The cosmological constant and the energy of gravitational radiation
We propose a definition of mass for characteristic hypersurfaces in asymptotically vacuum space-times with non-vanishing cosmological constant $Λ\in {\mathbb R}^*$, generalising the definition of Trautman and Bondi for $Λ=0$. We show that our definition reduces to some standard definitions in several situations. We establish a balance formula linking the characteristic mass and a suitably defined renormalised volume of the null hypersurface, generalising the positivity identity of one of us (PTC) and Paetz proved when $Λ=0$.
gr-qc↗