On the Weyl transverse frames in type I spacetimes

TL;DR

This paper develops a covariant method to explicitly find transverse frames in type I spacetimes and provides an algorithm to compute associated Weyl scalars, simplifying the analysis of spacetime curvature.

Contribution

It introduces a generic, covariant procedure for obtaining explicit transverse frames and Weyl scalars in type I spacetimes, applicable from any initial frame.

Findings

Explicit expressions for transverse frames derived

Algorithm for Weyl scalars $ ext{ extPsi}_2^T$, $ ext{ extPsi}_0^T$, $ ext{ extPsi}_4^T$ provided

Simplifies the process of analyzing Weyl curvature in type I spacetimes

Abstract

We apply a covariant and generic procedure to obtain explicit expressions of the transverse frames that a type I spacetime admits in terms of an arbitrary initial frame. We also present a simple and general algorithm to obtain the Weyl scalars $\Psi_2^T$, $\Psi_0^T$ and $\Psi_4^T$ associated with these transverse frames. In both cases it is only necessary to choose a particular root of a cubic expression.