Buchdahl compactness limit and gravitational field energy

Understand

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 $\Phi(R) = (M-Q^2/2R)/R \leq 4/9$ 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, $Q^2/M^2 \leq 9/8 > 1$.