  According to Einstein’s Machian convictions, since inertia is  determined only by matter, there can be no inertial structure or  field in the absence of matter. Consequently, it is impossible,  Einstein conjectured, to find a solution to the field  equations—that is, to determine the metric  \(g_{ij}\)—if the energy-momentum tensor  \(T_{ij}\) representing the mass-energy content of  the universe is zero. The non-existence of ‘vacuum  solutions’ for a static universe demonstrated, Einstein  thought, that Mach’s Principle had been successfully incorporated  into his theory of general relativity. Einstein also believed that  his solution was unique because of the assumptions of isotropy and   homogeneity.[79] 