Thermodynamics, geodesics and gravitational weak lensing of kiselev black holes surrounded by hernquist dark matter halos

In this study, we explore the thermodynamics, massless-particle motion, photon sphere, shadow, and gravitational weak lensing of Schwarzschild BHs embedded in a Hernquist dark matter halo, surrounded by a quintessential field. The spacetime metric is constructed using a modified lapse function incorporating the Schwarzschild term, the Hernquist density profile parameterized by ρ s and r s , and the quintessential contribution with equation of state parameter ω q . We derive the Hawking temperature and heat capacity as functions of the event horizon, revealing the thermodynamic influence of the dark matter halo and quintessence. For massless particles, the photon sphere radius is computed numerically, and shadow contours are constructed to demonstrate environmental deformations of the black hole. In the weak lensing regime, the optical geometry formalism in the equatorial plane is employed to obtain the Gaussian curvature K of the effective two-dimensional metric. The deflection angle α is evaluated via a double integral over null geodesics, showing enhanced lensing due to the extended mass of the Hernquist halo and the repulsive effect of quintessence. Our results underscore the diagnostic power of multi-messenger signatures in probing dark matter and quintessence around supermassive black holes.