Evolution of black hole shadow in the presence of ultralight bosons

Kerr black holes coupled to quantized bosonic fields display a special version of the Hawking effect, governed by the superradiance condition. This leads to rapid growth of boson cloud through spontaneous creation, leading to slowing down of the black hole, and detectable as growth of the black hole shadow. This can be developed into a technique for searching or constraining the existence of ultralight bosons. We study this phenomenon for spin-0 bosons in the shadow of a black hole, with a detailed analysis of Sgr$A^*$, and put estimates on the evolution time scales and subsequent change in the black hole shadow features. Our study shows that there is a small window of parameters where the increase of shadow of a supermassive black hole may be visible, but only if the sensitivity of measurements increases from current 25 $\mu$as to about 0.1 $\mu$as.