Rotating bodies of finite size in the context of general relativity remain very
poorly understood; one of the issues is in establishing the precise nature
of the conditions that must be satisfied in order to match with a suitable
Several well-known fluid solutions exist, but so far only one of them describes
a bounded matter distribution. This is the Wahlquist solution, which happens
to possess an unusual shape to its boundary, and because of this many
consider it not to describe an isolated rotating body. So far, this claim is
yet to be decisively proved.
Recent work has suggested that this may well be the case, but it did not
consider the issue of the exterior appearance of the boundary. An attempt is
made to follow up the investigations regarding the apparent non-asymptotic
flatness of the Wahlquist solution to second order, and to eventually arrive
at a physical interpretation for the shape of the fluid. The slow rotation
matching conditions are developed from first principles, and we demonstrate
that by perturbing the boundary of the Wahlquist solution, it is possible to
generate invariant Cauchy boundary data as viewed in the exterior Weyl
The exterior metric is then obtained to first and second order in the rotation
speed using the Ernst potential method, where we show that it is possible
to perform up to second order Cauchy matching of the interior and exterior
fields. It is shown that while the first order solution is asymptotically flat,
the second order solution is not so, and we show that the non-asymptotic
flatness is due to the interior multipole expansion of a field originating from
two-point masses present outside the fluid.
A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy at Loughborough University.