- #1

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 ds

^{2}=E(du

^{2}+dv

^{2}) with E a harmonic function?

In (1+1)-dimensions is well-know that the Einstein Tensor is null, and the field equation becomes Λg

_{ij}=8π GT

_{ij}where 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 (g

_{ij}) and stress-energy tensor (T

_{ij}).

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?