Logarithmic Newman-Penrose constants for arbitrary polyhomogeneous spacetimes

TL;DR

This paper explores the calculation of asymptotic expansions in polyhomogeneous spacetimes using the Newman-Penrose formalism and establishes the existence of logarithmic Newman-Penrose constants for general cases.

Contribution

It demonstrates the existence of logarithmic Newman-Penrose constants in generic polyhomogeneous spacetimes, extending previous understanding of asymptotic properties.

Findings

Logarithmic Newman-Penrose constants exist for generic polyhomogeneous spacetimes.

A method for calculating asymptotic expansions using Newman-Penrose formalism is discussed.

The study broadens the scope of asymptotic invariants in general relativity.

Abstract

A discussion of how to calculate asymptotic expansions for polyhomogeneous spacetimes using the Newman-Penrose formalism is made. The existence of logarithmic Newman-Penrose constants for a general polyhomogeneous spacetime (i.e. a polyhomogeneous spacetime such that $\Psi_0=\O(r^{-3}\ln ^{N_3})$) is addressed. It is found that these constants exist for the generic case.