In this paper, we study the relativistic scalar particle described by the Klein–Gordon equation that interacts with the uniform magnetic field in the context of the Som–Raychaudhuri space–time. Based on the property of the biconfluent Heun function equation, the corresponding Klein–Gordon oscillator and generalized Klein–Gordon oscillator under considering the Coulomb potential are separately investigated, and the analogue of the Aharonov–Bohm effect is analyzed in this scenario. On this basis, we also give the influence of different parameters including parameter α and oscillator frequency ω, and the potential parameter ξ2 on the energy eigenvalues of the considered systems.

中文翻译：

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Som-Raychaudhuri时空背景下广义克莱因-戈登振子的研究

在本文中，我们研究了在 Som-Raychaudhuri 时空背景下与均匀磁场相互作用的 Klein-Gordon 方程描述的相对论标量粒子。基于双合流 Heun 函数方程的性质，分别研究了考虑库仑势的相应 Klein-Gordon 振子和广义 Klein-Gordon 振子，并分析了该情景下的 Aharonov-Bohm 效应的类比。在此基础上，我们还给出了不同参数的影响，包括参数α和振荡器频率ω, 和潜在参数ξ2关于所考虑系统的能量特征值。