Conserved Quantities for Polyhomogeneous Space-Times

Abstract

The existence of conserved quantities with a structure similar to the Newman-Penrose quantities in a polyhomogeneous space-time is addressed. The most general form for the initial data formally consistent with the polyhomogeneous setting is found. The subsequent study is done for those polyhomogeneous space-times where the leading term of the shear contains no logarithmic terms. It is found that for these space-times the original NP quantities cease to be constants, but it is still possible to construct a set of other 10 quantities that are constant. From these quantities it is possible to obtain as a particular case a conserved quantity found by Chrusciel et al.

21 pages, LaTex, to be published in CQG

Cited by in corpus (21)

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• General null asymptotics and superrotation-compatible configuration spaces in $d\ge 4$
• Tractor geometry of asymptotically flat spacetimes
• Symmetries of the gravitational scattering in the absence of peeling
• Polyhomogeneous expansions from time symmetric initial data
• Polyhomogeneity and zero-rest-mass fields with applications to Newman-Penrose constants
• Asymptotic properties of the development of conformally flat data near spatial infinity
• Conserved quantities in a black hole collision
• BMS charges in polyhomogeneous spacetimes
• Cosmic branes and asymptotic structure
• "Peeling property" for linearized gravity in null coordinates
• A comment on the Outgoing Radiation Condition and the Peeling Theorem
• Asymptotic behaviour of the Weyl tensor in higher dimensions
• On the existence and convergence of polyhomogeneous expansions of zero-rest-mass fields
• Linear Newman-Penrose charges as subleading BMS and dual BMS charges
• Bondi Mass, Memory Effect and Balance Law of Polyhomogeneous Spacetime
• On Killing vector fields and Newman-Penrose constants