Using the shadow of a black hole to examine the energy exchange between axion matter and a rotating black hole

We find that a slowly rotating axion-modified black hole resulting from the backreaction of an axion field on a rotating Kerr black hole can have a $D$-shaped shadow as that for a highly counterrotating Kerr black hole. This is attributed to the fact that the energy exchange between the axion matter and the black hole influences the rotation of the black hole, so the black hole angular momentum first decreases to zero and then starts to rotate to the opposite direction. Further increasing the coupling leads to ``human-face-like''-shaped shadows and new lensing due to the chaotic scattering, which are novel and drastically different from those for a Kerr black hole. Our analysis provides the first counterexample to that slowly rotating black hole has nearly circular shadow.