Einstein field equations

[PhysicsEnjoyer31415]

TL;DR

I am still in high school but can someone explain these to me in short detail . I know what tensors are and i can solve Basic Inertia tensor matrices to find torque without official education on it . What do i need to do in order to learn these equations and understand them exactly.(Time is not a concern for me right now ) .Any video suggestions or books?or anything will be helpful .Please also explain what the symbols mean .Thanks

 

[Ibix]

Start with special relativity. All treatments of general relativity will assume you understand special relativity. Then make sure you know calculus, including differential equations and partial differentiation. And linear algebra generally.

Taylor and Wheeler's Spacetime Physics is free to download from Taylor's website, and should be in reach for a sufficiently motivated high school student.

A former mentor here, Ben Crowell, wrote a book called Relativity for Poets, which is downloadable via www.lightandmatter.com. It's a non-mathematical treatment, and about as good as you can get without maths.

Regarding the field equations, roughly speaking $G_{ab}$ describes the curvature of spacetime. $\Lambda g_{ab}$ describes the contribution of the cosmological constant, and is sometimes rolled into the term on the right. $T_{ab}$ is the stress-energy tensor, which describes all the energy (including mass) terms that are sources of gravity.

 

[Nugatory]

Any video suggestions or books?or anything will be helpful .Please also explain what the symbols mean

A good start, after you are comfortable with Taylor and Wheeler (recommendation from @Ibix above) would be
https://preposterousuniverse.com/wp-content/uploads/2015/08/grtinypdf.pdf

 

[TSny]

What do i need to do in order to learn these equations and understand them exactly.(Time is not a concern for me right now ) .Any video suggestions or books?or anything will be helpful .Please also explain what the symbols mean .Thanks

View attachment 345799

It's unlikely that a particular video or book suggestion will happen to hit the "sweet spot" for you. This video might be too elementary. It builds up to Einstein's equation with interesting historical commentary. It also discusses the meaning of the symbols in the equation, but not in much depth.

Einstein's equation in the video does not contain the term $\Lambda g_{\mu \nu}$. The $G_{\mu \nu}$ in your equation represents all of the left-hand side of Einstein's equation in the video.

 

[PhysicsEnjoyer31415]

Thank you people

 

[haushofer]

These notes by Baez are also nice:

https://arxiv.org/abs/gr-qc/0103044