- #1
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?
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?