[Paper Review] Leaky covariant phase spaces: Theory and application to $Λ$-BMS symmetry

Adrien Fiorucci|arXiv (Cornell University)|Dec 14, 2021

Noncommutative and Quantum Gravity Theories4 citations

TL;DR

This thesis develops a unified covariant phase space framework for radiative gravitational degrees of freedom in asymptotically (A)dS spacetimes with leaky boundary conditions, enabling finite surface charges and a consistent flat limit. It introduces the Λ-BMS algebra as the asymptotic symmetry algebra in de Sitter spacetime and establishes its connection to memory effects and infrared structure 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.

Motivation & Objective

• To provide a unified description of radiative phase spaces in General Relativity for arbitrary cosmological constants using covariant phase space methods.
• To handle divergences in the presymplectic structure via holographic renormalization, ensuring finite surface charges for all boundary diffeomorphisms and Weyl rescalings.
• To identify the asymptotic symmetry algebra as the Λ-BMS algebroid in de Sitter spacetime through a boundary gauge fixing that isolates radiative degrees of freedom.
• To construct a flat limit at the level of the phase space, connecting (A)dS and asymptotically flat gravity, and renormalizing the flat phase space when boundary structure fluctuates.
• To analyze the physical implications of super-Lorentz transformations as genuine asymptotic symmetries, including memory effects and infrared structure enhancement.

Proposed method

• Uses covariant phase space methods in the Starobinsky/Fefferman-Graham gauge to describe generic asymptotically locally (A)dS spacetimes with fluctuating boundary structures.
• Applies holographic renormalization to the presymplectic form to remove divergences and obtain finite surface charges for all boundary diffeomorphisms and Weyl rescalings.
• Implements a boundary gauge fixing that isolates radiative components without constraining the Cauchy problem, reducing the symmetry algebra to the Λ-BMS algebroid.
• Translates results from Starobinsky/Fefferman-Graham coordinates to Bondi gauge via a diffeomorphism, identifying analogues of Bondi news, mass, and angular momentum aspects with a cosmological constant.
• Constructs a flat limit at the level of the phase space by matching the solution space structure, enabling renormalization of the asymptotically flat phase space.
• Uses the Barnich-Troessaert bracket to compute the charge algebra, which includes a field-dependent 2-cocycle in odd dimensions.

Experimental results

Research questions

• RQ1 How can a unified description of radiative phase spaces in General Relativity be achieved for all values of the cosmological constant using covariant phase space methods?
• RQ2 What is the structure of the asymptotic symmetry algebra in de Sitter spacetime when boundary fluctuations are allowed and radiative degrees of freedom are isolated?
• RQ3 How can a consistent flat limit be performed at the level of the phase space, and what role does the boundary gauge fixing play in this process?
• RQ4 What are the physical consequences of super-Lorentz transformations as asymptotic symmetries in asymptotically flat gravity, particularly regarding memory effects?
• RQ5 How do the generalized BMS symmetries act on gravitational vacua, and what is the role of finite Hamiltonian generators conjugate to these symmetries?

Key findings

• Finite surface charges are obtained for all boundary diffeomorphisms and Weyl rescalings via holographic renormalization of the presymplectic structure.
• The asymptotic symmetry algebra is identified as the Λ-BMS algebroid in de Sitter spacetime, which reduces to the generalized BMS algebra in the flat limit.
• The charge algebra under the Barnich-Troessaert bracket includes a field-dependent 2-cocycle in odd spacetime dimensions, indicating a non-trivial central extension.
• The flat limit is successfully constructed at the level of the phase space, allowing the renormalization of the asymptotically flat phase space when boundary structure fluctuates under super-Lorentz transformations.
• Transitions among gravitational vacua under generalized BMS symmetries are linked to the displacement memory effect and the refraction/velocity kick memory effect.
• A physical prescription is given for finite Hamiltonian generators canonically conjugate to generalized BMS transformations on solutions that are stationary at early and late times, revealing an enhancement of the infrared structure of gravity.