 
Summary: arXiv:grqc/0104035v225Jul2001
REVISITING WEYL'S CALCULATION OF THE
GRAVITATIONAL PULL IN BACH'S TWOBODY
SOLUTION
SALVATORE ANTOCI, DIERCKEKKEHARD LIEBSCHER, AND LUIGI MIHICH
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 fourvector. The norm of this force is calculated for Bach's two
body solution, that 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 happen thus to grow without limit
when the test body (respectively the vanishing mass l ) is kept at rest
in a position closer and closer to Schwarzschild's twosurface.
1. Introduction
It is well known since a long time (see e.g. ([1])) that a test body kept
at rest in Schwarzschild's gravitational field undergoes a fouracceleration
