On the degrees of freedom of gravitational radiation with a positive cosmological constant
Results towards the isolation of the radiative degrees of freedom of the gravitational field with a positive cosmological constant in full General Relativity are put forward. On three-dimensional Riemannian manifolds, a class of differential operators associated with triads of orthonormal forms is proposed. The space of all such operators is shown to have the structure of an affine space where each point is labelled by 2 functions. Based on results by Friedrich and using a recent characterisation of gravitational radiation in the presence of a positive cosmological constant, the 2 coordinates of this space are understood as half of the radiative degrees of freedom at infinity. Remarkably, they determine utterly the presence of gravitational radiation in space-times with algebraically-special rescaled Weyl tensor at the conformal boundary.