Are vacuum solutions to the Einstein field equations always divergence free? How would one test this assumption?
You simply have to check if Einstein's tensor is zero, no?actually, let me rephrase this question (it doesn't make much sense). If I understand correctly, the stress-energy tensor for the vacuum case is always the zero tensor. Since the Einstein equation is also divergence free, how does one verify the validity of vacuum solutions? It seems that for dust solutions, there's the option to test whether the divergence of the stress-energy tensor is zero. I am wondering if there's anything analogous in the vacuum case.