Diagonal Metric and General Relativity: A Fundamental Question

[isidrago]

I have an apparently simple question, which is foundamental for a new approach to General Relativity.

Is any diagonal metric with constant determinant a solution of Eintein Equations in vacuum?

Does someone have the answer?

 

[Matterwave]

A solution of the EFE's is not a single metric, but a metric field. A constant metric everywhere in space-time is trivially a solution to the vacuum EFE's. Assuming the metric field has the correct signature, then this metric field is isomorphic to the Minkowski metric, and does not represent anything other than flat space-time.

 

[isidrago]

You don't understand. I don't mean a metric entirely constant.
I mean that only the DETERMINANT of the diagonal metric is constant.

Can you say something in this case?

 

[atyy]

I think you may get a cosmological constant in general if you impose the constraint of constant determinant. Something like http://arxiv.org/abs/0809.1371 or http://arxiv.org/abs/0904.4841 (just refer to the parts about classical GR).