Conserved Quantities for Polyhomogeneous Space-Times

TL;DR

This paper investigates conserved quantities in polyhomogeneous space-times, identifying conditions under which certain quantities remain constant and deriving new conserved quantities related to the Newman-Penrose framework.

Contribution

It determines the form of initial data compatible with polyhomogeneous space-times and constructs a new set of conserved quantities when the original NP quantities are not constant.

Findings

Original NP quantities are not conserved in certain polyhomogeneous space-times.

A new set of 10 conserved quantities can be constructed under specific conditions.

Recovered a conserved quantity previously identified by Chrusciel et al.

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.