A black hole is a place where gravity is so strong that even light cannot escape. But around it there is a glowing ring of gas, and in the center a dark void known as the shadow. The size of this shadow depends on how spacetime is curved.
In this work, physicists took not an ordinary black hole but a charged one, and with an additional scalar field (something like an invisible background permeating everything around). They calculated how the shadow changes depending on the charge of the black hole and the strength of this field. It turned out that the greater the charge, the smaller the shadow, as if the hole were shrinking.
Then the scientists compared their calculations with actual shadow images of two giant black holes: one in the galaxy M87 and one at the center of our Milky Way (the object SgrA*). This allowed them to place constraints: the charge and the field cannot be too large, otherwise the shadow would be noticeably smaller than observed.
Additionally, the authors estimated how quickly such a hole radiates energy in the form of high-frequency light, and calculated a special coefficient describing how strongly a light ray is deflected when passing near the hole. This is important for understanding what we see in the images.
The shadow of a black hole is about 2.5 times larger than its event horizon, the boundary from which nothing can return.