## Wednesday, November 30, 2016

### gravitational fields for non-conservative systems

Einstein'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?