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Deriving the Metric from the EnergyMomentum Tensor 
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#19
Dec1612, 11:39 AM

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#20
Dec1612, 05:55 PM

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#21
Dec1612, 07:28 PM

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#22
Dec1612, 07:57 PM

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#23
Dec1612, 10:27 PM

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PF Gold
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As for g within T, the physical parts of it (e.g. pressure and density) do not contain the metric. This is what you might specify; then the EFE contain g on both sides as an undetermined variable to solve for. Alternatively, if you are given the full T as function in some arbitrary coordinates, you have no idea a priori how the the metric figures in T. I guess one special case is you know the form of T in terms of g and physical quantities, you are given the physical quantities and the complete expression of T. Then, you could get g. Of course, if you pick these things arbitrarily, the chance of satisfying the EFE is zero. 


#24
Dec1712, 01:13 AM

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#25
Dec1712, 01:20 AM

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PF Gold
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I assumed you had just T, not T and and density and pressure functions that you knew all constituted a valid solution. With just T, you've got no way to read off the metric. And the only way you have pressure, density, and T that satisfy the EFE is to first solve the EFE with metric undetermined. I believe my interpretation of the question is the most likely  but again, we'll never know without input from OP. 


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