Shadow and gravitational lensing produced by the nonlinear accretion of a scalar field onto a black hole

The hypothesis that classical scalar fields could constitute dark matter on galactic and cosmic scales has garnered significant interest. In scenarios where supermassive black holes (SMBHs) form through the accretion of matter onto black hole seeds, a critical question arises: what role does dark matter play in this process? We conduct a numerical investigation into the nonlinear dynamical evolution of black hole shadows and gravitational lensing effects resulting from the accretion of an ultralight, real scalar field onto a non-rotating black hole. The scalar field is minimally coupled to Einstein's gravity, and our simulations focus on wave packets, parameterized by their wave number and width, as they interact with and are accreted by a dynamic black hole. Our results demonstrate significant growth in the apparent horizon, photon ring, and Einstein ring sizes compared to those of a Schwarzschild black hole. These findings suggest that the observed photon ring and black hole shadow in Sgr\,A*, and M87* may be influenced by the gravitational interaction between the black hole and ultralight scalar field dark matter.