Thermodynamics, Weak Gravitational Lensing, and Parameter Estimation of a Schwarzschild Black Hole Immersed in Hernquist Dark Matter Halo

Abstract: In this article, we obtain a novel black hole (BH) solution of a Schwarzschild BH immersed in a Hernquist dark matter (SBHD) halo. The thermodynamic properties of the resultant spacetime are then studied to gauge the impact of dark matter (DM) on the local and global stability of the composite system of the BH-DM halo. With the intention of finding imprints of DM, we then studied weak gravitational lensing (GL) and shadow. Both display significant dependence on the DM parameters - core radius $r_s$ and core density $\rho_s$. Finally, we constrain DM parameters by utilizing bounds on the deviation parameter $\delta$ for super-massive BHs (SMBHs) $M87^*$ and $Sgr A^*$ reported by Event horizon telescope (EHT), Keck, and VLTI observatories. Our analysis finds SBHD congruent with experimental observations, thereby making it a feasible candidate for an SMBH.