Hamiltonian charges in the asymptotically de Sitter spacetimes

We generalize a notion of 'conserved' charges given by Wald and Zoupas to the asymptotically de Sitter spacetimes. Surprisingly, our construction is less ambiguous than the one encountered in the asymptotically flat context. An expansion around exact solutions possessing Killing vectors provides their physical meaning. In particular, we discuss a question of how to define energy and angular momenta of gravitational waves propagating on Kottler and Carter backgrounds. We show that obtained expressions have a correct limit as Lambda -> 0. We also comment on the relation between this approach and the one based on the canonical phase space of initial data at I+.

Automated summary

The paper generalizes the concept of 'conserved' charges given by Wald and Zoupas to asymptotically de Sitter spacetimes, which surprisingly results in a less ambiguous construction compared to asymptotically flat contexts. The physical meaning of these charges can be understood through an expansion around exact solutions with Killing vectors, with a focus on defining energy and angular momenta of gravitational waves on specific backgrounds. The obtained expressions have a correct limit as Lambda -> 0, and the paper also discusses the relationship between this approach and one based on the canonical phase space of initial data at I+.