A non-monotonic behavior of the velocity gradient of a test particle revolving around a rapidly rotating black hole in the locally non-rotating frame of reference is known as the Aschenbach effect. This effect can serve as a distinguishing signature of rapidly rotating black holes, being potentially useful for the measurements of the astrophysical black hole spins. This paper is the generalization of our previous research to the motion of spinning particles around a rotating black hole with non-zero cosmological constant. We show that both the particle’s spin s and the cosmological constant \(\Lambda \) modify the critical value of the black hole spin \(a_c\), for which the Aschenbach effect can be observed; \(a_c\) can increase or decrease depending on the signs of s and \(\Lambda \). We also found that the particle’s spin s can mimic the effect of the cosmological constant \(\Lambda \) for a given \(a_c\), causing thus a discrepancy in the measurements of s, \(\Lambda \) and \(a_c\) in the Aschenbach effect.

测试粒子的速度梯度在局部非旋转参照系中围绕快速旋转的黑洞旋转的非单调行为被称为Aschenbach效应。这种效应可以作为快速旋转的黑洞的显着特征，对于天体物理黑洞自旋的测量可能很有用。本文是对先前研究的概括，是对具有非零宇宙学常数的旋转黑洞周围旋转的粒子运动的概括。我们表明，粒子的自旋s和宇宙常数\（\ Lambda \）都改变了黑洞自旋\（a_c \）的临界值，对此可以观察到阿申巴赫效应；\（a_c \）可以根据s和\（\ Lambda \）的符号增加或减少。我们还发现，对于给定的\（a_c \），粒子的自旋s可以模仿宇宙常数\（\ Lambda \）的影响，从而导致s，\（\ Lambda \）和\（ a_c \）在阿申巴赫效应中。