Spatially local energy density of gravitational waves

We propose a new set of BMS charges at null infinity, characterized by a super-translation flux that contains only the `hard’ term. This is achieved with a specific corner improvement of the symplectic 2-form, and we spell the conditions under which it is unique. The charges are associated to a Wald-Zoupas symplectic potential, and satisfy all standard criteria: they are covariant, provide a center-less realization of the symmetry algebra, have vanishing flux in non-radiative spacetimes, and vanish in Minkowski. We use them to define a notion of spatially localized energy density of gravitational waves, and explain how it can be measured doing experiments which are purely local in space and over an extended period of time.