  We prove that the Bondi mass of an asymptotically flat, vacuum, spacetime
cannot become negative in any even dimension $d \ge 4$. The notion of Bondi
mass is more subtle in $d > 4$ dimensions because radiating metrics have a
slower decay than stationary ones, and those subtleties are reflected by a
considerably more difficult proof of positivity. Our proof holds for the
standard spherical infinities, but also extends to infinities of more general
type which are $(d-2)$-dimensional manifolds admitting a real Killing spinor.
Such manifolds typically have special holonomy and Sasakian structures. The
main technical advance of the paper is an expansion technique based on
"conformal Gaussian null coordinates". This expansion helps us to understand
the consequences imposed by Einstein's equations on the asymptotic tail of the
metric field. As a by-product, we derive a coordinate expression for the
geometrically invariant formula for the Bondi mass originally given by Hollands
and Ishibashi.
