Conformal Einstein equation and symplectic flux with a positive cosmological constant

2025/04/29 by Sk Jahanur Hoque, Hoque, Sk Jahanur, Pavel Krtouš +3
Physics and Astronomy · #Astrophysical Phenomena and Observations #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th)

paper · pdf · doi:10.48550/arxiv.2504.20845

openalex publication_date 2025/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We analyze the conformal Einstein equation with a positive cosmological constant to extract fall-off conditions of the gravitational fields. The fall-off conditions are consistent with a finite, non-trivial presymplectic current on the future boundary of de Sitter. Hence our result allows a non-zero gravitational flux across the boundary of the de Sitter. We present an explicit gauge-free computation to show that the Gibbons-Hawking boundary term, counterterm in the action, and fall-off condition of gravitational field in conformal Einstein equation are crucial to reproduce the finite symplectic flux.

Citations

• The symplectic potential for leaky boundaries
• Quadrupole formulae with cosmological constant: comparison
• Analysis of gravitational radiation generated by type D black holes with positive cosmological constant
• de Sitter Teukolsky waves
• Finite charges from the bulk action
• Asymptotics with a positive cosmological constant: III. The quadrupole formula
• Asymptotics with a positive cosmological constant: II. Linear fields on de Sitter space-time
• Asymptotics with a positive cosmological constant: I. Basic framework
• A perturbative and gauge invariant treatment of gravitational wave memory
• Asymptotic Symmetries and Charges in De Sitter Space
• The ambient metric
• Comparison between various notions of conserved charges in asymptotically AdS-spacetimes
• Conformal Infinity
• The Asymptotic Structure of Space-Time
• Asymptotic Flatness and Bondi Energy in Higher Dimensional Gravity
• Lecture Notes on Holographic Renormalization
• Mass, Entropy and Holography in Asymptotically de Sitter Spaces
• Asymptotically Anti-de Sitter Space-times: Conserved Quantities
• A General Definition of "Conserved Quantities" in General Relativity and Other Theories of Gravity
• A Stress Tensor for Anti-de Sitter Gravity
• The Cauchy problem for quasi-linear symmetric hyperbolic systems
• Asymptotic Symmetries in Gravitational Theory
• Gravitational waves in general relativity VIII. Waves in asymptotically flat space-time
• Gravitational waves in general relativity, VII. Waves from axi-symmetric isolated system
• An Approach to Gravitational Radiation by a Method of Spin Coefficients

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