Dynamical Black holes in the FLRW universe

Observations show that massive black holes, thought to be at the center of galaxies and galaxy clusters, are dynamical objects and interact with their environments. Black holes are characterized by their mass and angular momentum, and they are time-varying objects embedded in the cosmological Friedman-Lemaitre-Robertson-Walker (FLRW) universe. Finding analytical solutions for the dynamical black holes with all these properties is very important in theoretical physics. In the present work, we obtain Einstein’s field equations for our predicted dynamical black hole geometry and obtain analytical solutions using the energy-momentum tensor obeying imperfect fluid dynamics. Misner-Sharp-Hernandez mass, turnaround radius, and apparent horizon are analyzed and compared with the recent observations.