How did Einstein’s equations prove the existence of black holes?

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Einstein’s equations didn’t prove the existence of black holes. People solved Einstein’s equations with a solution that predicted black holes. Many decades later astronomers found evidence of objects out there that fit the expectations of what a black hole would be. And, so far all the evidence has held up for what we’ve observed and the predictions have been correct.

The simplest way to put it is that Einstein proved that it was possible to bend light with gravity. Extrapolating from this suggests that a large enough mass could bend light so severely that the light would never escape. This didn’t necessarily prove black holes but it showed us what to look for.

ELI5?

SERIOUSLY?!

You want Reddit to break down physics equations not even students from MIT can figure out?

Edit: black holes, despite the evidence? Still don’t technically exist according to our equations which are based on Einsteins original equations. They’re just there. Doing their thing. For no reason.

None of us know. Especially those of us that claim we know. We don’t know.

Edit: the JW launch was supposed to help us better understand such things. It’s only been a few months so far, but already everything we thought we knew? Is being ripped apart.

ELI5. Ok.

So these equations are pretty “vague” in a way. It didn’t prove they exist. When you have those equations you look for solutions. Physics is often written in differential equations. Like x”=-D×x. This is a differential equation and there are solutions to it. Here we have one solution. Its A×sin(u×t+k) where A and k are free parameters and u²=D. This is the equations that describes the motion of an object on a spring. And that A×sin(-||-) is the function for the position of the object.

Now Einstein’s equations are similar you imput some energy conditions, how much, in what distribution and you can find solutions that satisfy the equations.

The Schwarzschild solution was found by the guy its named after during WWI when he found a letter of Einstein. He tried to find a solution for packing some mass into one point. He found the solution (the solution is the resulting spacetime curvature) and thats it. Later physicists realise an object like that must be black so named it black ball but black hole sounded cooler.

The solution did prove they existed it only stated that a black hole is a solution to the equation. A spinning black hole is also a solution. So is one with charge.

We’d like to think that given sensible energy conditions so less than the energy of the universe and certainly not negative the resulting spacetime curvatures are physically possible. And black holes were the kind of energy conditions that seemed a bit too out there, but they weren’t. Wormholes are a bit out there too its really hard to say.

Some physicists try doing the reverse, engineering a spacetime curvature they want and figuring out the required energy conditions. Like with warp drive attempts which results in requiring negative mass.

What do you know about General Relativity?

Because the high level version is basically: if you add enough mass/energy in a small enough volume, you get enough gravity going on that even light can’t escape that are of space.

Basically, everything in that area of space has to move towards the center in pretty much the same way that everyone has to move forward in time in a normal region of space.

You can still move in other directions. Yup can move slower or faster towards the center, but moving away from it is going to be impossible.

That’s a black hole.

Einstein Field Equation predicts that.