Hamiltonian charges in the asymptotically de Sitter spacetimes

TL;DR

This paper extends the concept of conserved charges to asymptotically de Sitter spacetimes, providing clearer definitions of energy and angular momentum for gravitational waves, with results consistent in the limit of zero cosmological constant.

Contribution

It introduces a less ambiguous method for defining conserved charges in asymptotically de Sitter spacetimes, expanding on Wald and Zoupas' approach and analyzing physical interpretations.

Findings

Derived expressions for energy and angular momentum of gravitational waves.

Ensured the correct limit as the cosmological constant approaches zero.

Compared the new approach with the canonical phase space method.

Abstract

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 $\Lambda \to 0$. We also comment on the relation between this approach and the one based on the canonical phase space of initial data at $\mathcal{I}^+$.