Degrees of freedom of gravitational radiation with positive cosmological constant
arXiv:2307.02919 · doi:10.1103/PhysRevD.108.064028
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.
26 pages, 2 figures, typos corrected