The h Bar

5:37 AM

@newUser I know some authors write the Kruskal-Szekeres coordinates as $u$ and $v$ while others use $U$ and $V$, but I can't remember if there's a difference. If there is a difference it's a minor one.

Anyhow the horizontal axis is just the axis on which we plot $u$ or $U$ and likewise on the vertical axis we plot $v$ or $V$.

Slereah

6:46 AM

@JohnRennie The capitalization usually indicates a conformal transformation for Kruskal coordinates

or something to that effect I think?

John Rennie

If I could be bothered to dig out my copy of MTW I'm sure it would be in there.

Sadly MTW is too heavy to lift this early in the morning :-)

It appears the capital letters are the light cone version $U = v - u$, $V = v + u$

So the U and V axes are at 45° to the u and v axes ...

Slereah

8:27 AM

Aren't $u$ and $v$ already the light cone versions

Or is that what Carroll calls $T$ and $R$

John Rennie

8:41 AM

@Slereah yes, though they are more usually called $T$ and $X$.

Slereah

Ah yes

user27286

9:03 AM

I also posted this in Quantum computing chat but I am posting it here again because of relevancy (I suppose). I am a bit tired trying to understand section 10.5 of Nielsen Chuang (Stabilizer codes)...especially I was reading it and then when it comes to Figure 10.7 everything is blank. Can anybody explain me? or maybe we can have a meeting to discuss this? I don't know.

john

11:31 AM

A freely falling observer in a homogeneous gravitational field, according to the equivalence principle, can’t feel the presence of the gravitational field.

If the field is not homogeneous, we can choose a local frame in which the field slightly change and can be approximated as homogeneous. A freely falling observer in this frame wouldn’t feel the gravitational field.

But freely falling the observer would, soon or later, move to a region in which the gravitational field is different. Then it would fall with different acceleration, and then detect the presence of the gravitational field.

Where am I wrong?

Secret

11:45 AM

What REALLY Happens When Crushed Between Two Portals?!?!

►

well unless the clocks in the two ends are not synchronised, then this happens instead

Can We Break the Universe?

►

Charlie

1:08 PM

Have I got this right, that the point of dimensional regularization is that the Feynman diagrams that are divergent in 4-dimensions aren't divergent in D-dimensions, and we can basically treat the dimension D as a variable and take the limit as we approach D=4, and this makes the divergences simpler

if so, it's pretty neat

Slereah

2:51 PM

physicsandphysicists.blogspot.com/2009/10/…

@Charlie It can be, yes

Not all divergences are so easily removed, but many are

ACuriousMind

3:25 PM

@Slereah ...is ThorLabs implying they're not human?

John Rennie

4:07 PM

@john a freely falling observer will never feel any acceleration regardless of whether the gravitational field changes or not. However of the field changes rapidly enough they may be able to detect tidal forces.

john

4:26 PM

@JohnRennie But the reference frame is always the same or it moves to another inertial frame?

John Rennie

4:56 PM

@john there are no inertial frames in GR. The best we can do is choose coordinates that are locally inertial in the sense that Newton's laws hold near the origin.

The classic choice of coordinates is to use the rest frame of the freely falling observer i.e. the coordinates in which the observer is stationary at the origin. These are known as the Fermi normal coordinates if you feel the urge to Google them.

You might object that surely this is an accelerating frame, but in GR acceleration is relative. You might think this is an accelerating frame, but the freely falling observer does not. Indeed motion in this frame is the same as if the observer was floating motionless in flat spacetime far from any gravitational fields.

john

5:10 PM

@JohnRennie Sorry my bad, I was meaning local inertial frame

John Rennie

The rest frame of a freely falling observer is a locally inertial frame.

newUser

@JohnRennie I am reading Poisson's book, the chapter about Black Holes. I am studying the Kerr BH and there is a sentence that I don't get. Can you help me? Why is $t^\alpha$ not null at the event horizon? $t^\alpha=dx^\alpha/dt$ and so $t^\alpha t_\alpha = g_{tt}$ which is indeed zero at the event horizon. What am I getting wrong?

Slereah

Also there are no global frames in GR

So talking about "frames" is already tricky

You can't even extend the frame of an observer in Minkowski space, if it's a general observer

John Rennie

@newUser which book?

newUser

@JohnRennie A Relativist's Toolkit by Eric Poisson

Pag. 191

John Rennie

5:22 PM

Ah, so $t^\alpha$ is the Killing vector.

newUser

yes, it is

both $t^\alpha$ and $\phi^\alpha$ are killing vectors

John Rennie

I must admit I'd have thought the Killing vector is null whenever $g_{tt} = 0$.

123

Hello Guys..

newUser

5:55 PM

@JohnRennie great... this is comforting me, but there must be something that we are missing then

@JohnRennie are you familiar with the derivation of the Wald Entropy formula? The entropy of the BH can be seen as a Noether charge of the killing vector in Eq.5.58. It is crucial that the killing vector becomes null on the bifurcation of the BH

this cannot be true if I repeat the same computation with only $t^\alpha$

M.N.Raia

6:17 PM

Hi everyone! Hope you are all safe and healthy.

So. my advisor wants me to do the following research project: 1) Get a light curve from a astrophysical object like a quasar 2) Apply a algorithm to obtain the periods of this curve

I reallu do not know how to do that. I mean, to obtain the light curve is just a matter of get data from a database. But what suppose to mean " Apply a algorithm to obtain the periods of this curve" ?

really*

an*

ACuriousMind

@M.N.Raia ...why don't you ask your advisor what they meant?

M.N.Raia

I would like to ask here first.

If you don't mind.

ACuriousMind

I mean, they probably meant "obtain the orbital period of the object from the light curve", but are you really gonna take the chance to do the wrong thing because some guy in a chat room told you so? :P

user 85795

lol

M.N.Raia

Yep this "obtain the orbital period of the object from the light curve" is quite the thing. So how can I do that?

(beg your pardon if I sound rude)

ACuriousMind

6:30 PM

I don't know how precisely to do that, my knowledge of astronomy is very superficial. The light curve should be a bunch of roughly periodic data, e.g. if the object is brighter on one side than the other and it rotates then it will come back to the same brightness after a full rotation

M.N.Raia

I see, to do that I must to construct a periodgram?

user929304

@ACuriousMind Hi, how's it going? long time no see!

ACuriousMind

@user929304 Hey! It's going fine, all things considered...how're you doing?

user929304

6:46 PM

@ACuriousMind good to hear! ye i feel you, I know how dire the crisis has become in Ger as well :/ I m good too, soon getting my physics degree ;)

ACuriousMind

congrats, any idea what you're gonna do after that?

user929304

@ACuriousMind no :/ currently i m teaching online to make a living, but ideally, i would like to continue with a master's study

@ACuriousMind a somewhat random question, but I'm curious as to whether you've heard or learned any of the following topics in your studies: derived algebraic geometry, categorification

ACuriousMind

@user929304 I did take a course on sheaf cohomology that included some stuff about derived categories, but I've forgotten most of it

user929304

@ACuriousMind Aha! personally, I have only recently started reading up on them (in the hope of progressing rapidly enough to postulate for a thesis in mathematical physics).

user929304

7:06 PM

@ACuriousMind if I am honest with you, I am really (embarrassingly) struggling with pure Mathematical language of type: "(Associative algebra). Suppose R is a commutative ring. An associative R-algebra is a ring B that is also an R-module and such that the ring multiplication is R-bilinear..."., I know what rings are, what an algebra is, what associativity is, but put together in that definition goes right past me.

Wanted to ask you, if you'd recommend an introductory book on analysis for someone like me that would help me better acquaint myself with such a mathematical language coming from an applied physics background

ACuriousMind

@user929304 that's pretty normal - mathematical definitions are often tuned for "elegance", not comprehensibility :P I think it is rather usual to have to look at examples - what kind of things are and are not the thing under definition - to "understand" what a definition is getting at

user929304

@ACuriousMind well put! examples help tremendously! Is there any book that helped you particularly in getting used to such a formal language in your own studies?

ACuriousMind

no, I didn't really read many textbooks, the lectures were enough

user929304

@ACuriousMind fair enough :) I'll keep grinding at it :/

user929304

7:30 PM

@ACuriousMind I have to go, good chatting with you again, stay healthy, cya!

user 85795

in English Language & Usage: Multi-Layered Discourse Room, 2 mins ago, by Martin Hopf