Buchdahl compactness limit for a pure Lovelock static fluid star

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 and N indicate spacetime dimensions and Lovelock order, respectively. 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 criterion that gravitational field energy exterior to the star must be less than half its gravitational mass, having no reference to the interior at all.