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The behaviour of a relativistic scalar particle subject to a scalar potentialunder the effects of the violation of the Lorentz symmetry in the cosmic stringspacetime is discussed. It is considered two possible scenarios of the Lorentzsymmetry breaking in the CPT-even gauge sector of the Standard Model Extensiondefined by a tensor $\left(K_{F}\right)_{\mu\nu\alpha\beta}$. Then, byintroducing a scalar potential as a modification of the mass term of theKlein-Gordon equation, it is shown that the Klein-Gordon equation in the cosmicstring spacetime is modified by the effects of the Lorentz symmetry violationbackgrounds and bound state solution to the Klein-Gordon equation can beobtained.

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