The Essential General Relativity
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22-01-2014, 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.
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22-01-2014, 03:32 PM
RE: The Essential General Relativity
Sorry, Guv.

Lost me at "Gμν"

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23-01-2014, 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 3-D would have one index, so we write it as V sub i, where i=1,2,3, meaning, it has three components. In 4-D, 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.

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23-01-2014, 10:49 AM
RE: The Essential General Relativity
(23-01-2014 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 3-D would have one index, so we write it as V sub i, where i=1,2,3, meaning, it has three components. In 4-D, 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.

Smile

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.
Tongue

... this is my signature!
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25-01-2014, 09:55 AM
RE: The Essential General Relativity
(23-01-2014 10:49 AM)cjlr Wrote:  
(23-01-2014 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 3-D would have one index, so we write it as V sub i, where i=1,2,3, meaning, it has three components. In 4-D, 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.

Smile

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.
Tongue

Indeed. Einstein was famously invoking certain symmetries to make that happen, a practice that has continued since. Big Grin
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