Degrees of freedom of gravitational radiation with positive cosmological constant

Abstract

Results on the isolation of the radiative degrees of freedom of the gravitational field with a positive cosmological constant in full General Relativity are put forward. Methods employed in a recent geometric characterisation of gravitational radiation are used and, inspired by Ashtekar's work on asymptotically flat space-times, a space of connections is defined. Ground differences emerge due to the space-like character of the conformal boundary, and one has to put into play a fundamental result by Friedrich concerning the initial value problem for space-times with a positive cosmological constant. Based on this, half of the radiative degrees of freedom are identified; remarkably, they utterly determine the gravitational radiation content for space-times with algebraically special rescaled Weyl tensor at infinity. Directions for defining the phase space in the general case are proposed.

arXiv comment26 pages, 2 figures, typos corrected

References in corpus (17)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• Observation of Gravitational Waves from a Binary Black Hole Merger
• Gravito-electromagnetism
• Super-energy tensors
• The $\Lambda$-BMS${}_4$ group of dS${}_4$ and new boundary conditions for AdS${}_4$
• Asymptotics with a positive cosmological constant: I. Basic framework
• Null infinity, the BMS group and infrared issues
• Uniformly accelerating black holes in a de Sitter universe
• New form of all black holes of type D with a cosmological constant
• Mass-loss of an isolated gravitating system due to energy carried away by gravitational waves with a cosmological constant
• Gravitational radiation condition at infinity with a positive cosmological constant
• Asymptotic Structure with a positive cosmological constant
• Classification of Kerr-de Sitter-like spacetimes with conformally flat Scri
• Characterization of (asymptotically) Kerr-de Sitter-like spacetimes at null infinity
• A review of total energy-momenta in GR with a positive cosmological constant
• A novel characterisation of gravitational radiation in asymptotically flat space-times

Cited by in corpus (3)

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