# Revisiting Weyl's calculation of the gravitational pull in Bach's two-body solution

@article{Antoci2001RevisitingWC,
title={Revisiting Weyl's calculation of the gravitational pull in Bach's two-body solution},
author={Salvatore Antoci and D.-e. Liebscher and L. Mihich},
journal={Classical and Quantum Gravity},
year={2001},
volume={18},
pages={3463-3471}
}
• Published 12 April 2001
• Physics
• Classical and Quantum Gravity
When the mass of one of the two bodies tends to zero, Weyl's definition of the gravitational force in an axially symmetric, static two-body solution can be given an invariant formulation in terms of a force 4-vector. The norm of this force is calculated for Bach's two-body solution, which is known to be in one-to-one correspondence with Schwarzschild's original solution when one of the two masses l, l' is made to vanish. In the limit when, say, l'→0, the norm of the force divided by l' and…
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## References

SHOWING 1-10 OF 27 REFERENCES
The Gravitational equations and the problem of motion
• Mathematics
• 1938
Introduction. In this paper we investigate the fundamentally simple question of the extent to which the relativistic equations of gravitation determine the motion of ponderable bodies. Previous
Equations of Motion in General Relativity
This paper contains a new derivation of the equations of motion of bodies moving slowly in their (weak) gravitational field, up to terms of the order (v/c)2. In contrast to the method developed
Alternative space-time for the point mass
Schwarzschild's actual exterior solution (${g}_{\mathrm{S}}$) is resurrected, and together with the manifold ${M}_{0}={R}^{4}\ensuremath{-}{r=0}$ is shown to constitute a space-time possessing all
Black holes: the legacy of Hilbert's error
The historical postulates for the point mass are shown to be satisfied by an infinity of space–times, differing as to the limiting acceleration of a radially approaching test particle. Taking this ...
Phys. Rev. D
• Phys. Rev. D
• 1979
Phys. Rev
• Phys. Rev
• 1960
Publ. Math. Debrecen
• Publ. Math. Debrecen
• 1960