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

TL;DR

This paper explores the structure of the conformal boundary in asymptotically de Sitter spacetimes, showing that a positive Bondi-type mass can be defined and is related to gravitational radiation and energy conditions.

Contribution

It introduces a positive Bondi-type mass in asymptotically de Sitter spacetimes and links it to spinorial methods and the twistor equation, extending mass concepts beyond asymptotically flat cases.

Findings

Penrose's quasi-local mass can be zero despite gravitational radiation.

A Witten--type functional is finite only if the Witten spinor solves the twistor equation.

The functional is positive under the dominant energy condition and vanishes only for de Sitter spacetime.

Abstract

The general structure of the conformal boundary $\mathscr{I}^+$ of asymptotically de Sitter spacetimes is investigated. First we show that Penrose's quasi-local mass, associated with a cut ${\cal S}$ 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 ${\cal S}$, and it yields a positive functional on the 2-surface twistor space on ${\cal S}$, 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 $\mathscr{I}^+$ in the cut ${\cal S}$ is locally isometric to the de Sitter spacetime. For non-contorted cuts this functional yields an invariant analogous to the Bondi mass.