标题： 在Gödel型Som-Raychaudhuri宇宙弦时空中的Klein-Gordon粒子与相关的时空退化现象 显示英文标题

标题： Klein-Gordon particles in Gödel-type Som-Raychaudhuri cosmic string spacetime and the phenomenon of spacetime associated degeneracies

摘要： 我们认为，只有精确、全面且明确的基本模型（Klein-Gordon（KG）振子和KG-Coulomb模型）的解才能帮助理解引力场对这类量子系统动力学的影响。在目前的方法论提议中，研究并报告了由Gödel型Som-Raychaudhuri（SR）宇宙弦时空产生的引力场对KG振子（一般为KG粒子）的影响。为此，我们重新审视了在拓扑平凡的Gödel型时空背景下的KG振子，并使用教科书上的方法报告了其涵盖偶性和奇性情况的精确解。接下来，我们讨论了幂级数展开法的局限性，该方法暗示双合流Heun函数/多项式解。因此，我们回顾了所谓的伪摄动位移L展开技术（PSLET），作为一种替代且更复杂的方法。示例包括：(i) 拓扑平凡的Gödel型时空中的一维KG振子；(ii) Gödel SR型宇宙弦时空中准自由的KG振子；(iii) 零涡旋情况下Gödel SR型宇宙弦时空中KG-Coulomb粒子；(iv) Gödel SR型宇宙弦时空中Cornell型洛伦兹标量势中的无质量KG粒子。从PSLET的零阶（主导）修正中获得了相应的精确能量，其中所有高阶修正均恒为零。所报告解的全面精确性显然表明与时空（STAD）现象相关的简并性。 显示英文摘要

摘要： We argue that only exact, comprehensive, and explicit solutions for the fundamental models, the Klein-Gordon (KG) oscillators and the KG-Coulomb, would help to understand the effects of gravitational fields on the dynamics of such quantum mechanical systems. In the current methodical proposal, the effects of the gravitational fields generated by a G\"odel-type Som-Raychaudhuri (SR) cosmic string spacetime on KG-oscillators (KG-particles in general) are studied and reported. In so doing, we revisit the KG-oscillators in a topologically trivial G\"odel-type spacetime background and use textbook procedures to report its exact solution that covers even and odd parities. Next, we discuss the drawbacks associated with the power series expansion approach that implies the biconfluent Heun functions/polynomials solution. We, therefore, recollect the so called pseudo perturbative shifted L expansion technique (PSLET) as an alternative and more sophisticated method/technique. Illustrative examples are used: (i) a KG-oscillator in a topologically trivial G\"odel-type spacetime, (ii) a quasi-free KG-oscillator in G\"odel SR-type cosmic string spacetime, (iii) a KG-Coulombic particle in G\"odel SR-type cosmic string spacetime at zero vorticity, and (iv) a massless KG-particle in G\"odel SR-type cosmic string spacetime in a Cornell-type Lorentz scalar potential. The corresponding exact energies are obtained from the zeroth (leading) order correction of PSLET, where all higher order correction identically vanish. The comprehensive exactness of the reported solutions manifestly suggest degeneracies associated with spacetime (STAD) phenomenon.