Buchdahl compactness limit and gravitational field energy

Abstract

The main aim of this paper is essentially to point out that the Buchdahl compactness limit of a static object is given by \it{gravitational field energy being less than or equal to half of its non-gravitational matter energy}. It is thus entirely determined without any reference to interior distribution by the exterior unique solutions, the Schwarzschild for neutral and the Reissner-Nordstr{$\ddot{o}$}m for charged object. In terms of surface potential, it reads as $\Phi (R)=(M-Q^2/2R)/R\le 4/9$ which translates to surface red-shift being less than or equal to $3$. It also prescribes an upper bound on charge an object could have, $Q^2/M^2\le 9/8>1$.

Almost matches with the published version