Revisiting Weyl's calculation of the gravitational pull in Bach's twobody solution
Abstract
When the mass of one of the two bodies tends to zero, Weyl's definition of the gravitational force in an axially symmetric, static twobody solution can be given an invariant formulation in terms of a force 4vector. The norm of this force is calculated for Bach's twobody solution, which is known to be in onetoone 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 2surface.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 September 2001
 DOI:
 10.1088/02649381/18/17/307
 arXiv:
 arXiv:grqc/0104035
 Bibcode:
 2001CQGra..18.3463A
 Keywords:

 General Relativity and Quantum Cosmology
 EPrint:
 11 pages, 2 figures. Text to appear in Classical and Quantum Gravity