We investigate the behaviour of a massive scalar field under the influence of a Coulomb-type and central linear central potentials inserted in the Klein-Gordon equation by modifying the mass term in the spacetime with Lorentz symmetry violation. We consider the presence of a background constant vector field which characterizes the breaking of the Lorentz symmetry and show that analytical solutions to the Klein-Gordon equation can be achieved.

中文翻译：

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洛伦兹对称违反环境中具有标量场的中心势

我们通过修改时空中具有洛伦兹对称性违背的质量项，研究了在Klein-Gordon方程中插入的库仑型和中心线性中心电势的影响下大质量标量场的行为。我们考虑到背景常数矢量场的存在，该背景场表征了洛伦兹对称性的破坏，并表明可以实现Klein-Gordon方程的解析解。