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arXiv:gr-qc/0104035v225Jul2001 REVISITING WEYL'S CALCULATION OF THE
 

Summary: arXiv:gr-qc/0104035v225Jul2001
REVISITING WEYL'S CALCULATION OF THE
GRAVITATIONAL PULL IN BACH'S TWO-BODY
SOLUTION
SALVATORE ANTOCI, DIERCK-EKKEHARD 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
two-body solution can be given an invariant formulation in terms of a
force four-vector. The norm of this force is calculated for Bach's two-
body solution, that 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 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 two-surface.
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 four-acceleration

  

Source: Antoci, Salvatore - Dipartimento di Fisica, Universita' di Pavia

 

Collections: Physics