The Essential General Relativity



22012014, 03:23 PM




The Essential General Relativity
Just published a new blog on The Essential General Relativity. I wanted to condense a 400 page textbook on the subject in a 1 page blog. I know, that is totally crazy, but I think I managed it.
Comments would be greatly appreciated as I can edit it to make it better. 

1 user Likes zaybu's post 
22012014, 03:32 PM




RE: The Essential General Relativity
Sorry, Guv.
Lost me at "Gμν" 

23012014, 09:37 AM




RE: The Essential General Relativity
It's commonly known as the "Einstein tensor". But what's in a name? Anyway, it has two indices, μ and ν, so it's a tensor of second rank. With one index, it would be a vector. No index makes it a scalar. So when you did your high school algebra, your x, y, and z were scalars, even though no one ever told you. A vector in 3D would have one index, so we write it as V sub i, where i=1,2,3, meaning, it has three components. In 4D, i would take on the values 1,2,3,4. And so on. Now, for Gμν, both indices take on the value of 0,1,2,3, IOW, it has 16 components ( the 0 is for time).
Hope that helps. 

1 user Likes zaybu's post 
23012014, 10:49 AM




RE: The Essential General Relativity
(23012014 09:37 AM)zaybu Wrote: It's commonly known as the "Einstein tensor". But what's in a name? Anyway, it has two indices, μ and ν, so it's a tensor of second rank. With one index, it would be a vector. No index makes it a scalar. So when you did your high school algebra, your x, y, and z were scalars, even though no one ever told you. A vector in 3D would have one index, so we write it as V sub i, where i=1,2,3, meaning, it has three components. In 4D, i would take on the values 1,2,3,4. And so on. Now, for Gμν, both indices take on the value of 0,1,2,3, IOW, it has 16 components ( the 0 is for time). Yup. Simply, a tensor is essentially a way of relating vectors  describing how each component of one affects each component of the other (and vice versa) when they interact. The vectors here are four dimensional (t, x, y, z), so we need 4x4=16 components to describe their interaction. A lot of physics consists of finding ways of looking at things in which as many of those terms as possible are zero. ... this is my signature! 

25012014, 09:55 AM




RE: The Essential General Relativity
(23012014 10:49 AM)cjlr Wrote:(23012014 09:37 AM)zaybu Wrote: It's commonly known as the "Einstein tensor". But what's in a name? Anyway, it has two indices, μ and ν, so it's a tensor of second rank. With one index, it would be a vector. No index makes it a scalar. So when you did your high school algebra, your x, y, and z were scalars, even though no one ever told you. A vector in 3D would have one index, so we write it as V sub i, where i=1,2,3, meaning, it has three components. In 4D, i would take on the values 1,2,3,4. And so on. Now, for Gμν, both indices take on the value of 0,1,2,3, IOW, it has 16 components ( the 0 is for time). Indeed. Einstein was famously invoking certain symmetries to make that happen, a practice that has continued since. 



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