How math tells us that something exists in outer space ?

Question

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) ?

In: 407

Answer 1

Einstein didn’t prove the existence of black holes. What he did was propose a set of generalized equations and conceptualization of space-time and gravity.

One of the possible solutions of those equations was an “object” that we now called a black hole. First, Einstein was not the one who discovered this – it was another scientist working on Einstein’s equations that generated this particular solution. His name was Schwarzchild.

At the time, it was not known if such a solution was simply a fancy mathematical outcome of the equations and if such an object actually existed in the universe. There was no “proof” of anything, to be precise. It was only later that actual observations of the motion of stars etc gave evidence that black holes actually exist.

Ironically, the existence of black holes actually points to a “failing” in Einstein’s theory. The mathematical singularity in the equation that “predicts” the black hole is strong indication that the theory is incomplete and insufficient.