensional free vector field AM cannot be localized on Randall-Sundrum (RS)-like thick branes, namely, the thick branes embedded in asymptotic Anti-de Sitter (AdS) spacetime. In order to localize a vector field on the RS-like thick brane, an extra coupling term should be introduced. In this paper, we generalize the geometrical coupling mechanism by adding two mass terms (αRg M N AM AN + βR M N AM AN ) into the action. We decompose the fundamental vector field AM into three parts: transverse vector partµ, scalar parts φ and A5. Then, we find that the transverse vector partµ decouples from the scalar parts. In order to eliminate the tachyonic modes ofµ, the two coupling parameters α and β should satisfy a relation. Combining the restricted condition, we can get a combination parameter as γ = 3 2 ± √ 1 + 12α. Only if γ > 1/2, the zero mode ofµ can be localized on the RS-like thick brane. We also investigate the resonant character of the vector partµ for the general RS-like thick brane with the warp factor A(z) = − ln(1 + k 2 z 2 )/2 by choosing the relative probability method. The result shows that, only for γ > 3, the massive resonant Kaluza-Klein modes can exist. The number of resonant Kaluza-Klein states increases with the combination parameter γ, and the lifetime of the first resonant state can be long enough as the age of our universe. This indicates that the vector resonances might be considered as one of the candidates of dark matter. Combining the conditions of experimental observations, the constrain shows that the parameter k has a lower limit with k 10 −17 eV, the combination parameter γ should be greater than 57, and accordingly, the mass of the first resonant state should satisfy m1 10 −15 eV.