8*pi in the Einstein field equations?

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pellman
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A typical formulation of the Einstein equations is

[tex]R_{\mu\nu}-\frac{1}{2}Rg_{\mu\nu}+\Lambda g_{\mu\nu}=\frac{8\pi G}{c^4}T_{\mu\nu}[/tex]

The [itex]\frac{G}{c^4}[/itex] make the units work out. What about the 8*pi? Why is this necessary?
 
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The field equations have to agree with Newtonian gravity in the Newtonian limit.
 
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