Geodesic motion of particles in the vicinity of the κ-deformed Schwarzschild black hole

In this study, we investigate the geodesic motion of a test particle around the Schwarzschild black hole in a [Formula: see text]-deformed spacetime. We compute a modified Lagrangian to obtain the [Formula: see text]-deformed effective potential and find the particle trajectories based on the constants of motion. For the same value of angular momentum, we obtain a significant deformation in the orbits of the particles due to the non-commutativity of the [Formula: see text]-deformed spacetime. The noncommutative effects become more significant for higher values of the angular momentum. The radius of the individual trajectories becomes smaller and their velocities decrease compared to the commutative case. The radius of the innermost stable circular orbit ([Formula: see text]) is also found using the modified effective potential. Though the equations get modified due to the non-commutativity of the [Formula: see text]-deformed spacetime, the [Formula: see text] remains the same. We then study a large number of freely streaming particles moving in this [Formula: see text]-deformed spacetime and analyze the movement of these particles around the black hole due to the non-commutativity of the spacetime. We concentrate on particles with different angular momentum moving around the black hole. We find that the motion of the particles are modified due to the non-commutativity of the spacetime. The particles move slower along their respective trajectories in the deformed spacetime. So, they remain closer to the black hole for a longer period of time, indicating that the accretion of freely streaming particles around the black hole would be modified by the non-commutativity of the spacetime.