Particle motion and luminosity of accretion disks around rotating accelerating black holes

We investigate the motion of test particles and the properties of accretion disks in rotating, accelerating black hole spacetimes with a non-zero cosmological constant. To do so, we explore the impact of both rotation and acceleration on massive particle dynamics in motion around these configurations. In this respect, we derive the geodesic equations in the Plebański-Demiański spacetime and analyse the characteristics of circular orbits, including the innermost and outermost stable circular orbits. Accordingly, we find that acceleration produces a small correction to the innermost stable circular orbit (ISCO) in the slowly accelerating regime, while its influence becomes more pronounced for the outermost stable circular orbit (OSCO) and hence for the radial extension of the stable-orbit region. Further, we examine the precession of non-circular orbits and find that the precession is in the same direction as the rotation of the test particle regardless of the direction of the black hole spin. We also investigate the thermal spectra of geometrically thin, optically thick accretion disks described by the Novikov-Thorne model. We consider both co-rotating and counter-rotating disks and show that the radiative flux and luminosity are significantly larger for co-rotating disks. We compare the spectral features and luminosity of accretion disks around accelerating black holes with those around non-accelerating Kerr black holes, revealing that acceleration generally reduces the luminosity and flux of emitted light. Our results provide insights into the complex interplay between black hole acceleration, rotation, and the surrounding accretion disk dynamics.