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arXiv · 1903.03436

Buchdahl compactness limit and gravitational field energy

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

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Naresh Dadhich. 2019-03-04. Buchdahl compactness limit and gravitational field energy. https://doi.org/10.1088/1475-7516/2020/04/035

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