[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.