Conserved charges in asymptotically de Sitter spacetimes

Abstract

We present a covariant phase space construction of hamiltonian generators of asymptotic symmetries with "Dirichlet" boundary conditions in de Sitter spacetime, extending a previous study of Jäger. We show that the de Sitter charges so defined are identical to those of Ashtekar, Bonga, and Kesavan (ABK). We then present a comparison of ABK charges with other notions of de Sitter charges. We compare ABK charges with counterterm charges, showing that they differ only by a constant offset, which is determined in terms of the boundary metric alone.We also compare ABK charges with charges defined by Kelly and Marolf at spatial infinity of de sitter spacetime. When the formalisms can be compared, we show that the two definitions agree. Finally, we express Kerr-de Sitter metrics in four and five dimensions in an appropriate Fefferman-Graham form.

Hamiltonian charges in the asymptotically de Sitter spacetimes

“…We have filled this gap in section 4.2. Analogous results were also derived in [20,29] but under much stricter boundary conditions. Namely, it was assumed that g (0)…”

“…However, to our best knowledge, this note contains the first proof that these results are unambiguous. Similar work was also 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 i o and i + along I + [31].…”

Charge algebra in Al(A)dSn spacetimes

“…This Λ-BMS n algebra has the interesting property to reduce to the (generalized) BMS n algebra in the flat limit [25,26,30,[48][49][50][51][52][53][54][55][56][57][58]. Furthermore, the Λ-BMS n algebra may be deeply involved in the investigation of the infrared structure of gravity in presence of non-vanishing cosmological constant [59][60][61][62][63][64] and the possible interplay between symmetries [40,42,43,59,61,65], memory effects [64,[66][67][68][69][70][71][72] and consistency conditions for correlation functions [59,61,[73][74][75][76][77], playing a similar role than the BMS n group in asymptotically flat spacetimes (see e.g. [29,[78][79][80][81] for partial reviews).…”

Gravitational radiation condition at infinity with a positive cosmological constant

“…Observe that there are linear and quadratic terms in Λ in (24). Finally, it is straightforward to verify that ( 25) is lightlike for Λ = 0.…”

“…Signs of attention to this situation date back to [15], and were amplified in [16] where the predicament was clearly presented. Some advances have been made [17][18][19][20][21][22][23][24] (see [25,26] for reviews), usually trying to adapt techniques from the Λ = 0 case to the new scenario. Frustratingly, we still lack a fully satisfactory solution.…”