I'm not exactly sure as to how i can do that. Do i simply write the energy momentum tenosrs for perfect fluids, and apply it to both? It is doesn't sound too difficult actually. One way to make the problem much simpler is to assume you're in a frame such that yuo can ssume one of the bodies is...
Not sure exactly what it would look like. We'd have to drop the static assumption obviously. Two body motion is planar so we can drop one of the angles obviously. Now last i checked, the potential for two bodies from the perspective of a one of thebodies depnds solely on its distance from their...
How do we solve for it? I still don't know much about non linear equations. Unfortunately, this reduces to R=-4(cosmos constant) which is not a system thus making simplicfication difficult. I'm assuming that we can still use the previous arguments and assume that the metric coompontents Gtt and...
I already do understand this. This is actually the first time I've encountered taylor series(outside of derivation). Its cool. anyway I understand einstein's equation, thus I'm happy it was my original objective. I started studying mathematics last june(conics) and I'm so happy to have finally...
ok the first part makes pefect sense. however i still don't quite understand what you said about the second part.
I:E why does the inverse matrix term equal epsilonN^munu rather tahn n^uv +h^uvepsilon
i think I understand now, but any extra explanation would be better.
so essentially what we're doing i we are guessing that that certain term is the inverse. and since epsilon is small we can ignore the higher order terms in epsilon without making too much of an error.
I still don't think I udnerstand it all that well, but I have a better idea.
Still why...
My question is how to do we taylor series expand it. with respect to what
?
where do we get that c is equal to -1 and what do you mean by first order?
so essentially how do we approximate it?
where do we get the negative sign? and aren't the two matrices multitplied by one another equal to the indeitity map and just that. Where do the higher order terms come from?
my question is how do you derive the inverse from a series expansion(i'm assuming that the term first order means that there is a series expansion).
also:
http://www.mth.uct.ac.za/omei/gr/chap7/node3.html [Broken]
In step 23 they show the formula for the christoffel symbols, but in the...
Wait can you explain how we get the formula for the inverse of the perturbed metric ? I mean derive it via the the expansion(seeing as how you said first order I'm assumign you used one).
Please I'm very close and would appreciate it.
How come in the weak field approximation, where the metric is equal to,
ds^2=-(1+2phi)dt^2 + dr^2(1-2phi). where of course dr is the three distance. why is phi multiplied by 2?
I have two more stupid question regarding a different approach. please just explain it to me as i want to to see...
So essentially it used because its the simplest, most general(encodes curvature) involves the inverse metric, the ricci tensor, etc.. and such. So essentially its simple and encodes all the information that we may want tin the field equations...
This is the first time I've emcountered this...
Can someone explain to me why this is the appropriate action?It makes some sens that that would be used, but I'd like a detailed explanation from someone familiar with the topic.
Why is it the one that yields the proper equations?
Ok well could someone tell me? I'm assuming it has to do with integration. frankly i'd like to leanr about differential forms in such a way that I know how they arise.
Yes but how exactly do we get the general formula (p +q)!/p!q!A_[u,1...u,pB_u,p+1...u,p+q]. for some reason I'm scared to figure this out on my own. I usally do, but I'm too anxious. Please help. I think i understand the P!Q! but I don't quite get the the term (p+q)!. As in i don't know why its...
Could someone explain to me what this is and explain the formula to me? I don't think I understand the formula.
I don't think I quite understand why that's the antisymmetrized tensor product. Maybe its because i don't want o think about it too much.
I'm sorry but his notes don't talk about the geometric intepretation. He just mentions the torsion tensor and says he'll assume the christoffel symbols are symmetric(thus no torsion).
I myself read the first few chapters of a first course on general relatvity. I thought chapters one through four were amazing. The chapters after that were terrible from a mathematical point of view. Is wald's book good?
Well it all makes sense right now. i haven't been sleeping properly for awhile but it has been clarified. I guess it looked weird from a computational standpoint.
I already know how to solve linear equations, multiply matrices, compute inverses and I have some grasp of vector spaces, though I must admit I didn't study them within a formal context, I just pciked some stuff up myself.
what makes you think that anyway? look I'm just having considreable...
I think that after i understand this i'll give up for now. I probably don't have all the prerequisite skills for this kind of thing anyway. I'm only 15 afterall and have run into some annoyances for studying on my own.
wait what does dx^a on it's own mean? That's all i need to know. thanks we're very close. also i thought that the gradient acted on a tanget vector to a curve, how do we know that the partials are the basis in that case? Aren't the partial derivatives just a basis for the directional derivative...
the basis of the gradient how do we derive it from that. and yes I know that the basis has to be independent. How do we derive the baiss by comparing that to 3.12?
Please explain it. I can't wait to continue with this.
so these partial derivatives are the partial derivative of two independent coordinates? Then how do we derive the basis from that?
sorry man. Everything else in the book was fine when i understood the notation and all ,but this seems somehow different.
but why are they equal zero? the kornecker delta gives me no more trouble. why does it equal zero when the indices are different? After all, aren't they related by the equation right before 3.18?
The kornecker delat is very simple now and everything else in the chapter makes perfect sense. I...
Seriosuly though, I must understand this. This is really getting in my way. first off why is the derivative x alpha with respect to x beta equal to the kornecker delta, or why is it defined as such?
also how does he get to the conclusion that dx^aplha is the basis of the gradient one form...
I'm using a first course in general relativity. Unfortunately though my problem with this thing is really hindering my progress through the book. I've flipped through spacetime and geometry. It seemed good. How old are you? I'm 15.
He. funny thing is that I don't even get straight A's. They must be pretty dim. Or maybe i just stick to problems way longer. another possiblity is tha they nevr learned math the right way. They had learned it through memeorization.
Exactly. I don't understand how he gets 3.20 by comparing...
Ok thhe follwoing questio is extremely silly. everything else that I've read in the book makes sense but this part doesn't. i just can't seem to udnerstand it because of a combination of stupidity and notation. Near the end of page 69 an identity is derived to show how the components of the...
There's one more thing I don't quite understand. what is the tensor product? why do we have it? why can EVERY m, l tensor be formed with it? That's what I've been having a real problem with. Everything else is pretty clear.
look I know I'm extremely stupid. no one has to rub it in.
EDIT...
There are three symbols in relativity textbooks that I've never encoutered before and need lots of help with.
1.Einstein summation convetion : Though not really a symbol i still don't quite understand what is meant by it.
2. Upper case lambda with super scripts and subscripts: It seems to...
most of the math I learned was within the context of physics. That's why i expressed concern over mathematical notation. Of course i ten to do math within a slightly more rigorous framework. Actually, I was terrible at math until I began studying mechanics.
EDIT: Define fairly decent.
Firstly are there books that explain all the notation beforehand.
Also what I mean was that I couldn't find the book at any of the Canadian versions of american webistes, like amazon.com. I'm used to rodering things. I guess I'll need to go to the u of t bookstore.
That's in postscript? How can I run postscript? Is it really that good? I heard that his book is based on it.
i'm short on money now, so yes lecture notes should do. For now though, I'm reading explroing black holes til I've mastered all of the prerequisite tensor calculus and diff geom...
Hello I am a high school student who's interested in general relativity and would like to know about some good books. I know vector calculus, a bit of the calculus of variations, a bit about vector spaces and linear algebra, and of course and introductory knowledge of special realtivity. I also...