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Relativistic scalar particle subject to a confining potential and Lorentz symmetry breaking effects in the cosmic string spacetime

The behaviour of a relativistic scalar particle subject to a scalar potential under the effects of the violation of the Lorentz symmetry in the cosmic string spacetime is discussed. It is considered two possible scenarios of the Lorentz symmetry breaking in the CPT-even gauge sector of the Standard Model Extension defined by a tensor $\left(K_{F}\right)_{μναβ}$. Then, by introducing a scalar potential as a modification of the mass term of the Klein-Gordon equation, it is shown that the Klein-Gordon equation in the cosmic string spacetime is modified by the effects of the Lorentz symmetry violation backgrounds and bound state solution to the Klein-Gordon equation can be obtained.