Algebraic classification of the Weyl tensor in higher dimensions based on its "superenergy" tensor

TL;DR

This paper introduces a novel algebraic classification method for the Weyl tensor in higher dimensions using its superenergy tensor, facilitating explicit computation of principal directions and types related to gravitational radiation.

Contribution

It presents a new approach to classify the Weyl tensor in arbitrary dimensions through principal directions of its superenergy tensor, enabling explicit calculations and broader tensor classification.

Findings

Provides a method to compute Weyl aligned null directions explicitly

Allows determination of algebraic type via principal eigenvalues

Enables exploration of gravitational radiation compatibility

Abstract

The algebraic classification of the Weyl tensor in arbitrary dimension n is recovered by means of the principal directions of its "superenergy" tensor. This point of view can be helpful in order to compute the Weyl aligned null directions explicitly, and permits to obtain the algebraic type of the Weyl tensor by computing the principal eigenvalue of rank-2 symmetric future tensors. The algebraic types compatible with states of intrinsic gravitational radiation can then be explored. The underlying ideas are general, so that a classification of arbitrary tensors in general dimension can be achieved.