标题： 标量粒子在施瓦茨希尔德-基塞列夫-勒泰利尔时空中的暗相出现 显示英文标题

标题： Emergence of Dark Phases in Scalar Particles within the Schwarzschild-Kiselev-Letelier Spacetime

摘要： 这项工作聚焦于标量粒子径向波函数中暗相（暗能量印记）的出现。 我们通过在包含黑洞、类精质流体和弦云的球对称时空中提出克莱因-戈登方程的新解来实现这一点。 我们确定了时空度规的精确解，分析了其物理参数的可接受范围，并讨论了事件视界的形成。 随后，我们详细阐述了克莱因-戈登方程的解，并探讨了三种不同的暗相情况，分别对应于类精质状态参数$\alpha_{Q}$取值为$0$、$1/2$和$1$。 值得注意的是，当$\alpha_{Q} = 1$时具有特殊意义，因为目前对暗能量有观测约束。 显示英文摘要

摘要： This work focuses on the emergence of dark phases (dark energy imprints) in the radial wave function of scalar particles. We achieve this by presenting novel solutions of the Klein-Gordon equation in a spherically symmetric spacetime, encompassing a black hole, a quintessential fluid, and a cloud of strings. We determine the exact solution for the spacetime metric, analyze the admissible ranges for its physical parameters, and discuss the event horizon formation. Subsequently, we detail the solution of the Klein-Gordon equation and explore three distinct cases of dark phases, corresponding to the quintessence state parameter $\alpha_{Q}$ taking the values $0$, $1/2$, and $1$. Notably, the case where $\alpha_{Q} = 1$ holds particular significance due to current observational constraints on dark energy.