Gravitational currents and charges from conformal Killing-Yano tensors

TL;DR

This paper introduces higher-form conserved currents derived from conformal Killing-Yano tensors in spacetimes, enabling new covariant boundary charge expressions and topological charges independent of field equations, with applications to black holes and supergravity.

Contribution

It constructs novel conserved currents from conformal Killing-Yano tensors, relating them to boundary integrals and topological charges, expanding understanding of gravitational charges.

Findings

Derived covariant boundary charge expressions.

Identified topological charges independent of field equations.

Applied to black hole and supergravity solutions.

Abstract

We construct a set of higher-form conserved currents on spacetimes admitting conformal Killing-Yano tensors. We find relations between these currents that allow the charge given by integrating one of these currents over a region to be re-expressed as an integral of a covariant quantity over the boundary. In many cases, only a non-covariant form of the boundary integral was previously known. For a special class of these currents the conservation does not rely on field equations, so they give conserved topological charges in any gravitational theory. We discuss the relation of our currents to the Komar current and derive several new properties of conformal Killing-Yano tensors. We study a number of applications of our construction to charges of black hole solutions of Einstein-Maxwell theory, and D-brane solutions of type II supergravity.