# gravitational fields for non-conservative systems

30 Nov 2016Einsteinâ€™s field equation links the Einstein-tensor \(G_{\mu\nu}\) to the energy-momentum tensor \(T_{\mu\nu}\), which is divergence-free, \(\nabla_\mu T^{\mu\nu}=0\). Energy-momentum conservation is usually established by considering fields whose Lagrange-density \(\mathcal{L}\) does not have an explicit dependence on time or position, leading to the definition of \(T^{\mu\nu}\) with the corresponding continuity. In what way would fields \(\phi\) with \(\mathcal{L}(\phi,\nabla_\mu\phi,x^\mu)\) source a gravitational field?