Gravitational currents and charges from conformal Killing-Yano tensors

TL;DR

This work generalizes gravitational charge construction by exploiting conformal Killing-Yano (CKY) tensors to build higher-form conserved currents. It establishes a nested, covariant framework where primary and secondary currents yield charges that can be expressed as boundary integrals, with many charges becoming topological in suitable settings; on Einstein spaces, these currents relate to generalized Komar charges. The authors derive explicit formulas for 2-form and higher-rank currents, discuss integrability conditions, and apply the construction to Kerr-Newman, AdS-Kerr, and D-brane spacetimes to extract physically meaningful quantities such as mass distributions and brane tensions. The results provide covariant, robust tools for measuring energy-momentum and other charges in spacetimes with CKY structure, offering new connections between Penrose-type and Komar-type charges and potential implications for asymptotic symmetries and quasi-local definitions.

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.