I was watching a video about black holes, and when they mentioned that Einstein proved black holes exist with maths, it hit me.
I’ve never asked myself that question, how do numbers tell you that something exist in outer space and what to expect from it? especially things that we never knew they existed in the first place (exp black/white holes) ?
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Einstein didn’t prove the existence of a black hole.
He defined a theory (general relativity) that showed that if something is massive enough in a small enough radius, there is a radius for which light orbits it, and we can call those objects black holes, and it defined most of the properties of black holes.
There was no guarantee that those objects actually exist. We proved that by observation afterward. However, they were likely to exist since they didn’t need anything exotic. Just high density or high mass (the bigger the black hole, the less density is required to make it a black hole).
Even without general relativity, you could have black holes if you assume that light is accelerated the same way than anything else by gravity, but most other properties of black holes require general relativity: how they cause time dilatation, how their rotation affects space-time, how they cause gravitational wave while absorbing matter including colliding with another black hole, etc.
Black hole radiation comes from quantum mechanics, though.
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