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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It doesn’t. A lot of things could be solutions to equations. In our case we are talking about Einstein’s equations. (The solutions to the equations is sapcetime geometry given some matter distribution.)
Now just because something is a valid solution doesn’t mean its physically realistic. A black hole in the simplest form is the solution for a point mass. Cool but if there is no mechanism that can compress matter below isn’t Schwarzschild radius, black holes won’t exist.
Now in our case we have mechanisms creating black holes. But that doesn’t mean that any valid solution must exist. Of course the point of these equations is to allow us to work out any scenario. We just assume everything we are able to work out is valid, and if we get something familiar we are happy, and when we get something new/weird we are excited. Then we can do experiments to see if the predictions are correct. If yes its good, if no its great because we found new physics.
The point of models is to quantify physics. The models don’t tell what exists, but what can exist. What ends up existing depends on what mechanisms are available.
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