# dual tensors and the Bianchi-identity

05 Jul 2023Is there a tensor dual to the Riemann-curvature which encodes the vacuum field equation in analogy to \(\tilde{F}_{\mu\nu}\) in electrodynamics with \(\partial^\mu\tilde{F}_{\mu\nu}=0\)?

Is there a tensor dual to the Riemann-curvature which encodes the vacuum field equation in analogy to \(\tilde{F}_{\mu\nu}\) in electrodynamics with \(\partial^\mu\tilde{F}_{\mu\nu}=0\)?