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

Abstract

We investigate the dynamic shadows of a black hole with a self-interacting massive complex scalar hair. The complex scalar field \psi evolves with time t, and its magnitude on the apparent horizon |\psi_{h}| starts from zero, undergoes a sharp rise followed by rapid oscillations, and eventually converges to a constant value. The variation in the photon sphere radius r_{ps} is similar to that of the magnitude |\psi_{h}|. Owing to the emergence of the complex scalar hair \psi, the apparent horizon radius r_{h} starts increasing sharply and then smoothly approaches a stable value eventually. The shadow radius R_{sh} of the black hole with an accretion disk increases with time t_{o} at the observer's position. In the absence of an accretion disk, the shadow radius R_{sh} is larger and also increases as t_{o} increases. Furthermore, we slice the dynamical spacetime into spacelike hypersurfaces for all time points t. For the case with an accretion disk, the variation in R_{sh} is similar to that in the apparent horizon r_{h}, because the inner edge of the accretion disk extends to the apparent horizon. In the absence of an accretion disk, the variation in R_{sh} is similar to that in the photon sphere radius r_{ps}, because the black hole shadow boundary is determined by the photon sphere. As the variation in r_{ps} is induced by \psi, it can be stated that the variation in the size of the shadow is similarly caused by the change in \psi. Regardless of the presence or absence of the accretion disk, the emergence of the complex scalar hair \psi causes the radius R_{sh} of the shadow to start changing. Moreover, we investigate the time delay \Delta t of lights propagating from light sources to the observer. These findings not only enrich the theoretical models of dynamic black hole shadows but also provide a foundation for testing black hole spacetime dynamics.