Errr, the stress-energy tensor T^{\alpha\beta} is the matter tensor. Did you mean the metric tensor g_{\mu\nu} or the Ricci curvature tensor R_{\mu\nu}? "Grav

Errr, the stress-energy tensor T^{\alpha\beta} is the matter tensor. Did you mean the metric tensor g_{\mu\nu} or the Ricci curvature tensor R_{\mu\nu}? "Gravitational field" is one of those shifty things in GR that makes one sympathetic to MTW's refusal to identify the term with any particular mathematical object. You're right though; there are plenty of exact solutions to the Einstein Field Equation which are vacuum solutions -- no matter, just gravity.