  Killing-Yano tensors are natural generalizations of Killing vectors to
arbitrary rank anti-symmetric tensor fields. It was recently shown that
Killing-Yano tensors lead to conserved gravitational charges, called Y-ADM
charges. These new charges are interesting because they measure, for example,
the mass density of a p-brane, rather than the total ADM mass which may be
infinite. In this paper, we show that the spinorial techniques used by Witten,
in his proof of the positive energy theorem, may be straightforwardly extended
to study the positivity properties of the Y-ADM mass density for p-brane
spacetimes. Although the resulting formalism is quite similar to the ADM case,
we show that establishing a positivity bound in the higher rank Y-ADM case
requires imposing a condition on the Weyl tensor in addition to an energy
condition. We find appropriate energy conditions for spacetimes that are
conformally flat or algebraically special, and for spacetimes that have an
exact Killing vector along the brane. Finally we discuss our expression for the
Y-ADM mass density from the Hamiltonian point of view.
