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- A structure theorem for stationary perfect fluids, Class. Quantum Grav. 22 (2005) 1599-1606. Preprint
The purpose of this paper is to compare and contrast certain aspects of the relativistic theory of stationary perfect fluids and the
non-relativistic theory of Euler flows. Under certain assumptions, we show that the fluid region is divided into a finite number of
cells of two types: if the cell does not intersect the boundary it is fibred by tori invariant under the flow, if the cell intersects
the boundary it is fibred by annuli invariant under the flow. The flow lines on a torus are either all closed or all dense, while the
flow lines on an annulus are all closed.
- Weyl-type fields with geodesic lines of force, J. Math. Phys. 40 (2000) 2032-2045. Preprint
The static electrogravitational equations are studied and it is shown that an aligned type D metric which has a Weyl-type relationship between
the gravitational and electric potential has shearfree geodesic lines of force. All such fields are then found and turn out to be the fields
of a charged sphere, charged infinite rod and charged infinite plate. A further solution is also found with shearing geodesic lines of force.
This new solution can have m>|e| or m<|e|, but cannot be in the Majumdar-Papapetrou class (in which m = |e|). It is algebraically general
and has flat equipotential surfaces.
- Interior Weyl-type solutions to the Einstein-Maxwell field equations, Gen. Rel. and Grav. 31 (1999) 1645-1674. Preprint
Static solutions of the electro-gravitational field equations exhibiting a functional relationship between the electric and gravitational
potentials are studied. General results for these metrics are presented which extend previous work of Majumdar. In particular, it is shown
that for any solution of the field equations exhibiting such a Weyl-type relationship, there exists a relationship between the matter density,
the electric field density and the charge density. It is also found that the Majumdar condition can hold for a bounded perfect fluid only if
the matter pressure vanishes (that is, charged dust). By restricting to spherically symmetric distributions of charged matter, a number of
exact solutions are presented in closed form which generalise the Schwarzschild interior solution. Some of these solutions exhibit functional
relations between the electric and gravitational potentials different to the quadratic one of Weyl. All the non-dust solutions are well-behaved
and, by matching them to the Reissner-Nordstrom solution, all of the constants of integration are identified in terms of the total mass,
total charge and radius of the source. This is done in detail for a number of specific examples. These are also shown to satisfy the weak and
strong energy conditions and many other regularity and energy conditions that may be required of any physically reasonable matter distribution.
- (with B. Nolan) Yang's gravitational theory, Gen. Rel. and Grav. 30 (1998) 473-495. Preprint
Yang's pure space equations (C.N. Yang, Phys. Rev. Lett. v.33, p.445 (1974)) generalize Einstein's gravitational equations, while coming from gauge theory.
We study these equations from a number of vantage points: summarizing the work done previously, comparing them with the Einstein equations and
investigating their properties. In particular, the initial value problem is discussed and a number of results are presented for these equations
with common energy-momentum tensors.
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