Symmetries of the asymptotically de Sitter spacetimes

Abstract

We start a systematic investigation of possible isometries of the asymptotically de Sitter solutions to Einstein equations. We reformulate the Killing equation as conformal equations for the initial data at ${\mathcal{I}}^{+}$. This allows for partial classification of possible symmetry algebras. In particular, if they are not maximal, they may be at most $4$-dimensional. We provide several examples. As a simple collorary it is shown that the only spacetime in which the Killing horizon intersects ${\mathcal{I}}^{+}$ (after a conformal completion) is locally the de Sitter universe.

arXiv comment14 pages

References in corpus (22)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• The dS/CFT Correspondence
• The $\Lambda$-BMS${}_4$ group of dS${}_4$ and new boundary conditions for AdS${}_4$
• Asymptotics with a positive cosmological constant: I. Basic framework
• Asymptotics with a positive cosmological constant: II. Linear fields on de Sitter space-time
• Asymptotics with a positive cosmological constant: III. The quadrupole formula
• Killing Initial Data
• (A)dS${}_4$ in Bondi gauge
• A Positive Energy Theorem for Asymptotically deSitter Spacetimes
• Gravitational Waves from Compact Sources in de Sitter Background
• Gravitational waves in a de Sitter universe
• BMS-like symmetries in cosmology
• Charges and Fluxes on (Perturbed) Non-expanding Horizons
• Non-Expanding horizons: Multipoles and the Symmetry Group
• A positive Bondi--type mass in asymptotically de Sitter spacetimes
• Asymptotic Structure with a positive cosmological constant
• Asymptotics with a positive cosmological constant: IV. The `no-incoming radiation' condition
• Classification of Kerr-de Sitter-like spacetimes with conformally flat Scri
• Energy of gravitational radiation in the de Sitter universe at the scri and at a horizon
• Energy of weak gravitational waves in spacetimes with a positive cosmological constant
• Hamiltonian charges in the asymptotically de Sitter spacetimes
• Non-singular extension of the Kerr-NUT-(anti) de Sitter spacetimes

Cited by in corpus (2)

• Quadrupolar radiation in de Sitter: Displacement memory and Bondi metric
• Radiative Asymptotic Symmetries of 3D Einstein-Maxwell Theory