The Trautman-Bondi mass of initial data sets

Details The Trautman-Bondi mass of initial data sets The Trautman-Bondi mass of initial data sets

2003-07-25

arxiv.org/abs/gr-qc/0307109v2

Adv.Theor.Math.Phys. 8 (2004) 83-139

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

latex2e, 51 pages in A4, minor typos corrected

Scientific paper

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.

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