Graduate Questions about derivation of GR and applications of it

[trees and plants]

Hello friends. I have this question about how the Einstein field equations were derived, the assumptions behind them and the possible applications of them. What could their solutions be?Also, how are they used in cosmology and in the big bang theory?What about astrophysics? Thank you very much.

 

[weirdoguy]

So basically you're asking us to write a whole textbook here...

 

[Vanadium 50]

You should get something like this https://en.wikipedia.org/wiki/Gravitation_(book)

 

[trees and plants]

I have read some things about the derivation at least.I think Einstein said that he started with R_ij=0 and then proceeded to put to the equations the stress energy momentum tensor and the other tensors.I do not know the steps he did to prove it.I want to know the steps he did,not necessarily to prove it wrong,but to learn from it.As well, what do four dimensions mean about the material world and what do they not mean?It is just that some phenomena are better expressed through four dimensions?Thank you.

 

[Ibix]

I'd suggest Sean Carroll's GR lecture notes - chapter 4 derives the field equations, if memory serves, and they're free to download. Also you don't need to do weight training to lift them like you do with Misner, Thorne and Wheeler.

 

[trees and plants]

So Einstein started from the gravitational law and the gravitational potential expressed in differential form and moved to the steps , I find a little difficulty knowing if the steps are correct in the proof,but ok.About the other question I made concerning the four dimensions?How is it possible and what does it mean about the material world?

 

[Ibix]

So Einstein started from the gravitational law and the gravitational potential expressed in differential form and moved to the steps

There's an informal proof in Carroll based on guessing a tensorial generalisation of Poisson's equation, but the formal proof starts with the Hilbert action.

About the other question I made concerning the four dimensions?How is it possible

How is it possible? Why shouldn't it be?

what does it mean about the material world?

Everything is four dimensional in this model.

 

[trees and plants]

I have also heard about the Hilbert action expressed as an integral.So, it means that for some physical phenomena someone's eyes are flawed to describe them?Is what I am saying correct?

 

[PeterDonis]

I have this question about how the Einstein field equations were derived, the assumptions behind them and the possible applications of them. What could their solutions be?Also, how are they used in cosmology and in the big bang theory?What about astrophysics? Thank you very much.

I want to know the steps he did,not necessarily to prove it wrong,but to learn from it.As well, what do four dimensions mean about the material world and what do they not mean?It is just that some phenomena are better expressed through four dimensions?

All this is way, way too broad for a single PF thread. As others have said, you need to take some time to read a textbook presentation (the references you have been given are good ones). Then you can start a new thread to ask a more focused question about some particular point that you do not understand.

This thread is closed.