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, $Q^2/M^2\le 9/8>1$.

arXiv commentAlmost matches with the published version

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Cited by in corpus (15)

• Limits on stellar structures in Lovelock theories of gravity
• A quantum bound on the compactness
• Compact stars in $f(T)=T+\xi T^{\beta }$ gravity
• Maximum Force for Black Holes and Buchdahl Stars
• Extending the weak cosmic censorship conjecture to the charged Buchdahl star by employing the gedanken experiments
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• Horndeski fermion-boson stars
• Classification theorem and properties of singular solutions to the Tolman-Oppenheimer-Volkoff equation
• Universality of the Buchdahl sphere
• Dynamical backreaction of a mass-acquiring scalar field on first-order phase transitions
• Limits on the mass of compact objects in Hořava-Lifshitz gravity
• Hamiltonian surface charges in General Parallel Relativity
• Topological Shell Structures in Neutron Stars: Effects on Equilibrium, Oscillations, and Gravitational-Wave Signatures
• Vanishing Compactness Gap and Fermionic Compact Dark Matter in Hořava-Lifshitz Gravity