A black hole itself is invisible because no light can escape from it. We can't see black holes, but we can find them by examining their effects on objects around them.
We identify suspected supermassive black holes in the center of galaxies by studying the orbits of stars and clouds of gas in that vicinity and the speed with which they move. If those motions indicate the presence of more mass than can be accounted for by counting the stars in that area, the best explanation for the extra mass is a black hole.
When a smaller black hole and a star orbit each other, the black hole can be identified if it pulls matter from its companion star. As the matter swirls into the black hole it heats up, emitting x-rays that can be detected by astronomers.
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