Conserved gravitational charges from Yano tensors

TL;DR

This paper introduces Y-ADM charges, new conserved gravitational charges derived from Yano tensors in asymptotically flat spacetimes, extending the concept of ADM charges to higher-rank tensor fields.

Contribution

It demonstrates how Yano tensors can be used to construct conserved gravitational charges, generalizing ADM charges to include higher-rank tensor fields in flat and p-brane spacetimes.

Findings

Y-ADM charges are conserved quantities associated with Yano tensors.

These charges are integrals over specific spatial infinity slices or spheres surrounding branes.

Y-ADM charges provide a new way to characterize p-branes in gravitational theories.

Abstract

The defining properties of Yano tensors naturally generalize those of Killing vectors to anti-symmetric tensor fields of arbitrary rank. We show how the Yano tensors of flat spacetime can be used to construct new, conserved gravitational charges for transverse asymptotically flat spacetimes. The relationship of these new charges to Yano tensors parallels that of ordinary ADM conserved charges to Killing vectors. Hence, we call them Y-ADM charges. A rank n Y-ADM charge is given by an integral over a co-dimension $n$ slice of spatial infinity. In particular, a rank (p+1) Y-ADM charge in a p-brane spacetime is given by an integral over only the D-(p+2) dimensional sphere surrounding the brane and may be regarded as an intensive property of the brane.