  We obtain the Buchdahl compactness limit for a pure Lovelock static fluid
star and verify that the limit following from the uniform density
Schwarzschild's interior solution, which is universal irrespective of the
gravitational theory (Einstein or Lovelock), is true in general. In terms of
surface potential $\Phi(r)$, it means at the surface of the star $r=r_{0}$,
$\Phi(r_{0}) < 2N(d-N-1)/(d-1)^2$ where $d$, $N$ respectively indicate
spacetime dimensions and Lovelock order. For a given $N$, $\Phi(r_{0})$ is
maximum for $d=2N+2$ while it is always $4/9$, Buchdahl's limit, for $d=3N+1$.
It is also remarkable that for $N=1$ Einstein gravity, or for pure Lovelock in
$d=3N+1$, Buchdahl's limit is equivalent to the criteria that gravitational
field energy exterior to the star is less than half its gravitational mass,
having no reference to the interior at all.
