# A Metric with Harmonic Coefficient and General Relativity

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1. Jun 17, 2016

### Alexander Pigazzini

Goodmorning everyone,
is there any implies to use in general relativity a metric whose coefficients are harmonic functions?
For example in (1+1)-dimensions, is there any implies for using a metric ds2=E(du2+dv2) with E a harmonic function?
In (1+1)-dimensions is well-know that the Einstein Tensor is null, and the field equation becomes Λgij=8π GTijwhere Λ is the cosmological constant and G is the gravitational constant.
Here there is a direct correspondence (without considering the constants) of the metric tensor (gij) and stress-energy tensor (Tij).
In this case, if the coefficients of metric tensor are harmonic function, then also the coefficients of the stress-energy tensor are harmonic too.
What it means / implies that the metric coefficients and the stress-energy tensor coefficients are harmonic functions?

2. Jun 22, 2016

### Greg Bernhardt

Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?

3. Jun 24, 2016

### Alexander Pigazzini

1. Is there any possible implies or interest to use in general relativity a metric whose coefficients are harmonic functions?
2. What is the meaning (physical) if the stress-energy tensor (Tij ) has the components that are harmonic functions?