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 black hole, influenced by an additional GB parameter $\alpha$ and a DM parameter $\beta$, deviates from the Kerr black hole geometry, 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 $D$ as 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° and 50°. 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.