Salvatore Antoci et al 2001 Class. Quantum Grav. 18 3463 doi:10.1088/0264-9381/18/17/307
Salvatore Antoci1, Dierck-Ekkehard Liebscher2 and Luigi Mihich1
Show affiliationsWhen 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 calculated at the position of the vanishing mass is found to coincide with the norm of the acceleration of a test body kept at rest in Schwarzschild's field. Both norms thus happen to grow without limit when the test body (respectively, the vanishing mass l') is kept at rest in a position that becomes closer and closer to Schwarzschild's 2-surface.
83C05 Einstein's equations (general structure, canonical formalism, Cauchy problems)
Issue 17 (7 September 2001)
Received 25 April 2001
Published 14 August 2001
Salvatore Antoci et al 2001 Class. Quantum Grav. 18 3463
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