I have a question about: quantamagazine.org/…. It says an AdS observer would see a light signal reach the boundary at infinity in finite time because such a wave is travelling at (or near) the speed of light. How does this explain that? Aren't we talking about the observer's perspective?

@PM2Ring FWIW that one's sort of borderline, but yeah, when in doubt, safer to flag than not.

Does an observer who is not in free fall still see the metric as locally flat in GR?

I want to say no, but I can't really see why not. They will see locally things accelerate, so the geodesic equation can't just be trivial with the vanishing connection coefficients.

Hmm maybe I've just answered my own question actually

Ah and if the connection is non-vanishing the metric must be non-trivial

Thank you for coming to my TED talk, exits quietly.

Anyone familiar with AdS?

Thank you that is also helpful

On the Kruskal–Szekeres diagram, I see in the exterior region of the black hole (I region) the constant r hyperbolas curves are timelike and the constant t lines are spacelike, but in the interior region of the black hole (II region) the constant r hyperbolas curves are spacelike and the constant t lines are timelike. This is very strange.

@CaptainBohemian it's the well known result that the Schwarzschild $r$ coordinate becomes a time coordinate inside the horizon, and likewise $t$ becomes a spatial coordinate inside the horizon.

It's just a weirdness of the Schwarzschild coordinate system, not a weirdness of the spacetime .

That's one advantage of the KS coordinates. u is a spatial coordinate everywhere and v is a time coordinate everywhere.

@JohnRennie Does the Schwarzschild metric $g=-(1-\frac{r_s}{r})c^2dt^2+(1-\frac{r_s}{r})^{-1}dr^2+r^2d\Omega^2$ also apply inside the black hole $r<r_s$?

Yes it does

Remember that coordinates are just convenient labels for points in spacetime and they don't have to be directly related to anything physically meaningful. Inside the horizon $r$ and $t$ are weird, but that doesn't matter. You can still use them to compute physically meaningful quantities like proper times.

@JohnRennie So that $r=r_s$ at whatever finite t values is just the origin (being 2-dimensional) of the Kruskal–Szekeres diagram but $r=r_s$ at $t=\pm \infty$ runs across $T=\pm X$ (being 3-dimensional) is also an artifact of the coordinates rather than a physical reality?

It happens because the Schwarzschild coordinates become singular at the event horizon.

The KS coordinates remain well behaved, but since the Schwarzschild coordinates are singular at the horizon it necessarily means the mapping between the two sets of coordinates becomes singular at the horizon.

There is nothing weird at the horizon. If you fell into a black hole large enough not to have fatal tidal forces at the horizon then you would pass straight through the horizon without even realising.

Well, full marks to SpaceX. They have nailed it.

Whatever you might think of Elon Musk as a person he does appear to be an inspirational leader.

@JohnRennie I agree

I'm watching how the 2 guys are about to step on the ISS

a lot preparation just to open a door xDD

I gotta admit the space suits of 2 the astronauts look a bit funny to me

@JohnRennie why would anyone think anything bad about elon musk?

@JingleBells You can literally type that question into Google and find out!

@ACuriousMind I wanted to hear John Rennie's take on this and why he thinks some people might dislike him.

@JingleBells I've never met Elon Musk. Like most of us all I know about him is what I read in the papers. The impression he gives is of being rather brattish - petulant and impulsive. But then (a) I don't know how accurate the reporting is and (b) I don't know if Musk does it deliberately for the publicity.

I doubt that being an arsehole is good way to motive people, and Musk has the rare distinction of revolutionising not one but two unrelated industries. That makes him an exceptional person.

@FakeMod Ah. My "favourite" editor. I had to reject one of his edits yesterday where he changed 300 g to 300mg. And I hate how he never puts a space between the number and the units. He's still doing "glitter-roll" edits on homework dumps, but at least he seems to have stopped editing recently closed posts. I am concerned that he will soon have enough rep to edit without approval, but maybe he'll slow down when he can no longer earn rep on edits.

@FakeMod Me too. I've hardly earned any rep on any sites via edits. BTW, one of the 10k privileges is a short-cut for editing tags. physics.stackexchange.com/help/privileges/moderator-tools

I think Qmechanic is the only one who really makes use of that ;)

Huh, it would indeed be almost double.

@JohnRennie The hatch opening was dope and that guy kept smiling all the time lol

@ACuriousMind :) I use it on SO. We get lots of Python questions without the generic python tag, just a version tag like python-3.x, which is annoying when you want to dupe hammer but only have the generic gold badge. So it ends up taking 2 people to close the question: 1 to retag, 1 to hammer it.

On Physics.SE, inline tag editing would be very handy for adding the homework tag, and getting rid of irrelevant tags that newbies often add.

yeah, I use it mostly for adding the Hw tag

@JingleBells Probably because of stuff like this