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In newtonian theory Poisson's equation holds: ## \nabla ^{2} U = 4 \pi G \rho ##. So: given a density ##\rho ##, it is possible to find a potential U. On the other hand, I can choose a random function U and give it a gravitational significance if it gives, by Poisson's eq., a density which is always positive.

In General Relativity I must use Einstein's equation: ## G_{\mu \nu} = 8 \pi G T_{\mu \nu} ##.

Thus, given a certain tensor field ##T_{\mu \nu}## i solve the equations and find the right metric ##g_{\mu \nu}##. But I could choose an arbitrary metric, put it in ## G_{\mu \nu}## and see which stress energy tensor describes the matter that bends the space as the given metric tensor says. The problem is exactly the same as in Newtonian theory. But now how can I tell if this stress energy tensor has a physical significance?