# weak field Lorentz-covariant gravity

08 Nov 2023The weak field metric \(h_{\mu\nu}\) obeys a covariant Poisson equation, \(\Box h_{\mu\nu} = 8\pi G T_{\mu\nu}.\) What is the general expression for gauging \(h_{\mu\nu}\) and which gauge condition is assumed to yield the above equation? Could you formulate a Lagrange density for the field \(h_{\mu\nu}\) and would this be gauge invariant?