Killing-Yano tensors in spaces admitting a hypersurface orthogonal Killing vector

TL;DR

This paper introduces methods for efficiently finding Killing-Yano, conformal Killing-Yano tensors, and conformal Killing vectors in spacetimes with a hypersurface orthogonal Killing vector, simplifying calculations through decomposition techniques.

Contribution

The authors develop a decomposition-based method for finding these tensors and vectors, reducing computational complexity compared to direct integration.

Findings

Methods successfully applied to example spacetimes

Decomposition simplifies the equations involved

Approach reduces computational effort in finding symmetries

Abstract

Methods are presented for finding Killing-Yano tensors, conformal Killing-Yano tensors, and conformal Killing vectors in spacetimes with a hypersurface orthogonal Killing vector. These methods are similar to a method developed by the authors for finding Killing tensors. In all cases one decomposes both the tensor and the equation it satisfies into pieces along the Killing vector and pieces orthogonal to the Killing vector. Solving the separate equations that result from this decomposition requires less computing than integrating the original equation. In each case, examples are given to illustrate the method.