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.

• Received 27 May 2022
• Accepted 8 August 2022

DOI:https://doi.org/10.1103/PhysRevD.106.044037