Dynamics and Merger Rate of Primordial Black Holes in a Cluster

The PBH clusters can be sources of gravitational waves, and the merger rate depends on spatial distribution PBHs in cluster which changes over time. It is well known that collisional systems experience core collapse leads to significant increase central density shrinking core. After collapse, expands almost self-similarly (i.e., profile extends size without changing its shape). These dynamic processes affect PBHs. In this paper, dynamics considered using Fokker–Planck equation. We calculate cosmic time scales show dependence has a unique signature. Namely, it grows by about an order magnitude at moment characteristics cluster, then decreases according R∝t−1.48. was obtained for monochromatic power-law mass distributions with some fixed parameters. Obtained results used test model via observation waves high redshift.