Dynamic shadow of a black hole with a self-interacting massive complex scalar hair

We research dynamic shadows of a black hole with a self-interacting massive complex scalar hair. The complex scalar field ψ evolves with time t, whose magnitude on apparent horizon |ψₕ| starts from zero, undergoes a sharp rise followed by rapid oscillations, and eventually converges to a constant value. The variation of the photon sphere radius rₚₛ is similar to that of the magnitude |ψₕ|. The emergence of the complex scalar hair ψ causes the apparent horizon radius rₕ to start increasing sharply, and smoothly approaches a stable value eventually. The shadow radius Rₛₕ of the black hole with an accretion disk increases with tₒ the time at the observer's position. In the absence of an accretion disk, the shadow radius Rₛₕ is larger and also increases as tₒ increases. Furthermore, we slice the dynamical spacetime into spacelike hypersurfaces for all time points t. For the case with an accretion disk, the variation of Rₛₕ is similar to that of the apparent horizon rₕ, because the inner edge of the accretion disk extends to the apparent horizon. In the absence of an accretion disk, the variation of Rₛₕ is similar to that of the photon sphere rₚₛ, because the black hole shadow boundary is determined by the photon sphere. Since the variation of rₚₛ is induced by ψ, it can be stated that the variation in the size of the shadow is likewise caused by the change of ψ. Regardless of the presence or absence of the accretion disk, the emergence of the complex scalar hair ψ causes the radius Rₛₕ of the shadow to start changing. These findings not only enrich the theoretical models of dynamic black hole shadows but also provide a foundation for testing black hole spacetime dynamics.