The Trautman-Bondi mass of initial data sets

Abstract

We give a definition of mass for conformally compactifiable initial data sets. The asymptotic conditions are compatible with existence of gravitational radiation, and the compactifications are allowed to be polyhomogeneous. We show that the resulting mass is a geometric invariant, and we prove positivity thereof in the case of a spherical conformal infinity. When R(g) - or, equivalently, the trace of the extrinsic curvature tensor - tends to a negative constant to order one at infinity, the definition is expressed purely in terms of three-dimensional or two-dimensional objects.

latex2e, 51 pages in A4, minor typos corrected

References in corpus (4)

• Towards the classification of static vacuum spacetimes with negative cosmological constant
• Energy of Isolated Systems at Retarded Times as the Null Limit of Quasilocal Energy
• Uniqueness of the Trautman--Bondi mass
• The mass of asymptotically anti-de Sitter space-times

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• The cosmological constant and the energy of gravitational radiation
• The hyperbolic positive energy theorem
• Bondi mass cannot become negative in higher dimensions
• Hamiltonian dynamics in the space of asymptotically Kerr-de Sitter spacetimes
• On the canonical energy of weak gravitational fields with a cosmological constant $\Lambda \in \mathbb{R}$
• Reduction Arguments for Geometric Inequalities Associated With Asymptotically Hyperboloidal Slices
• Recent progress on the positive energy theorem
• On Mason's rigidity theorem
• Positivity of the Bondi mass in Bondi's radiating spacetimes
• The Positive Mass Theorem near null infinity
• Hyperbolic positive energy theorems