We study the geodesics of massive particles around an accelerating Schwarzschild black hole. We show that the radius of the innermost stable circular orbit and the angular momentum of a particle at this orbit decrease by increasing the acceleration. Apart from quantitative influence, the acceleration qualitatively changes the physics. We show that in accelerating black hole spacetime there exists an outermost stable circular orbit in flat, de Sitter, and anti–de Sitter backgrounds. Investigations of radial geodesics show that the acceleration acts like a repulsive force in the sense that test particles around accelerating black holes can move radially outward, unless there exists a large negative value of cosmological constant in the background to compensate the repulsive force. We also investigate the precession of perihelion of orbits around accelerating black holes. The precession would be larger compared to the nonaccelerating case. It is also shown that the precession in anti–de Sitter background could be opposite to the particle motion.

中文翻译：

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围绕加速黑洞的类时间轨道

我们研究加速施瓦西黑洞周围大质量粒子的测地线。我们表明，最内层稳定圆形轨道的半径和该轨道上粒子的角动量随着加速度的增加而减小。除了定量的影响外，加速度还定性地改变了物理学。我们表明，在加速黑洞时空中，在平坦、德西特和反德西特背景中存在一个最外层稳定的圆形轨道。对径向测地线的研究表明，在加速黑洞周围的测试粒子可以径向向外移动的意义上，加速度的作用类似于排斥力，除非背景中存在较大的宇宙学常数负值来补偿排斥力。我们还研究了围绕加速黑洞的轨道近日点的进动。与非加速情况相比，进动会更大。还表明反德西特背景中的进动可能与质点运动相反。