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 Λ → 0. We also comment on the relation between this approach and the one based on the canonical phase space of initial data at ℐ+.
Highlights
JHEP05(2021)063 a lot of attention in the last few years Since null infinity I is spacelike in asymptotically de Sitter spacetimes, this task is much harder — no natural timelike asymptotic symmetry is available
Similar work was done in [29] but with much more severe boundary conditions, which excluded gravitational waves carrying any de Sitter charges. There is another Hamiltonian approach, based on the initial data at I+, given by Friedrich [30], with a suitable fall-off as one approaches io and i+ along I+ [31]. Thanks to these boundary conditions, it is possible to distinguish between gauge and symmetry vector fields on I+ and associate global fluxes associated with symmetries across all of I+
Since the only universal structure in the problem at hand is that of a smooth manifold I+, asymptotic symmetries are all diffeomorphisms of null infinity
Summary
We will start with a quick review of the asymptotically de Sitter spacetimes. This is going to be rather a practical introduction to the topic, for a more thorough discussion see [20]. Where Cμνσδ is the Weyl tensor of g It follows from the pioneering work of Friedrich [30] that a conformal class [(ga(0b), Tab)] is the full Cauchy data for gμν, at least in the neighborhood of the de Sitter solution. Equations of motion (2.1) follow from the finite action (see [23, 35] for a derivation using holographic renormalization). Presymplectic current is finite on the slices ρ = const. One can show that integral of ω is equal to the presymplectic form on F
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