Asymptotic structure of spacetime and the Newman-Penrose formalism: a brief review

TL;DR

This paper reviews the Newman-Penrose formalism and the asymptotic structure of spacetime, highlighting recent developments, summarizing key historical articles, and computing relevant quantities for stationary axisymmetric spacetimes.

Contribution

It provides a concise overview of recent progress in the Newman-Penrose formalism and asymptotic spacetime structure, including new calculations for specific spacetime classes.

Findings

Summarizes recent advances in Newman-Penrose formalism

Computes spin coefficients and Weyl scalars for stationary axisymmetric spacetimes

Highlights key historical articles and developments

Abstract

A brief review about the Newman-Penrose formalism and the asymptotic structure of the spacetime is given. The goal of this review is to describe the latest developments in these topics and make a summary of the most important articles published by Newman and collaborators. Additionally, we discuss some aspects of this approach, and we compute the spin coefficients and the Weyl scalars for a general stationary axisymmetric spacetimes in a tetrad basis different from that defined by the principal null geodesic directions.