Obtaining the multiple Debever null directions

TL;DR

This paper derives explicit formulas for multiple Debever null directions in algebraically special spacetimes using electric and magnetic parts of the Weyl tensor, and implements algorithms in a Mathematica package.

Contribution

It introduces new algorithms and a Mathematica package for determining Petrov-Bel types and multiple Debever null directions from the Weyl tensor.

Findings

Explicit expressions for multiple Debever null directions are obtained.

Algorithms are successfully applied to example spacetimes.

The methods facilitate tensor analysis in general relativity.

Abstract

The explicit expression of the multiple Debever null directions of an algebraically special spacetime are obtained in terms of the electric and magnetic parts of the Weyl tensor. An algorithm for the determination of the Petrov-Bel type and the algorithm to obtain the multiple Debever null directions are implemented as functions of a new package of xAct, a Mathematica suite of packages for tensor manipulations. These functions are applied to two examples.