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Buchdahl compactness limit and gravitational field energy
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Buchdahl compactness limit and gravitational field energy
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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, $Q^2/M^2 \leq 9/8 > 1$.
Forward citations
Cited by 2 Pith papers
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Neutron stars in $f(Q) = Q +\xi Q^2$ gravity
In f(Q)=Q+ξQ² gravity with realistic EOSs, negative ξ increases neutron-star maximum masses while positive ξ decreases them, with exterior spacetime remaining Schwarzschild.
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Buchdahl stars and bounds with cosmological constant
Generalized Buchdahl bounds on horizonless object compactness are derived in the presence of a cosmological constant, preserving universality while yielding method-dependent results.
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