 
Summary: arXiv:grqc/0107007v331Jan2003
GRAVITATIONAL SINGULARITIES VIA ACCELERATION:
THE CASE OF THE SCHWARZSCHILD SOLUTION AND
BACH'S GAMMA METRIC
SALVATORE ANTOCI, DIERCKEKKEHARD LIEBSCHER, AND LUIGI MIHICH
Abstract. The so called gamma metric corresponds to a twoparameter
family of axially symmetric, static solutions of Einstein's equations found
by Bach. It contains the Schwarzschild solution for a particular value of
one of the parameters, that rules a deviation from spherical symmetry.
It is shown that there is invariantly definable singular behaviour beyond
the one displayed by the Kretschmann scalar when a unique, hypersur
face orthogonal, timelike Killing vector exists. In this case, a particle can
be defined to be at rest when its worldline is a corresponding Killing or
bit. The norm of the acceleration on such an orbit proves to be singular
not only for metrics that deviate from Schwarzschild's metric, but also
on approaching the horizon of Schwarzschild metric itself, in contrast to
the discontinuous behaviour of the curvature scalar.
1. Introduction
In the early days of general relativity there was little doubt that in the
new theory the Christoffel symbols had the role of "components" of the
