[guscost]

Another member of the peanut gallery here. I've not been bold enough to make any claim in writing (it would probably be full of misconceptions), but the black hole hypothesis always seemed a bit half-baked, and I've definitely said words to that effect in conversation.

In the hypothesis Einstein's field equations obviously break down, and instead of acknowledging that any explanation will be enormously difficult to test we seem to have bought into this completely untested idea that matter can continue bending space-time around into a singularity and all that. Can someone with a better understanding point out what logic is (probably) missing here?

The other thing that sets off my hand-wave-o-meter is the pretending that we are somehow already observing these things ("new telescope detects hints of black holes") or have concluded that they exist without any positive evidence. Instead of "the mass at the center of the galaxy which is so large that we currently have no good way of modeling it without a black hole" we hear "the supermassive black hole at the center of the galaxy" and so on.

[scott_s]

My understanding of what Laura Mersini-Houghton's paper is claiming is that stars cannot collapse into black holes, but they can get damned close. So those things that we have observed are not "black holes", but things that are damned close. In the paper, she and her co-author write, "Both effects (slowdown and mass-loss) balance such that the evaporating star remains very slightly outside its event horizon."

Even if this paper is correct, I don't think it's warranted to be so smug about people thinking they found black holes. We had a theory, and we had positive evidence for that theory. That's reasonable. If this paper is correct, then it turns out those things are not actually "black holes", but objects "very slightly outside" of being black holes. That's not too bad.

Disclaimer: I am not a physicist.

[guscost]

What is an example of this positive evidence?

Also is it at all plausible that the center of the galaxy is evaporating slightly outside its event horizon in this way?

Anyway I'm not sure that the two of us are going to answer any of these questions without some help.

[lutusp]

> What is an example of this positive evidence?

Are you asking what observational evidence exists for black holes? There are very massive, very dense objects at the center of most galaxies, objects that by their mass and density fall well inside the theoretical limits for black holes. At the center of our galaxy, there is a very massive, compact object, around which many stars are orbiting, in orbits that reveal the object's mass and approximate size:

http://astro.uchicago.edu/cosmus/projects/UCLA_GCG/

This is pretty good evidence -- if the object weren't within the mass/density realm that allows for black holes, the orbiting stars couldn't approach it as closely as they do without colliding.

Again, this doesn't prove anything, it only supports the idea that black holes are possible, and that our observations agree with that idea.

[guscost]

I don't disagree with any of that, but the evidence in question still depends on several big assumptions.

[lutusp]

It's the other way around. The evidence doesn't depend on the assumptions, the assumptions depend on the evidence.

The observations are very good and offer little latitude for interpretation -- there is a very massive, very dense object at the focus of multiple stellar orbits near the center of our galaxy, and both the mass and the density of the object are easily and unambiguously derived from the orbits.

It's the same with other galaxies -- a massive, dense central object dominates the orbital dynamics of the galaxy near its center. We're obviously not free to say that means black holes exist, it's just another piece of evidence. But it's a way to exclude certain alternatives.

[guscost]

Maybe it could be worded better. In order to say that gathering this evidence is the same as directly observing a black hole, we have to make several big assumptions.

[scott_s]

We have observed things in our universe which match our expectations of black holes: http://en.wikipedia.org/wiki/Black_hole#Observational_eviden...

That we have observed something is not in dispute, as I understand it. What's in dispute is what, exactly, these things are.

[lutusp]

> The other thing that sets off my hand-wave-o-meter is the pretending that we are somehow already observing these things "new telescope detects hints of black holes" or have concluded that they exist without any positive evidence.

Actually, the evidence is pretty good. We have orbital velocities around the mass at the center of our galaxy that cannot exist unless there is a very massive, very dense object at one focus of the ellipses:

http://astro.uchicago.edu/cosmus/projects/UCLA_GCG/

This doesn't prove anything by itself, it only reduces the number of possible explanations.

We also have general relativity, which basically says that, once you exceed a certain spacetime curvature, you enter into the realm where black holes (or something like them) are inevitable.

The observations are very good, and the theory has stood the test of time, producing very reliable and consistent results. None of this is conclusive, there are difficulties with general relativity at the smallest scales, but the black hole idea is a reasonable conclusion to draw based on both theory and evidence.

> In the hypothesis Einstein's field equations obviously break down ...

General relativity doesn't break down for a black hole per se, only the realm inside it. If we observe phenomena from a great distance up to the event horizon, GR reliably predicts the outcomes. Within the black hole, i.e. between the event horizon and the hypothetical singularity at the center, we have a the region for which claims like "all physics breaks down" are appropriate.

But the fact that general relativity cannot explain everything isn't by itself a reason to doubt what it can explain. But it is a reason to look for a more complete theory, one for which GR is a subset. The same can be said about quantum theory -- it also has domains of excellent agreement with observation, and other places where it's less useful.

> ... we seem to have bought into this completely untested idea that matter can continue bending space-time around into a singularity and all that.

But that idea isn't hypothetical, it's pretty easy to see that it falls out of the mathematics. I won't present the general relativity treatment, but here's one from special relativity that's easier to understand. This equation tells us the relationship between space and time in SR:

t' = t √(1-v^2/c^2)

t = time

v = space velocity

c = speed of light

t' = time rate of passage at velocity v relative to velocity 0

Now try increasing v so it equals c (try traveling at the speed of light). See? Time stops, which in SR is roughly equivalent to an infinite curvature in GR.

Photons travel at the speed of light. This means in their frame of reference v = c, and therefore t' = 0. Does this mean that photons don't experience time? That's exactly what it means. In a photon's frame of reference, it's created in an atomic interaction, then it's taking part in another atomic interaction somewhere else, with no intermediate time having passed.

The above example is pretty remarkable when you think about it, but it doesn't mean the laws of physics have broken down, any more than they do at a black hole's even horizon.

[guscost]

This is a very good answer, thanks for taking the time to write it. I will say that "pretty good" evidence is not consistent with the language we usually see in the media[1] but that's really another issue.

Can't SR only model photons at c because some term disappears with zero mass which prevents infinite energies? Isn't it a whole different question whether GR is still reliable in the analogous case with massive objects?

[1] http://www.phdcomics.com/comics/archive.php?comicid=1174

[lutusp]

> I will say that "pretty good" evidence is not consistent with the language we usually see in the media[1] but that's really another issue.

That's the difference between science and journalism. In journalism, some things are proven true, while others are cast into doubt. In science, some things are proven false, while others are less doubtful than they once were, but never become true. The tl;dr: in science, things can only ever be proven false, never true.

As philosopher David Hume famously put it, "No amount of observations of white swans can allow the inference that all swans are white, but the observation of a single black swan is sufficient to refute that conclusion."

> Can't photons only travel at c because some term disappears with zero mass which prevents infinite energies?

I'm not sure I've successfully decoded your question, but only massless particles can travel at c. This is why, when it was established that solar neutrinos were changing their identities while traveling from the sun to our detectors, that meant they were experiencing time, which meant they had mass. All confirmed in later experiments.

> Isn't it a whole different question whether GR is still reliable at c when massive objects are involved?

From a mathematical standpoint GR is perfectly reliable from v = 0 to v = c, including places where large masses are present. Any velocity past c (or a sufficiently large amount of spacetime curvature) and GR is no longer able to provide reliable predictions. The reason is that the mathematical results include imaginary terms. As has been said by many, the relationship between mathematics and reality is much closer than we once imagined.

[guscost]

So the region within the event horizon is where we see the sufficiently large/infinite curvatures and the imaginary terms and GR can be said to break down? I've heard that from a frame of reference outside the event horizon the time dilates and light would seemingly never get there, hence the whole idea of a black hole.

Mind-boggling stuff, thanks again for writing out these explanations.

[lutusp]

> So the region within the event horizon is where we see the sufficiently large/infinite curvatures and the imaginary terms and GR can be said to break down?

Yes. At the event horizon, general relativity still predicts the outcome. Below it, no more conventional physics.

> I've heard that from a frame of reference outside the event horizon the time dilates and light would seemingly never get there, hence the whole idea of a black hole.

I've read that too, but in fact, because of the energies of accretion disks that are vacuuming up light and matter from the neighborhood, and the fact that some of the photons tend to orbit the horizon endlessly, it's actually a very hot place in most cases.

> ... thanks again for writing out these explanations.

You're most welcome.