In this paper, the effect of time is explored on the dynamics of neutral and charged particles around the Schwarzschild (Sch) black hole (BH) environed by quintessence. We introduce a general time conformal factor [Formula: see text] to the quintessential Sch spacetime, where [Formula: see text] is a time ([Formula: see text])-dependent function and [Formula: see text], a small parameter, that causes perturbation in the corresponding spacetime. The Noether symmetry equation is obtained with the help of Lagrangian corresponding to time conformal Sch spacetime environed by quintessence. Consequently, we get a 19 partial differential equations (PDEs) system. The solution of this system gives Noether symmetries, Noether approximate symmetries, and the corresponding conservation laws. The dynamics of neutral/charged particles are studied as well as graphically analyzed at the foot of these invariants.

中文翻译：

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时间共形典型施瓦西黑洞周围的粒子动力学

本文探讨了时间对精髓周围史瓦西（Sch）黑洞（BH）周围中性粒子和带电粒子动力学的影响。我们在典型的 Sch 时空中引入了一个通用的时间共形因子 [Formula: see text]，其中 [Formula: see text] 是依赖于时间（[Formula: see text]）的函数，而 [Formula: see text] 是一个小的参数，这会导致相应时空的扰动。诺特对称方程是借助拉格朗日方程得到的，对应于精粹环境下的时间共形Sch时空。因此，我们得到了一个 19 个偏微分方程 (PDE) 系统。该系统的解给出了诺特对称性、诺特近似对称性以及相应的守恒定律。