Leaky boundary conditions & the Λ-BMS algebroid

In this talk, I will discuss a new type of boundary conditions for Einstein’s gravity in the presence of cosmological constant, coined as “leaky boundary conditions,” that allow for some flux of gravitational radiation at the conformal boundary. The analysis of the solution space with generic asymptotically locally (A)dS boundary conditions is performed in the Starobinsky/Fefferman-Graham gauge without imposing much than the mere requirement of conformal compactification. In this set-up, the boundary structure is allowed to fluctuate and plays the role of source encoding the rate of energy and angular momentum lost by the system in the bulk by emission of gravitational waves. The holographic renormalization procedure is employed to obtain finite surface charges for the whole class of boundary diffeomorphisms and Weyl rescalings. A boundary gauge fixing is then proposed to isolate the radiative boundary degrees of freedom without constraining the Cauchy problem in asymptotically dS spacetimes. The residual gauge transformations form the infinite-dimensional Λ-BMS algebroid, which reduces to the Generalized BMS algebra of smooth supertranslations and super-Lorentz transformations in the flat limit. The analysis can be repeated in the Bondi gauge, in which I will provide a prescription to perform the flat limit of the phase space and demonstrate how to use this connection to renormalize the corresponding phase space of asymptotically locally flat spacetimes at null infinity including smooth super-Lorentz transformations. The concepts that will be introduced are of interest to study the holographic description of gravitational waves in AdS, discuss radiative phenomena at cosmological scales and, importantly, make the link with the recent advances in asymptotically flat holography through some flat limit process.