A positive Bondi--type mass in asymptotically de Sitter spacetimes

Abstract

The general structure of the conformal boundary ${\mathcal{I}}^{+}$ of asymptotically de Sitter spacetimes is investigated. First we show that Penrose's quasi-local mass, associated with a cut $\mathcal{S}$ of the conformal boundary, can be zero even in the presence of outgoing gravitational radiation. On the other hand, following a Witten--type spinorial proof, we show that an analogous expression based on the Nester--Witten form is finite only if the Witten spinor field solves the 2-surface twistor equation on $\mathcal{S}$, and it yields a positive functional on the 2-surface twistor space on $\mathcal{S}$, provided the matter fields satisfy the dominant energy condition. Moreover, this functional is vanishing if and only if the domain of dependence of the spacelike hypersurface which intersects ${\mathcal{I}}^{+}$ in the cut $\mathcal{S}$ is locally isometric to the de Sitter spacetime. For non-contorted cuts this functional yields an invariant analogous to the Bondi mass.

51 pages; typos corrected, one reference added; final version, appearing in Class. Quantum Grav

References in corpus (1)

• Positive mass theorems for asymptotically de Sitter spacetimes

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