Circular motion of a particle orbiting a black hole in a phantom background

The research explores the effect of a phantom scalar charge parameter on the circular trajectories of both photon-like and time-like particles around the perfect fluid dark matter black hole in the presence of a phantom field. It scrutinizes how this parameter impacts the effective potential, critical points, angular momentum, particle energy, critical radius, and the stability of circular orbits. Additionally, it looks into the innermost and outermost stable circular orbits (ISCO and OSCO). The findings indicate that when the phantom scalar charge [Formula: see text], there is a repulsive force that allows stable orbits to extend to greater distances. Contrarily, when [Formula: see text], this repulsive effect increases, leading to unpredictable changes in the orbit radius and possibly disrupting stable circular orbits. Furthermore, the study investigates photon spheres and black hole shadows, noting that for [Formula: see text], a single photon sphere is observed, whereas two photon spheres emerge in another situation around the perfect fluid dark matter black hole in the presence of a phantom field.