Sorry, I'm finding it difficult to grasp some of the basics
From a Schwarzschild metric
You can get the proper and coordinate times, and the time measured by an observer at some distance from the source.
I was wondering if you could similarly get a 'distance' from the metric, measured by a...
HOWEVER, may I ask
I don't see how you could then interpretate distances from this metric? ie from a Schwarzschild metric?
I know that for a stationary observer, the radial and the angular parts would equate to 0. And I know that in general the distance between 2 points separated by dr would...
Hello!
May I ask a few questions, I am trying to understand how the metric tensors work in general relativity. In particular, why you would want to make either the radial or transverse part look Euclidean? In what situations is that useful?
I am happy that in a very general form, the...
Hello!
I'm getting a bit confused with how to deal with sound waves that are within one critical bandwidth of each other.
I do not fully understand how you are meant to combine the intensities of sound waves when they lie within one critical bandwidth?! I would really appreciate some...
Hello! Cheers!
I think I see what you mean.
Do the metrics take into account the shape of the Universe? Or only the curvature of space-time by mass (since the shape "has no measurable effect on things like orbits")? I think I am confused because in the metrics I have seen, there is a term for...
Hello!
I'm trying to get my head around general relativity at the moment...(!), and there's one aspect of it that's really causing me a lot of kerfuffle.
I understand that in an appropriately sized local inertial frame, the laws of special relativity occur. On those scales the curvature...
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I have a few questions about how the Affine connection works.
I know the geodesic equation;
\Gamma^{\lambda}_{\mu \nu} = \frac{\partial x^{\lambda}}{\partial \xi^{\alpha}} \frac{\partial^{2} \xi^{\alpha}}{\partial x^{\nu} \partial x^{\mu}}
So, for example, if I had the...
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I'm getting muddled with the notation in my notes, in which I have
\overline{(E-\overline{E})(P-\overline{P})}
From which you can get
\overline{EP} - \overline{E} \ \overline{P}
I can see where these come from, but not where the
\overline{E \overline{P}} - \overline{\overline{E}...
The "Wave Zone" Definition
Hello!
We are trying to figure out exactly what the "Wave Zone" is when considering potentials.
We know that a moving charge will generate a "disturbance" in the surrounding fields, which propagates outwards at light speed.
This means that for great distances...
*OH* ok I think I get it, so for my term
\frac{\partial}{\partial p_{j}} ln p_{i}
all of the terms would be zero apart from the once instance in which the j = i in the summation? And that justifies getting rid of the summation sign? Is that right?
Thanks!
Hannah
And just to clarify, I might be wrong, but thought that I needed to differentiate wrt
\frac{\partial}{\partial p_{i}}
on
-k \sum_{i} p_{i} ln p_{i}
all with subscript "i" because I hope to differentiate each projection (?) separately? Sorry I'm maybe not making myself clear :-)
Hey, thanks, but
in your example, if I were to multiply that out via the product rule
- k \sum^{r}_{j=1}[\frac{\partial p_{j}}{\partial p_{i}} ln p_{j} + p_{j} \frac{\partial}{\partial p_{i}} ln p_{j}]
Where
\frac{\partial p_{j}}{ \partial p_{i} } = \delta _{ij} and that would sum over...
Hello!
I'm getting confused when differentiating summations.
I understand that if you differentiate an expression and it gives a kroneker delta, that then sums over the appropriate summation and it disappears. But in my notes it has
\frac{\partial}{\partial p_{i}} [-k \sum_{i=1}^{r} p_{i} ln...
Mentz114: Thanks, that pdf is great :-)
WannabeNewton: I've been reading about the covariant derivative, I *think* it's starting to fall into place....So when working with non orthogonal bases, you end up with extra terms when you differentiate the tensor...so in order to account for these...
Hello!
I am very VERY confused!
Would anyone please be kind enough to point me in the right direction.
I read that, in general, the derivative of a tensor is not a tensor.
What do you find when you differentiate a tensor, then?
I thought that you wanted to find the acceleration, to...
Great, thanks! With that further approximation that the sound waves are adiabatic, PV^{\gamma} = constant, does that also then put limitations on the pressures that can be described by the acoustic equation?
So when considering the higher pressure waves, you would derive an acoustics wave equation in which you didn't make small amplitude waves approximations? I get it now! Thank you :-)
Hello!
When considering the acoustics wave equation
\frac{\partial^{2}P}{\partial t^{2}} = c^{2} \nabla^{2} P
I don't really understand why you can say that the applicability of this equation varies for different sound pressure levels. I don't see why this shouldn't hold for all...
IDL and arrays.........help!
Hello!
I have 2 .fits files which I wish to read in to IDL.
Then I want to convert these into arrays with i columns and j rows.
I am going a bit mad trying to 'define' i and j and would really appreciate any help.
Say I had 2 files, A.fits and...
Hey
I'm getting very muddled with my units, and would really appreciate some clarity :-)
I have angular distances between galaxies at some redshift, in arcseconds
I want to calculate the distance in parsecs, taking into account the luminosity distance.
In the equation;
r =...
I've been thinking about blackbodies, and have become confused with regards to their temperature. Is the temperature constant throughout in a blackbody, or is there a temperature gradient dependant on which side is closest to the source of heat? Would it matter?