8:25 PM
So what is the Cauchy horizon in the Kerr metric, anyway

ur mum

I suspect it's the surface near the new universe since it's above the singularity
But I dunno
Hm, what book has the causal structure of Kerr
HE, probably
Wald also I guess

@0celo7 That's beyond disgusting.

8:30 PM
Wald has the Nordstrom black hole cauchy horizon
Let's investigate

It's obviously the outside one that will be the Cauchy horizon
There ain't no getting outta that one, AFAIK.

@Danu Really?

@0celo7 : you can't. And space isn't a lattice of strings. It's a 3D bulk, something like a ghostly elastic solid. But if it helps any see this article where Einstein referred a field as a state of space.

Cauchy horizon, not event horizon :p

@JohnDuffield Hmm, I thought you said it was a lattice of strings...
4 hours ago, by John Duffield
See my avatar. You can model Einstein's elastic space as being made up of a lattice of strings. Try to visualize it. Twang a string like you'd pluck a guitar. A photon is a wave propagating on an "open" string.
I must have misunderstood that.

8:33 PM
Hello all!

Schwarzschild has no Cauchy horizon, right?
Singularity is just at timelike infinity
No worries
Hey @TanMath

::finally decides to google what a Cauchy horizon is::

@ACuriousMind srs
we've been talking about them for weeks

@ACuriousMind : The set of all points that can only be reached by causal curves from the set

Hello @Ghost! nice to see you!

8:35 PM
@0celo7 So?

@ACuriousMind The one that is relevant for outside people.

@TanMath good to see you too

@ACuriousMind strange it took you this long to look them up!

0

There is already a Physics Overflow. Why then not being more lenient in the Q&A to be accepted in Phys.SE? Mathematics SE has 10 times as many questions. SO leads with +10M questions. Those other sites are thriving yet feel way more welcoming. In contrast, here there are way too many questions pu...

I'm starting to get annoyed.

@Danu Why?

8:38 PM

" Let us continue this discussion in chat."
Dammit @Danu
Don't we have enough already :p

WTF, how did I manage to vote that question up? Damn phone interface with its tiny buttons

Oh the JD one, @Danu ?

@Slereah Step into my domain...

Or the whole question?

8:38 PM
@0celo7 No, I'm not annoyed about that part right now.

@Slereah Those "continue" links create their own chatroom separate from this one

Ah, good

### Discussion between Danu and MASL

Imported from a comment discussion on meta.physics.stackexchan...

@0celo7 : no, you can model it as a lattice. Like you draw a line in it and watch how it waves.

Is it acceptable to minor-edit a post to reverse one's vote?

8:41 PM
@ACuriousMind Have done it before.

@Danu Well...that's not exactly an answer to my question ;)

Can't you just reclick on the button to remove your vote?

@ACuriousMind Yush?

> concise

@Slereah No.

8:41 PM
You're a meanie and everyone knows it!

@0celo7 I put it in quotation marks :)

@Slereah Votes are locked after five minutes unless the post was edited after you voted

@0celo7 You're just being your usual dramatic self ;)

Oh

@Danu no

8:42 PM
@0celo7 Yes.

You make me dramatic

@ACuriousMind so why didn't you unvote within 5 min?

@0celo7 Clearly.
But nobody else, as far as I know.
So I tend to see the cause as external to my persona ;)

@Danu ignore him, he's the meanie!

@Danu Aha!

8:43 PM
@TanMath Because I just now noticed that I upvoted it - I was of the firm conviction that I had downvoted it

You don't know what the baseline is

@TanMath He's harmless.
@0celo7 I play tennis. I know what the baseline is.

Maybe everyone is isomorphic to a stick in the mud
Except for me
So you are animating them

@Danu but annoying!

But I am not a stick!
So you animating me makes me "dramatic"

8:43 PM
animating? What?

@0celo7 i think it is time to put you on ignore again... see you later!

Okay, so the OP declared he doesn't need to read our homework policy to propose changes to our homework policy.

Be nice to each other, kids.

You haven't said anything particularly interesting / worth responding to

@Danu and ignore that guy as well!

8:45 PM
@0celo7 Stop it
@TanMath You too.

Sometimes ignoring is the best solution to everything!

@Danu I haven't done anything.

I'll intervene if you don't cut it out.

Intervene in what?

1 min ago, by 0celo7
Guess who gives a crap, @TanMath ?
That is not nothing.

8:46 PM
He wants to ignore me. That's fine, I have no reason to talk to him!
Free market at work.

Come on guys, let's talk physics. OK, have a look at some pictures of the electromagnetic spectrum. What's always the same regardless of wavelength?

@Danu what? I am just giving you some advice... you seem annoyed by that guy, so that is why I said that...
@Danu O gosh, he is soooo offensive.. I wish I could flag that post...

I don't even know why @TanMath has a problem, lol.

@JohnDuffield huh?

I don't think he likes GR.

8:47 PM
@0celo7 I love having you on ignore!

Then why are you responding? You're bad at this.

*person

Only one person has uncalm tits.

8:49 PM
Perhaps introducing a talking stick - where only the person who has the stick gets to talk - would be a good idea here.
It would at least be amusing.

Seriously?
Is the stick big enough to take fools out with it?

Is it a good idea to give a stick to people fighting

@HDE226868 yeah. and @0celo7 should have the least time with the stick!

Plus, a stick should be homeomorphic to a variety of different things, so perhaps any topologists could come up with creative things to deform it into.

I literally have no idea why he's upset, lol.
And he refused to tell me.

8:50 PM
@HDE226868 Better use something that cannot be used as an improvised weapon :P

A stick is just homeomorphic to a ball in general
Nothing special

@TanMath : it's one of those naïve little questions that's really interesting. If you've ever played a guitar you might appreciate what I'm getting at. Look at the depictions of the electromagnetic spectrum. What's the same regardless of wavelength?

@ACuriousMind I thought about that, but I figure that someone in here could use nearly anything as a weapon.

Let us talk physics now... I don't want to continue talking about @0celo7 's antics...Either somebody take action or let us stop talking about that crazy guy...
2

I vote for a talking gun, I will provide ammunition.

8:51 PM
@HDE226868 Talking...sponge?
We could call it Bob
3

Pillow

I'm not ready for pillowtalk appearing in here, I think

@JohnDuffield i don't know...

Look at the pictures. It's staring you in the face.

@ACuriousMind That's reminiscent of the SNL "Bag O' Glass" skit. Soft things are dangerous, because they're choking hazards! A little kid could swallow the sponge and die.
. . . It was funnier when it was acted out with a foam ball.

8:52 PM
@HDE226868 No children under 12 allowed in here, I think we're safe

@JohnDuffield It's alive??
@ACuriousMind You sure?

@0celo7 is still a young one
2

There was that Jimmy guy

Maybe we could choke him

@ACuriousMind you don't know if there are 10 yr olds here

8:53 PM
@0celo7 Yes, I am sure that no children under 12 are allowed in here, and you should not joke about being one, because that'll get your account deleted in no time

@ACuriousMind Really!

Wait, how is time defined for the age limit

Cool

Is it proper time

Wait, is that coordinate or proper time

8:53 PM
@ACuriousMind Yeah, I'm actually pretty sure that I'm the youngest. :-)

@Slereah yes, but it is suprising to think so based on the words he says...
@HDE226868 no, I think I am the yuongest! ;) hehehe...

Do you mean like "Homeomorphic"

@TanMath 17. You?

@ACuriousMind BTW, is there really an age limit? i never knew that!

@ACuriousMind Wait, by whom

8:55 PM
@TanMath Yes, it has to do with US laws

Does @dmckee have a duty to delete me if I say I'm 11?

@HDE226868 much younger.. I just don't wish to reveal.. I can say I am younger than 16...

@0celo7 By the community managers, or really any SE employee who stumbles upon it

@ACuriousMind but in stack overflow there are 10 and 11 y olds...

Is that the famous script kiddies I hear about

8:56 PM
Let's get back to this talking stick idea

How could it be implemented

^like this

5

I was browsing Stack Overflow, and I came across this question, asked by a user claiming to be under the age of 13, in this case, 7 years old. As far as I know, children under the age of 13 are not allowed to sign up for an account, but upon further investigation, I discovered that the following ...

8:56 PM

Wait

Ah, the one HDE posted is better

If we are on stack exchange
Shouldn't we use a stack
And
exchange it

US Law is Best Law

3

After a clarifying discussion I see that my downvote was not necessary. Do I have to wait until the post is edited and then upvote or is there another possibility?

@ACuriousMind : Related ^

8:58 PM
@Qmechanic Thanks

Also we can't call the sponge Bob
Bob is the one who exchange the sponge
And gives it to Alice

Hmm
Interesting idea
Are there black holes involved here?

You know I haven' seen any paper on CTCs use Alice and Bob
I am somewhat disappointed
Are Alice and Bob still used a lot in physics?

bob the talking sponge

They used to be used a lot in SR but I haven't really seen them in a while

8:59 PM
@Slereah yes...

is Alice Bob's sister?

I think Alice and Bob do not have a lot of backstory
They are stand ins
But
They like communicating

Alice and Bob are two commonly used placeholder names. They are used for archetypal characters in fields such as cryptography, game theory and physics. The names are used for convenience; for example, "Alice sends a message to Bob encrypted with his public key" is easier to follow than "Party A sends a message to Party B encrypted by Party B's public key." Following the alphabet, the specific names have evolved into common parlance within these fieldsâ€”helping technical topics to be explained in a more understandable fashion. == OverviewEdit == These placeholder names are used for convenience and...

They live in spaceships
And they probably discuss scandalous things because they encrypt a lot

I think Alice and Bob are two very adventurous experimentalists
They are married
So my fanfic is less creepy

9:01 PM
I like how they are often drawn like 1950's characters
He's a groovy cat and she's a swell gal

hello @Qmechanic

@TanMath : Hi

@Qmechanic you don't come to the bar that often..why?

So, what's the same? It isn't the wavelength. It's the...

@TanMath : I'm around.

9:04 PM
@JohnDuffield spectrum?

@Tanmath : No. Look at the picture. It's obvious once you see it.

@JohnDuffield the wave?

@Tanmath : nearly. What attribute of the wave is always the same?

@JohnDuffield oh! the amplitude!

@Tanmath : give that man a cigar!
Now, what's the dimensionality of action h?

9:08 PM
@JohnDuffield um.. I hope you read the convo...As I am below 16 yrs old, I don't smoke!
;)
@JohnDuffield huh?

@TanMath : what's the dimensionality of Planck's constant?

@JohnDuffield what do you mean by dimensionality?

@0celo7 Well, I refer it to the team and they delete you. This is one area in which you should leave the sarcasm at home. The COPA is a fairly humorless piece of legislation and the company takes ins requirements very seriously,

@Tanmath : I mean this: "The Planck constant has dimensions of physical action; these are the same as those of angular momentum, i.e., energy multiplied by time, or momentum multiplied by distance." If you've ever played a guitar you will know that you change the wavelength with your left hand and pluck the strings with your right, usually with a plectrum. When you pluck, the amplitude doesn't usually change. The distance doesn't usually change.

@JohnDuffield oh, ok...

9:28 PM
@TanMath : sadly I don't think many string theorists are guitarists.

@JohnDuffield huh?

Ah, back.

@0celo7 you said you read Zee's Einstein Gravity in a Nutshell from front to back. Can I ask you, what is the exact definition of a locally flat coordinate system at a point P? Is it that the metric is equal to delta_ij there, or is it that the metric is diagonal?

That's the metric being Minkowski at that point
aka Riemann normal coordinates

Metric is delta_ij and the Christoffel symbols vanish.

9:36 PM
He does not clearly define it (at least not in chapter I.6), and in the internet the definitions are not clear

Oh, both the metric and the first derivative

Which means the first derivative is zero.

Hey, who here knows about tensors? (i bet all of you do!)

@TanMath I do.

ok, just to be sure, if the metric is C delta_{ij} with a constant C, then the coordinate system is also locally flat?

9:37 PM
Tensor? I hardly know 'er

@BastianTreichler Yes, note that $C$ can just be absorbed into your basis vectors

@BastianTreichler Are we talking GR or generic riemannian manifold

So you can always find a basis for which the metric is $\delta_{ij}$ at that point

@0celo7 oh, of course!
thanks

In GR it's not $\delta$

9:38 PM
At the point!

There will be corrections as you move outwards!

Yes
Also the second derivative isn't $0$

I messed that bit up when I first learned, just making sure you get it.
True, listen to the Frenchman.

That's basically the mathematical equivalent of the equivalence principle

9:39 PM
@Slereah Sect. 1.6 in Zee is Riemannian.
I have an answer on that somewhere.

6

The statement is better in the following form: The Principle of Equivalence implies that there exists a coordinate system such that the metric of spacetime is locally $\eta_{\mu\nu}$. Note the word locally. If there is real curvature, then there exists no coordinate system $x$ such that $g_... @0celo7 yep I'm struggling with it at the moment.. tried to calculate the intrinsic curvature of the 2-dim sphere with the metric diag(1, sin^2 theta), but that seems to work at the equator only, because at other places it's not delta_{ij} right? @obe o.O Don't forget to put dollar signs around your Tex 9:41 PM @0celo7 my third fav song. @Slereah ok I'm in physical pain now My back aches @BastianTreichler : You can always rotate the coordinate system so that your point is at the equator Since it's a sphere all points are pretty much equivalent 9:42 PM It's homogeneous. @JohnDuffield That it is Maximally symmetric and all Symmetric along the killing vectors$\partial_\theta$and$\partial_\phi$And whatever the rotation on a sphere is @Slereah yep for the sphere that's okay, but if I'm calculating the curvature of the 2-torus, it's a different thing right? I basically need a different coordinate system for each value of$\theta$, to get a locally flat coordinate system for each point Ahahah The torus You can also rotate the coordinates of the torus but only in$\phi$, right? By just doing the coordinate transform$\theta + a$and$\phi + b$9:45 PM @Slereah Has a PhD in tori It's a coordinate transformation You don't have any restriction on it if I'm rotating it in$\theta$, I'm changing the intrinsic curvature, don't I? I mean that would map a point of negative curvature to one of positive? Nobody knows about tensors? (Except being diffeomorphic) weird! 9:45 PM We know about tensors, yes I do why would you even answer that. @BastianTreichler : you are just changing the coordinates @obe Huh? Nothing physical 9:46 PM @0celo7 this one is weird ::cringe:: @TanMath 0celo7 knows about tensors! hmm am I the only one who likes this kind of music? @obe yes @0celo7 : like I said, there's no evidence of any higher dimensions. Space is like the ball, not the uniformly-curved sphere. 9:48 PM Is "trying to drink the last milkshake drop with a straw" a genre of music @Slereah okay, but for the sphere it's enough to calculate the curvature at one point on the equator, for diag(1,$\text{sin}^2(x)$). Since it's symmetric and all, that curvature (+1) is everywhere the same, . For the 2-torus that's different @JohnDuffield what does that even mean @BastianTreichler : As said, it doesn't matter Changing coordinates does not change the curvature It matters on the torus. Those are just labels 9:49 PM On the inside you have negative curvature. On the outside positive. I know And on top it's flat? I CALCULATED IT TWO DAYS AGO Top and bottom @Slereah him! really? He does! He scooby-doo 9:50 PM @Slereah so I am having problems understanding how they work @Slereah I din't want to talk to him, ok? Well ask a question then hello @DanielSank @TanMath Why? @Slereah What is the difference between tensor and vector? How does the notation of tensors work? @BastianTreichler : It's a big thing in GR that scalars are invariant under coordinate changes @TanMath A vector is a tensor, but not vice versa 9:51 PM @TanMath Have a look at e.g. this answer of mine @ACuriousMind Seriously? How is that not off-topic? @Slereah well that's (more or less) clear to me. I just wanted to say the torus is not as simple as the sphere, because on the sphere you calculate the curvature at one point and you're done. @ACuriousMind what is the e stuff? is euler's number used? But finding the Riemann normal coordinates on the torus isn't hard, though @TanMath "We choose a basis$e_i$for$V$" 9:53 PM but i'm sure that's also clear to you, so I'm gonna leave that as it is. thanks for your help! Just do a coordinate transform that will put the metric flat at one point @ACuriousMind so it is like a unit vector? @TanMath Do you not know what a basis of a vector space is? @0celo7 : people refer to the surface of a ball when talking about uniform curvature. Then they say space might be similarly curved, but in a higher dimension. Only there is no evidence whatsoever of any such a higher dimension. Nor is there any evidence that space has some kind of intrinsic curvature or toroidal topology like the old asteroids game. @ACuriousMind A basis? no... I mean, there is a basis vector in QM, is that what you mean? 9:56 PM @Slereah just one more thing, is it true that if the surface is embedded in Euclidean$E^3$, then the the coordinate lines of a locally flat coordinate system are orthonormal? Not necessarily @TanMath See Wikipedia. You really should learn basic linear algebra before going near either tensors or quantum mechanics. But there exists an orthonormal coordinate system, yes @Slereah do you have a counterexample? Sure Take$R^2$9:57 PM @ACuriousMind so it is like the basis vectors in QM... Do the coordinate change$x \rightarrow x + y$It isn't orthonormal anymore forgot to add, "orthonormal at the point where they are locally flat" and$x \rightarrow x+y$is locally flat? damn Well if the metric is$\eta$(or$\delta$), then yes, it is an orthonormal basis @0celo7 I'm lenient on tensor questions because physicists deal with them very differently than most mathematicians. If you think this should be on math, go and vote to migrate ok (what a relief) what's$\eta\$?

9:59 PM
The metric tensor of Minkowski space

@ACuriousMind Do they really?

oh I see