New Bondi-type outgoing boundary condition for the Einstein equations with cosmological constant

In the middle of last century, Bondi and his coworkers proposed an outgoing boundary condition for the Einstein equations. Recently, more and more observations imply that the Einstein equations should include a nonzero cosmological constant. A spacetime with a positive cosmological constant approaches to a de Sitter space asymptotically. Bondi's original boundary condition is not valid for these asymptotically de Sitter spacetimes. But the traditional conformally flat boundary condition excludes the gravitational radiation for the asymptotically de Sitter spacetimes. In this work, a new Bondi-type outgoing boundary condition based on Bondi–Sachs coordinates is considered. With this new boundary condition, the gravitational wave behavior for the asymptotically de Sitter spacetime is similar to the one for the asymptotically Minkowski spacetime. The traditional conformally flat boundary condition falls into a special subclass of the new boundary condition.