A positive Bondi-type mass in asymptotically de Sitter spacetimes

Journal article

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 two-surface twistor equation on ${\mathcal{S}},$ and it yields a positive functional on the two-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.

Authors: Szabados, L; Tod, P

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: IOP Publishing
• Journal: Classical and Quantum Gravity
• Volume: 32
• Issue: 20
• Pages: ARTN 205011
• Publication date: 2015-10-01
• Acceptance date: 2015-08-12
• DOI: 10.1088/0264-9381/32/20/205011
• EISSN: 1361-6382
• ISSN: 0264-9381
• Keywords: two-surface twistors; Bondi mass; de Sitter spacetime; SBTMR