Exploring perfect fluid dark matter with EHT results of Sgr A* through rotating 4D-EGB black holes

We investigate the rotating 4D Gauss-Bonnet (GB) black holes surrounded by Perfect Fluid Dark Matter(PFDM) using the Event Horizon Telescope (EHT) observations of Sagittarius A* (Sgr A*). This rotating blackhole, influenced by an additional GB parameter alpha and a DM parameter beta, deviates from the Kerr black holegeometry, offering a more complex horizon structure. Our findings reveal that the shadow size decreases and oblateness increases with higher values of alpha,beta, and the spin parameter a. By plotting the shadow area A and oblateness Das functions of alpha and beta for various a values, we determine the unique black hole parameters through the intersection points of the A and D curves. We constrain the GB and DM parameters with the EHT shadow observational results of Sgr A* for an inclination angle of 90 degrees and 50 degrees. The results, which align with EHT observations of Sgr A*, suggest that dark matter may exist in significant quantities around the galactic centre, challenging the traditional Kerr black hole model and offering new avenues for understanding complex interactions. Thus, It is essential to consider that rotating 4D GB black holes surrounded by PFDM could be strong candidates for astrophysical black holes