Note on the symplectic structure of asymptotically flat gravity and BMS symmetries

Abstract

The Poisson brackets of the gravitational field at null infinity play a pivotal role in establishing the equivalence between the Ward identities involving Bondi-Metzner-Sachs (BMS) charges and the soft graviton theorem. In recent literature it was noticed that, in order to reproduce the action of BMS transformations via such Poisson brackets, one needs to add ad hoc boundary terms in the symplectic form. In this article we show that, introducing a suitable splitting of the gravitational field in bulk and boundary degrees of freedom and using techniques of covariant phase space formalism, it is possible to obtain the correct Poisson brackets between the boundary fields without any additional assumption. The same Poisson brackets are used to show that BMS charges canonically generate BMS transformations on the gravitational phase space. * Electronic address: falessio@na.infn.it † Electronic address: michele.arzano@na.infn.it

Hamiltonian derivation of dual gravitational charges

“…The recent interest on asymptotic charges, see for example Refs. [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36], is primarily motivated by the discovery of the importance of such charges in studies of gravitational scattering [37][38][39][40] and the application of such ideas to black hole physics [41][42][43]. The potential success of such investigations and applications of asymptotic gravitational charges relies crucially on a good understanding of just how many asymptotic charges there are, and preferably a classification of all such charges, as envisaged in Ref.…”

New dual gravitational charges

“…The recent interest on asymptotic charges, see for example Refs. [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36], is primarily motivated by the discovery of the importance of such charges in studies of gravitational scattering [37][38][39][40] and the application of such ideas to black hole physics [41][42][43]. The potential success of such investigations and applications of asymptotic gravitational charges relies crucially on a good understanding of just how many asymptotic charges there are, and preferably a classification of all such charges, as envisaged in Ref.…”

Weyl Charges in Asymptotically Locally AdS$_3$ Spacetimes

“…Note that we define A(x) to be the integrand coefficient of ω(x) in δ ω S[g] [80,54]. Taking a variation of (75) yields the symplectic structure [106,20,107]…”

“…Let us now discuss the action principle and the variatonal problem associated with (107). We find it convenient to discuss it in terms of coordinates (ρ, t, φ).…”