The h Bar

12:53 AM

Sorry, @ScientistSmithYT I can't talk today.

1:50 AM

Anyone? GR question: It is known that in 2-d, any (regular) metric solves einstein's equations. Is it possible to construct an asymptotically flat metric, that is regular at the origin (take periodic euclidean time) but with the correct discontinuity, if we put a shell with arbitrary stress tensor on it? Would starting with and trying this for a constant stress tensor get somewhere?

Scientist Smith YT

@PM2Ring Ok, I'll be up early tomorrow morning. Maybe I can talk tomorrow. Thanks for letting me know. :)

yuvraj singh

6:22 AM

Hi everyone good morning, I am little bit confuse how to derive this can any body help me, I have a charge particle, let suppose I leave the charge particles, in magnetic field, whose width is d1 how to find time spent by charge in the region if the question already said that region is small such that charge would not able to complete full circle

Slereah

7:27 AM

morgen

yuvraj singh

@Slereah can you help me in that

Secret

9:58 AM

Jake Rose

11:40 AM

Do you guys know of David skinner?

@JohnRennie guess who’s now swapped to astrophysics

I don’t think it was around when you were here though actually

John Rennie

@JakeRose you're doing astrophysics now?

David Skinner at DAMTP?

Jake Rose

@JohnRennie yeah, the cavendish wasn’t for me. Plus we get some lectures but the maths department which is cool

Yep, he’s our quantum lecturer via the part II maths course

Was wondering if he was more widely known

John Rennie

I was at Peterhouse, which is just a few doors along from DAMTP

Jake Rose

Ooooh nice.

Astro is pretty cool though

Nice department

John Rennie

11:56 AM

Not that I ever went there, being a NatSci. Though I attended some guest lectures there.

Jake Rose

We’re not technically based in DAMTP either. We have some lectures within the CMS though

John Rennie

What will you be working on?

Ryan Unger

more cambridge terminology

Slereah

Is it very damp

John Rennie

@RyanUnger :-)

DAMTP = Department of Applied Mathematics and Theoretical Physics

NatSci = Natural Sciences degree

Ryan Unger

11:59 AM

we have three students from Cambridge in the basement offices

I'm exposed to this crap all the time

John Rennie

@RyanUnger I'm sure all universities have their unique jargon. Those poor Brits are probably wondering what all you crazy Yanks are talking about .

Ryan Unger

none of them are brits

two germans and a Portuguese

John Rennie

Those poor ~~Brits~~ Germans and Portugese are probably wondering what all you crazy Yanks are talking about .

Slereah

12:15 PM

The britbongs

PM 2Ring

12:29 PM

@JohnRennie The other Cambridge.

Cambridge, Massachusetts

Cambridge ( KAYM-brij) is a city in Middlesex County, Massachusetts, and part of the Boston metropolitan area. Situated directly north of Boston, across the Charles River, it was named in honor of the University of Cambridge in England, an important center of the Puritan theology embraced by the town's founders.Harvard University, the Massachusetts Institute of Technology (MIT), Lesley University, and Hult Business School are in Cambridge, as was Radcliffe College, a college for women until it merged with Harvard on October 1, 1999. According to the 2010 Census, the city's population was 105,162...

Naveen Balaji

Hey all! Something that I have been wondering for a while now: Can we find a situation where the (2+1)-D situation of Einstein is reproduced in Maxwell's theory, i.e., the EOM on either side of a shell is zero, but it has a discontinuity at the shell?

It is known that in 2-d, any (regular) metric solves Einstein's equations. Is it possible to construct an asymptotically flat metric, that is regular at the origin (take periodic euclidean time) but with the correct discontinuity, if we put a shell with arbitrary stress tensor on it? Would starting with and trying this for a constant stress tensor get somewhere?

Slereah

Well for a start the stress energy tensor isn't arbitrary

You have $T_{\mu\nu} = 0$

Naveen Balaji

For the scalar/Maxwell field, the potential is continuous, its derivative has a step discontinuity, which means that the second derivative has a delta function discontinuity (roughly, the Laplace operator acting on phi in the LHS must lead to a delta function). The structure for Einstein's equations is same.

The Einstein "operator" (which is basically a second derivative) has a delta function discontinuity, but the first and second derivatives of the metric follow the same story as in Maxwell (ie., they are continuous and step discontinuous respectively).

In 1+1 dimensions, however, Einstein has a great simplification. On each side of the shell, Einstein is zero. This means that it is possible to try to fix the metric, by just demanding continuity conditions for the metric, and demanding that the jump in the derivative of the metric is fixed by the source.

Slereah

As far as I know the situation doesn't change if there is a discontinuity?

ie by definition, the Einstein tensor is zero

Naveen Balaji

How can we demand that the metric is regular at the origin as well? (Maybe demanding the absence of a conical deficit?). What could this lead to?

Slereah

12:37 PM

Therefore the stress energy tensor doesn't influence the metric

You can have a metric that is $C^0$ but that won't influence the stress energy tensor

Naveen Balaji

I agree that there is a possibility that this regularity problem cannot have a consistent solution in 1+1 dimensions. So I might have to look at a perturbative problem in 2+1 dimensions?

Slereah

The situation is a bit tricky in 2+1 dimensions, too

Gravity doesn't propagate in 2+1D

So I'm not quite sure what you'll get

Naveen Balaji

Well as for the (1+1) D case, my idea was as follows:

Slereah

But you can try to work out the stress energy tensor of a ring in 2+1D, sure

$T = \delta(r - R)$ or something

Naveen Balaji

Let the form of the metric outside to be such that
gamma_tt(r,t) =1
so that it is asymptoticaly Euclidean (or Minkowski). This will fix the metric right inside the shell to be also the same, but there will be a non-trivial
\partial_r gamma_tt
inside the shell which will be controlled by
S_tt (which is a function of t, and R)
It is easy to calculate gamma_tt, by writing a power series expansion for gamma_tt inside the shell:
1 + \Sigma_{n=1}^{\infty} a_n(t) (r-R)^n
I have set the first coefficient to 1, because at r=R, the metric should match the outside metric. The IRC will fix the a_1(t) i…

Slereah

12:41 PM

IIRC that is the spinning cosmic string metric or something

Which is a weird spacetime

Remember to include mathjax markers

Naveen Balaji

Well, there is this paper: Generalized gravitational Entropy by Juan Maldacena where the set up is that of fixing the metric on a shell/boundary as opposed to putting a source there, but many of the ideas should generalize.

Slereah

Also if you actually do a shell, remember that as 2+1D gravity doesn't propagate, everything is flat outside of the shell

So you baaaaaasically have Minkowski space?

Up to weird topology

Naveen Balaji

Yeah

In that paper, instead of putting a boundary condition at a cut-off surface, it should be possible to put a source and do a calculation similar to what they do in section 2.

Link to paper: arxiv.org/abs/1304.4926

Slereah

Carlip works it out in his book on 2+1D gravity

Naveen Balaji

Could you please send me the name of the book?

Slereah

12:45 PM

amazon.fr/Quantum-Gravity-2-1-Dimensions/dp/0521545889

The second chapter works out the black hole equivalents in 2+1D

Naveen Balaji

Thanks! So he considers a perturbative problem or something else?

Slereah

No, he just works out the spherically symmetric metric in 2+1D

Naveen Balaji

Oh ok.

What is your reflection of the idea to place sources instead of putting a boundary condition at a cut-off surface as sone in Maldacena's paper (section 2 btw)

Slereah

I ain't reading all that

You can use a source, sure

using thin-shell formalism

Naveen Balaji

Could you provide any other references I could follow especially for the 1+1 D case since I ain't completely sure as to how we can demand that the metric is regular at the origin as well in accordance to the setup I've mentioned above?

Slereah

12:52 PM

I'm not 100% sure what you want honestly

Naveen Balaji

frankly, I'm a bit lost too. I'll try my best to articulate it better. Is there any reference where they construct an asymptotically flat metric that is regular at the origin but which possesses the correct discontinuity.

Maxwell's equations with sources on shells lead to junction conditions for electric fields, what leads to junction conditions in GR? Well, the difference between the two is that Einstein's equations don't make sense as an equation on a distributional stress tensor and a distributional metric, while Maxwell's do...

In order for the equations to make sense, we introduce the notion of a regular metric which demands the curvature and stress tensor make sense as distributions. So since we view them to be distributions rather than smooth tensor fields, discontinuities will definitely be present

Slereah

Not sure?

Naveen Balaji

While in Maxwell's case we don't require the regularity condition.

Slereah

You may want to check out Synge

dair.dias.ie/23/1/…

Also Poisson talks about junctions

cambridge.org/core/books/relativists-toolkit/…

Naveen Balaji

Sure will check it out, thanks! Just to add some concluding remarks: Maybe something, as follows, is a possibility- In Maxwell's case we are demanding the field F to make sense as a function even when the source is singular. In Einstein's case, we are only demanding that Einstein tensor make sense as a distribution. Well, the analogy is not entirely perfect since the F derivative is what shows up in Maxwell's equations, but it is G itself that shows up in Einstein's equations

Slereah

1:03 PM

All will be answered if you read on junction conditions

That's the standard treatment of such sources in GR

Naveen Balaji

I have been reading literature on them since the past three months from Poisson and Geroch's paper. But something is not falling into place.

Slereah

5

A: Rigorous procedure of gluing together two spacetimes

Boy oh boy you're in luck because it's one of my favorite topic! You are indeed correct, there isn't a whole lot of literature on the topic of rigorous treatment of spacetime gluing. There's a whole pile of articles and books to peruse to get some unified picture of what this involves. Not parti...

I talk about the issue at length here, if you need additional sources

Naveen Balaji

Yeah, that answer was actually my guiding source in Jn conditions.

Slereah

1:19 PM

I'm not sure if anyone ever did a dumb old thin shell but I'd say probably?

Obviously exterior is Schwarzschild

Interior is more complicated IIRC

Slereah

1:30 PM

Though I think using the shell theorem as a guide you can assume Schwarzschild outside and Minkowski inside

Naveen Balaji

Sure, I will hopefully get somewhere and will update you here. Thank you for the references!

Intellex

1:59 PM

Could anyone please clarify this doubt : How does the air above hot air or land gets heated? Is that by conduction, or radiation? Or both.

Can the small air molecules be susceptible to heat radiation from ground?

Ryan Unger

@Slereah another GR lunch today

gravity.princeton.edu/events/…

Intellex

@RyanUnger, Could you please clarify the above doubt? Sorry for interrupting.

Ryan Unger

I don’t know any physics sorry

Intellex

@RyanUnger No problem. Thanks for your reply.

Slereah

2:21 PM

@RyanUnger neat

John Rennie

3:33 PM

@Intellex the air is heated by contact with the ground. The heated air rises pulling cold air to the ground where it is heated, then that air rises and so on. So the heating of the air by the ground is pretty efficient.

Air does not absorb at the infrared wavelengths given off by the ground so it isn't heated by radiation. Carbon dioxide does, hence the greenhouse effect, but the heating of carbon dioxide by radiation is small compared with the heating by contact with the ground.

Ryan Unger

@Slereah arxiv.org/pdf/1910.03411.pdf

Slereah

3:59 PM

Why do people keep using the Colombeau algebra for GR

And not another algebra of generalized functions

Ryan Unger

@Slereah it's not clear why they need any kind of nonlinear distributions

Slereah

Asymptotic functions seem more pleasant to work with

enumaris

5:28 PM

bowchickawowow

Scientist Smith YT

6:33 PM

I'm working on a project where I have a green 532 nm laser. I want to change the green color into white using some form of medium. How do I do this and what material should I use?

enumaris

White isn't a single wavelength so how do you imagine that would work out?

A laser is really good at outputting one single wavelength of light - it's what it was built for. Why would you want to use it to output white light?

Scientist Smith YT

7:15 PM

@enumaris Well it actually outputs multiple wavelengths. Both visible and infrared light wavelengths are emitted and transferred.

@enumaris I need white light to be able to use its energy at very far distances. The specifics of it are a need to know basis. Sorry, it's a secret thing I'm working on.

@enumaris Using certain doped compounds casted in a crystal or glass cube the infrared can be transformed into 532 nm green laser light. Given it's accurate within a +- 10% degree.

user8718165

7:39 PM

Hello people :-)

Scientist Smith YT

8:30 PM

@user8718165 Hello :)

enumaris

mmmk

Scientist Smith YT

8:59 PM

@enumaris It allows 808 nm in ans concerts just some of it into 532 nm light. It does emit greater than 85% infrared light. The rest has been converted to green light

Scientist Smith YT

9:23 PM

@enumaris Let me correct some of the spelling. andconverts/ not concerts.

DanielSank

9:46 PM

Wat

0

Q: ¿Cómo se puede entender que en el espacio vacío los cuerpos se muevan en distintas direcciones, según la teoría de Einstein?

Para Einstein, el espacio es como una manta que se curva según la masa de los cuerpos, entonces los objetos deberían moverse hacía arriba, hacía los lados, y hacía abajo muy poco, según la masa del cuerpo.

curvature

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