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I was looking up ways to solve the Einstein field equations when I came across a couple of sources.
http://www.thescienceforum.com/physics/30059-solving-einstein-field-equations.html
https://dl.dropboxusercontent.com/u/14461199/Light%20Deflection%20SM.pdf
If you look at these sources, you will notice that they both say that:
[itex]\Gamma[/itex][itex]\rho[/itex][itex]\mu[/itex][itex]\rho[/itex] = ∂/∂x[itex]\mu[/itex] of ln([itex]\sqrt{g}[/itex])
They call this a contracted Christoffel symbol.
Can anybody explain to me if this is actually an established property of Christoffel symbols or if this derivation of the contracted Christoffel symbol was just specific to the situation that the two sources were deriving?
If it is a property, then what is g? It has no indices, so it doesn't seem like a metric tensor.
Finally, how do you derive this property of Christoffel symbols if this is in fact a property?
http://www.thescienceforum.com/physics/30059-solving-einstein-field-equations.html
https://dl.dropboxusercontent.com/u/14461199/Light%20Deflection%20SM.pdf
If you look at these sources, you will notice that they both say that:
[itex]\Gamma[/itex][itex]\rho[/itex][itex]\mu[/itex][itex]\rho[/itex] = ∂/∂x[itex]\mu[/itex] of ln([itex]\sqrt{g}[/itex])
They call this a contracted Christoffel symbol.
Can anybody explain to me if this is actually an established property of Christoffel symbols or if this derivation of the contracted Christoffel symbol was just specific to the situation that the two sources were deriving?
If it is a property, then what is g? It has no indices, so it doesn't seem like a metric tensor.
Finally, how do you derive this property of Christoffel symbols if this is in fact a property?
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