Principal null directions of perturbed black holes

TL;DR

This paper explores how principal null directions serve as observable features of perturbed black holes, proposing a generalized framework for describing space-times beyond traditional metrics and analyzing their equivalences.

Contribution

It introduces a broader definition of perturbed space-times that includes various observable characterizations, extending previous frameworks like Stewart and Walker's.

Findings

Principal null directions are observable quantities of space-time.

A generalized framework for perturbed space-times is proposed.

Conditions for equivalence of different observable descriptions are studied.

Abstract

The properties of principal null directions of a perturbed black hole are investigated. It shown that principal null directions are directly observable quantities characterizing the space-time. A definition of a perturbed space-time, generalizing that given by Stewart and Walker is proposed. This more general framework allows one to include descriptions of a given space-time other than by a pair $(M,g)$ where $M$ is a four-dimensional differential manifold and $g$ a Lorentz metric. Examples of alternative characterizations are the curvature representation of Karlhede and others, the Newman-Penrose representation or observable quantities involving principal null directions. The conditions are studied under which the various alternative choices of observables provide equivalent descriptions of the space-time.