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arXiv · 2307.02919

Degrees of freedom of gravitational radiation with positive cosmological constant

Francisco Fernández-Álvarez
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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.

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Francisco Fernández-Álvarez. 2023-07-06. Degrees of freedom of gravitational radiation with positive cosmological constant. https://doi.org/10.1103/physrevd.108.064028

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