  We give a geometrical definition of the asymptotic flatness at null infinity
in spacetimes of even dimension $d$ greater than 4 within the framework of
conformal infinity. Our definition is shown to be stable against perturbations
to linear order. We also show that our definition is stringent enough to allow
one to define the total energy of the system viewed from null infinity as the
generator conjugate to an asymptotic time translation. We derive an expression
for the generator conjugate within the Hamiltonian framework, and propose to
take this notion of energy as the natural generalisation of the Bondi energy to
higher dimensions. Our definitions of asymptotic flatness and the Bondi energy
formula differ qualitatively from the corresponding definitions in $d=4$;
although the asymptotic structure of null infinity in higher dimensions
parallels that in 4-dimensions in some ways, the latter seems to be a rather
special case on the whole compared to general $d>4$. Our definitions and
constructions do not work in odd spacetime dimensions, essentially because the
unphysical metric seems to have insufficient regularity properties at null
infinity in that case.
