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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?
ln det g = 1
Does anyone know the derivation of this?
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Where?I read somewhere....
That is not the same as Ricci=0.I read somewhere that the vacuum Einstein equations can be written as
ln det g = 0
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?I read somewhere that the vacuum Einstein equations can be written as
ln det g = 1
Does anyone know the derivation of this?
Thanks, I didn't know this.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.