I always struggled with math, so I just don’t get how an astrophysicist could look at some numbers and symbols and say, “Aha, it’s proof of black holes!”
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A simple example that might illustrate this is escape velocity. If you look at the escape velocity equation, you’ll see
v = sqrt (2GM/R)
G is just some constant, so the only things that matter are M, R, and v. This equation is saying that if you are distance R from some mass M, your speed needs to be v for you to get away from that mass, otherwise you’re stuck either orbiting it or falling towards it.
Imagine you’re an astronomer armed with this equation, and you’ve got a bit of curiosity. You ask yourself, what happens if I keep R fixed but start increasing M? You’re staying at the same distance from the mass, but you’re making it more massive, essentially increasing its density. If you increase its density enough, you might find that v is now larger than the speed of light.
So, the math allows for some hypothetical object that’s so dense that not even light is fast enough to escape. You don’t know if it’s physically possible for something to be that dense, but the math (or at least, this particular equation) allows it to exist.
By leveraging more complicated equations, astronomers could learn a lot more about what black holes *should* be like without ever having observed one
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