Einstein equation in full form

debugas
debugas
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Topic 189390

i have come across this page
here

and i want to know how to get to it from the Einstein's short form equation
(as i understand R is a Ricci tensor in those lengthy equations)

Thank you in advance for any explanations/links

ragnar schroder
ragnar schroder
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Einstein equation in full form

Quote:

i have come across this page
here

and i want to know how to get to it from the Einstein's short form equation
(as i understand R is a Ricci tensor in those lengthy equations)

Thank you in advance for any explanations/links

The best way to start is probably http://math.ucr.edu/home/baez/gr/gr.html - if you have not done so already. This will give you a good overview.

Then learn the necessary basic differential geometry from f.i. http://pancake.uchicago.edu/~carroll/notes/ or http://people.hofstra.edu/faculty/Stefan_Waner/diff_geom/tc.html . A google search on "differential geometry tutorial" might be a good idea.

In order to learn the diff geo stuff, you need to have at least two semesters of college level calculus under your belt already.

After all this, the field equation should make a lot of sense to you.

In order to actually "solve" the equations numerically, you also have to go thru a course on differential equations. Then you should be in really good shape. Especially with a few college credits of numerical analysis.

There are some other ways to approach GR beside the std diff geo way, but imho it is the most accessible.

Greetings, Mr. Ragnar Schroder

barkster
barkster
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That's why I'm an engineer

That's why I'm an engineer and not a mathemagician.

Just round up to the nearest significant digit, shave off what you don't need, and call it "Close enough!" :-)

"No, I'm not a scientist... but I did stay at a Holiday Inn Express."

debugas
debugas
Joined: 11 Nov 04
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Thank you, Mr. Ragnar I am

Message 13212 in response to message 13210

Thank you, Mr. Ragnar
I am already familiar with differencial geometry and calculus and also some basics on tensor analysis.
What i was asking for is a good book/link on general relativity that discusses it all in full detail with all the math details

Chipper Q
Chipper Q
Joined: 20 Feb 05
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Credit: 708,571
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RE: I am already familiar

Message 13213 in response to message 13212

Quote:

I am already familiar with differencial geometry and calculus and also some basics on tensor analysis.
What i was asking for is a good book/link on general relativity that discusses it all in full detail with all the math details


This web-based course (Ph 237, from Caltech, on Gravitational Waves) might help you:
http://elmer.tapir.caltech.edu/ph237/

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