The cosmological constant and the energy of gravitational radiation

Abstract

We propose a definition of mass for characteristic hypersurfaces in asymptotically vacuum space-times with non-vanishing cosmological constant $\Lambda \in {\mathbb{R}}^{\ast }$, generalising the definition of Trautman and Bondi for $\Lambda =0$. 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 $\Lambda =0$.

66 pages, 1 figure

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