The Trautman-Bondi mass of hyperboloidal initial data sets

Chrusciel, Piotr T.; Jezierski, Jazek; Leski, Szymon

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The Trautman-Bondi mass of hyperboloidal initial data sets

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Chrusciel, Piotr T.
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Chrusciel, P. T., Jezierski, J., & Leski, S. (2004). The Trautman-Bondi mass of hyperboloidal initial data sets. Advances in Theoretical and Mathematical Physics, 8(1), 83-139. Retrieved from http://projecteuclid.org/euclid.atmp/1091475314.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-5151-1

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.