How are astronomers able to observe and study black holes?

     Although scientists can't detect or observe black holes with telescopes that detect x-rays, light, or other many other different forms of electromagnetic radiation and waves. But they can detect and study them by the effect of matter near it. If a black hole passes through a cloud of interstellar matter, it will draw matter inward (this process is known as accretion). A similar process occurs when a star passes through a black hole. When this happens, a star can break apart as it pulls it self toward it. As the attracted matter accelerates and starts heating up, it emits x-rays that are radiate into space. 
     Recent studies do show that black do have a very big influence towards neighborhoods around it. The black hole emits gamma ray bursts, devouring nearby stars, and spurring the growth of new stars in some areas while stalling it in others.

Info: https://science.nasa.gov/astrophysics/focus-areas/black-holes
 

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