A Systematic Construction of Kastor-Traschen Currents and their Extensions to Generic Powers of Curvature

TL;DR

This paper generalizes the construction of conserved currents in spacetimes with Killing-Yano tensors, extending to powers of the curvature tensor and highlighting connections to Lanczos-Lovelock theory.

Contribution

It provides a systematic method to construct divergence-free currents from powers of the curvature tensor, broadening the scope of Kastor-Traschen currents.

Findings

Constructed divergence-free currents from powers of the curvature tensor.

Identified a rank-4 divergence-free tensor from Lanczos-Lovelock theory.

Extended the algebraic framework for conserved currents in curved spacetimes.

Abstract

Kastor and Traschen constructed totally anti-symmetric conserved currents that are linear in the Riemann curvature in spacetimes admitting Killing-Yano tensors. The construction does not refer to any field equations and is built on the algebraic and differential symmetries of the Riemann tensor as well as on the Killing-Yano equation. Here we give a systematic generalization of their work and find divergence-free currents that are built from the powers of the curvature tensor. A rank-4 divergence-free tensor that is constructed from the powers of the curvature tensor plays a major role here and it comes from the Lanczos-Lovelock theory.