Transverse frames for Petrov type I spacetimes: a general algebraic procedure

TL;DR

This paper presents an algebraic method to transform a Newman-Penrose tetrad in Petrov type I spacetimes into a frame where specific Weyl scalars vanish, clarifying the spacetime's physical features.

Contribution

It introduces a general algebraic procedure to rotate tetrads in Petrov type I spacetimes to simplify Weyl scalars, revealing physical properties more clearly.

Findings

The procedure effectively sets  and  to zero in the Weyl scalars.

The new frame highlights the superposition of Coulomb and transverse effects.

The method applies to spacetimes with all Weyl scalars initially non-vanishing.

Abstract

We develop an algebraic procedure to rotate a general Newman-Penrose tetrad in a Petrov type I spacetime into a frame with Weyl scalars $\Psi_{1}$ and $\Psi_{3}$ equal to zero, assuming that initially all the Weyl scalars are non vanishing. The new frame highlights the physical properties of the spacetime. In particular, in a Petrov Type I spacetime, setting $\Psi_{1}$ and $\Psi_{3}$ to zero makes apparent the superposition of a Coulomb-type effect $\Psi_{2}$ with transverse degrees of freedom $\Psi_{0}$ and $\Psi_{4}$.