The question I've always ask is how did Einstein miss black holes? Schwarzschild immediately saw the obvious and checked the limits of Einstein's work.
This is similar to Minkowski seeing the obvious with spacetime, once finally bothering to look at Einstein's work, whom he had taught, years after the 1905 publication.
No one "missed" black holes. There are obvious degenerate singularities that appear when you take a simple exact solution like the Schwarzchild solution past sensible physical reality by e.g. pretending conveniences like "point masses" really exist. It took decades of theoretical development to show that black holes were actually possible, and it was still very surprising that they turned out to observably exist.
He didn't miss the possibility; he just convinced himself that this possibility could not actually be realized, and published, IIRC, at least two papers giving his arguments for why. Unfortunately for him, both arguments were invalid.
> Schwarzschild immediately saw the obvious
No, he didn't. He did come up with the solution that is named after him, but he had no idea it described what we now call a black hole.
The earliest recognition and acceptance of the fact that the Schwarzschild solution describes what we now call a black hole (though that term wasn't invented until several decades later) was in the classic paper by Oppenheimer and Snyder in 1939 that describes the gravitational collapse of an idealized exactly spherically symmetric body with zero pressure.
It's a little unfair to Schwarzschild. He discovered his solution, the first solution to Einstein's equations, while serving in WWI and actually before Einstein published his paper on general relativity. Schwarzschild died just a couple months after his paper describing the solution was published.
How is telling the truth about what he did and did not do unfair?
> He discovered his solution, the first solution to Einstein's equations, while serving in WWI
Yes.
> and actually before Einstein published his paper on general relativity.
Before the official publication in 1916, yes. As I understand it, Einstein sent Schwarzschild a preprint and Schwarzschild based his work on that.
> Schwarzschild died just a couple months after his paper describing the solution was published.
Yes, and this was undoubtedly a tragedy.
None of the above, however, contradicts what I said, which is that Schwarzschild did not realize that his solution described what we now call a black hole. The post I was responding to said Schwarzschild "saw the obvious", meaning saw a black hole in his solution. He didn't. Nobody did until the 1930s.
> The Schwarzschild radius is the defining boundary of a black hole
In our modern understanding, yes.
> which Schwarzschild first calculated.
He calculated that there was a constant that appeared in his metric, proportional to the mass, and with units of length. But he had no idea that this constant was related to the boundary of a black hole. Of course he didn't have much time to explore his solution further, since he was killed not long after sending his paper to Einstein. It's an interesting what if question to ask what he might have found if he had had years more to do physics.
> why did Schwarzschild beat Einstein in calculating the Schwarzschild radius first?
Einstein wasn't working on the specific solution for the case of a spherically symmetric vacuum surrounding a mass. He already knew that, to a first approximation, this solution would look like Newtonian gravity, and that the next order correction terms would explain the extra precession of Mercury's perihelion (which had been observed in the 19th century) and would predict gravitational redshift and the bending of light by the Sun (neither of which had yet been observed). Einstein was more interested in deriving the general form of the field equation than investigating further the specific properties of that particular solution. Whereas Schwarzschild focused on that solution.
Einstein and all the great scientists from that era didn't miss black holes, they thought the idea of black holes were stupid and looked down on people doing that kind of research. Freeman Dyson talks about this in a few interviews - though he doesn't seem to understand why they thought that as he personally loved black hole research.
A singularity is, afterall, a mathematical effect that occurs everywhere in science when the mathematics used to describe the system in one region is no longer valid in another. Only in modern, government funded 'science' do we start to find people taking mathematical errors seriously. Also, to preempt any responses I might get, no, massive dark objects at the center of our galaxy are not even close to being evidence that space-time singularities are real.
Aren't you conflating black holes with singularities, here?
Questions about singularities, I would assume, are inherently non-scientific in the sense that it would be impossible to ever come up with testable predictions about their behaviour. However, black holes, as 'a region of spacetime where gravity is so strong that nothing — no particles or even electromagnetic radiation such as light — can escape from it' (definition ripped from Wikipedia), seem like a testable concept with some evidence for their existence.
Fuzzballs were first proposed as a consequence of superstring theory in 2002, so it would be quite a feat for a scifi author to have come up with them in 1977.
Not the same thing as a black hole. A black hole is a region of spacetime that cannot send light signals to infinity, i.e., bounded by an event horizon. In the simplest such models, there is a singularity inside the event horizon; but that does not mean every possible model with an event horizon must contain a singularity.
Btw, the problem Einstein and others of his time had was with the event horizon, not the singularity; the singularity did not become a significant object of study until a decade or two after Einstein died.
I'm guessing from these responses that 'singularity' has turned into kind of pop-culture term expressing the center of a black hole.
A singularity is just where physical quantities go to infinity. There are many singularities at the event horizon. For example, as you fall into a black hole and approach the event horizon the time of an observer a distance away begins to speed up and approaches infinity - the universe comes to an end before you actually reach the event horizon. Many unphysical things like that happen. These are all singularities.
Importantly also, the energy density of space-time approaches the plank energy and this is a region where general relativity and quantum field theory do not agree with each other. So we know the equations are non-sense in this region for sure.
> I'm guessing from these responses that 'singularity' has turned into kind of pop-culture term expressing the center of a black hole.
It's not a pop culture term at all. It's a precisely defined technical term in GR. Everything I said about it is taken from that precise technical definition.
> A singularity is just where physical quantities go to infinity.
Correct. (Although this itself is something of a pop science version of the actual technical definition. But it will do for this discussion.)
> There are many singularities at the event horizon.
Wrong. All physical quantities are finite at the event horizon. Your counterexamples are based on misconceptions which have been well understood and corrected in the GR literature for decades.
> as you fall into a black hole and approach the event horizon the time of an observer a distance away begins to speed up and approaches infinity
Wrong. If you are free-falling into a black hole, light from the rest of the universe is redshifted, not blueshifted.
If you are hovering at a constant altitude above a black hole's horizon, light from the rest of the universe is blueshifted; but the blueshift is finite for any altitude above the horizon. It is impossible to hover at the horizon.
> the universe comes to an end before you actually reach the event horizon.
Wrong.
> Many unphysical things like that happen.
Wrong.
> the energy density of space-time approaches the plank energy
Wrong. The black hole is a vacuum solution: the stress-energy tensor is zero everywhere.
> this is a region where general relativity and quantum field theory do not agree with each other. So we know the equations are non-sense in this region for sure.
Wrong. The area at which GR and QM create compatibility problems is within a Planck time of the singularity, not the horizon.
As I said above, all of these misconceptions have been known of and corrected in the GR literature for decades.
I didn't believe you so I looked this all up and indeed everything you said is correct. My GR professor was famously one of the worst academics at the department and he never taught us any of that. His specialty was GR too.
Anyway, your response was needlessly hyperbolic. The only two misconceptions you are correcting here is that tidal forces can be quite weak at the event horizon and the universe does not come to an before passing through it.
> My GR professor was famously one of the worst academics at the department and he never taught us any of that. His specialty was GR too.
This is disappointing, but unfortunately I don't find it surprising. I have learned GR by self study over many years, starting with borrowing my office mate's copy of Misner, Thorne & Wheeler when I was in graduate school; I never actually took a course in it. But the reports I had from people who did were that the professors did not do a good job of explaining things. Unfortunately being good at research and being good at teaching are two very different things and not many people have both.
> The only two misconceptions you are correcting here is that tidal forces can be quite weak at the event horizon and the universe does not come to an before passing through it.
I did correct those two misconceptions, but those weren't the only ones in your post.
There's no particular reason to believe the singularity in the math describing black holes has physical existence. Lots of equations have singularities and usually it just means that you're using them outside the domain in which they're defined.
Maybe some heretofore unknown force kicks in and keeps the material inside the black hole from forming a singularity. Maybe they're actually fuzzballs:
You don't really have to have a fully worked-out explanation of why the black hole singularities aren't physical- nobody can see inside the black hole, so all we can say is that the existence of black holes is consistent with there being a physical singularity in the middle. But really anything could be happening in there, we just don't know. The singularity the GR predicts is arguably evidence against GR holding at the center of the black hole; there's very probably something else going on.
This makes no sense. When you apply the mathematics of fluid dynamics to the problem of water leaking through a dam wall, you get singularities.
It makes no sense to say "you either believe the amount of water in a dam wall becomes infinite and the universe collapses in on itself inside a dam, or you have a better theory, what is that theory?" (you would become a famous mathematician if you had that theory by the way).
This is similar to Minkowski seeing the obvious with spacetime, once finally bothering to look at Einstein's work, whom he had taught, years after the 1905 publication.