Leaky covariant phase spaces: Theory and application to $Λ$-BMS symmetry

TL;DR

This work develops a unified covariant phase-space framework for radiative gravity with any cosmological constant, focusing on leaky boundary conditions that allow energy flux through conformal boundaries. By leveraging holographic renormalization and Starobinsky/Fefferman–Graham (FG) gauges, it constructs finite surface charges and analyzes their algebras under Barnich–Troessaert brackets, revealing a Λ-BMS4 algebroid that reduces to Generalized BMS in the flat limit. The thesis then establishes a consistent flat-limit procedure linking radiative phase spaces across Λ=0, Λ>0, and Λ<0, and derives how memory effects and vacuum transitions emerge under super-Lorentz symmetries. In addition, it extends the formalism to arbitrary dimensions, clarifying how boundary diffeomorphisms and Weyl rescalings behave under holographic renormalization and how central extensions or field-dependent cocycles arise in the charge algebra. Overall, the work provides a robust, renormalized, covariant description of radiative phase spaces for asymptotically (A)dS spacetimes and their flat limits, enabling precise connections to soft theorems and memory effects in gravity.

Abstract

The present thesis aims at providing a unified description of radiative phase spaces in General Relativity for any value of the cosmological constant using covariant phase space methods. We start by considering generic asymptotically locally (A)dS spacetimes with leaky boundary conditions in the Starobinsky/Fefferman-Graham gauge. The boundary structure is allowed to fluctuate and plays the role of source yielding some flux of gravitational radiation at the boundary. The holographic renormalization procedure is employed to obtain finite surface charges for the whole class of boundary diffeomorphisms and Weyl rescalings. We then propose a boundary gauge fixing isolating the radiative boundary degrees of freedom without constraining the Cauchy problem in asymptotically dS spacetimes. The residual gauge transformations form the infinite-dimensional $Λ$-BMS algebroid, which reduces to the Generalized BMS algebra of smooth supertranslations and super-Lorentz transformations in the flat limit. The analysis is repeated in the Bondi gauge in which we identify the analogues of the Bondi news, mass and angular momentum aspects in the presence of a cosmological constant. We give a prescription to perform the flat limit of the phase space and demonstrate how to use this connection to renormalize the corresponding phase space of asymptotically locally flat spacetimes at null infinity including smooth super-Lorentz transformations. In that context, we discuss the memory effects associated with super-Lorentz vacuum transitions and finally provide a new definition of the BMS charges whose fluxes are compatible with soft theorems.

Figures (21)

• Figure 1: Asymptotic flatness at $\mathscr I^+$ in the Bondi gauge.
• Figure 2: BMS supertranslations.
• Figure 3: Structure of the jet bundle.
• Figure 4: Kinematical vs. dynamical boundary degrees of freedom (BDoF).
• Figure 5: Schematic contour for the variational principle.