A Ricci = 0

I read somewhere that the vacuum Einstein equations can be written as

ln det g = 1

Does anyone know the derivation of this?
 
Last edited:
Green Schwarz Witten, Volume II. page 440
 

martinbn

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I read somewhere that the vacuum Einstein equations can be written as

ln det g = 0

Does anyone know the derivation of this?
That is not the same as Ricci=0.
 

haushofer

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How can one equation contain all the information of 1/2*D*(D+1) equations?
 
That is what GSW says. Can someone look at it?
 

martinbn

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There is context that you haven't provided. They don't say that this is the vacum Einsein equations. They say that the Ricci = 0 for a Kahler manifold is equivalent to ln(det g) = 1.
 

Martin Scholtz

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I read somewhere that the vacuum Einstein equations can be written as

ln det g = 1

Does anyone know the derivation of this?
This cannot be true since it is not a differential equation for the metric. #Ric=0# are vacuum Einstein's equations and thus 2nd derivatives must appear. I don't have the book you cite, can you give us some context?
 

Martin Scholtz

Gold Member
19
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There is context that you haven't provided. They don't say that this is the vacum Einsein equations. They say that the Ricci = 0 for a Kahler manifold is equivalent to ln(det g) = 1.
Thanks, I didn't know this.
 

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