On the status of the geodesic law in general relativity.
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Date
1998
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Abstract
The geodesic law for test particles is one of the fundamental principles of general
relativity and is extensively used. It is thought to be a consequence of the field laws
but no rigorous proof exists. This thesis is concerned with a precise formulation of
the geodesic law for test particles and with the extent of its validity. It will be shown
to be true in certain cases but not in others.
A rigorous version of the Infeld/Schild theorem is presented. Several explicit
examples of both geodesic and non-geodesic motion of singularities are given. In the
case of a test particle derived from a test body with a regular internal stress-energy
tensor, a proof of the geodesic law for an ideal fluid test particle under plausible,
explicitly stated conditions is given. It is also shown that the geodesic law is not
generally true, even for weak fields and slow motion, unless the stress-energy tensor
satisfies certain conditions. An explicit example using post-Newtonian theory is given
showing how the geodesic law can be violated if these conditions are not satisfied.
Description
Thesis (Ph.D.)-University of Natal, Durban, 1998.
Keywords
General relativity (Physics), Geodesy--Mathematics., Gravitation., Theses--Mathematics.