Einstein actually predicted that black holes exist in his theory of relativity. We can’t observe black holes directly, which is a problem, but we can detect them by looking at how things nearby behave, like from extra hot radiation of stars nearby
It’s true, Einstein’s models said “if this is true, and it looks like it is, then black holes should exist”. It took scientists a long time to figure out a way to search for black holes, seeing as how they wouldn’t show up in a telescope and they emit no light. Some of Einstein’s predictions we still haven’t figured out a way to measure. Scientists came up with a clever way of measuring “twists” in gravity wells caused by the rotation of the earth only a couple of years ago!
In the end, scientists managed to discover black holes by watching for weird little irregularities in the movement of other stars. They could measure the size of these irregularities and calculate how strong the gravity of something had to be to cause that change. The results indicated that something really really massive was behind the movements, but it didn’t show up on any instruments, which fits the description of a black hole very well.
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