Logarithmic Newman-Penrose constants for arbitrary polyhomogeneous spacetimes

A discussion in how to calculate asymptotic expansions for polyhomogeneous spacetimes using the Newman-Penrose formalism is done. The existence of logarithmic Newman-Penrose constants for a general polyhomogeneous spacetime (i.e. a polyhomogeneous spacetime such that Ψ0 = O(r −3 ln N3)) is addressed. It is found that these constants exist for the generic case. As an application stationary polyhomogneous spacetimes are studied. It is found that for these spacetimes Ψ0 = O(r −5 ln N5 r). The logarithmic NP constants are calculated for these stationary spacetimes. A connection between these logarithmic constants and the Hansen multipole moments is done. 1