It is shown that the interaction of a class of positive energy tachyons decreases the area of the horizon of theT-S, ∂=3 metric even in the case of a reversible transformation (M_ir=constant). This is a violation of the second law of black hole physics.

Energy bands of dysprosium have been calculated considering the effects of correlation and spin-polarisation. The exchange and correlation contributions to the spherically symmetric crystalline potential have been taken in the forms suggested by (i) Kohn and Sham and (ii) Overhauser. The exchange and correlation potential of von Barth and Hedin has been used to study the effect of spin-polarisation on the band structures. The resulting bandwidth, density of states, magnetic moment and spin-splitting have been computed and compared with experimental results. Some discrepancies remain; theoretical calculations done so far agree reasonably among themselves, so accurate experimental data are probably called for.

The contact conduction electron density in metallic dysprosium has been calculated following the APW formalism and taking into account the effects of correlation and spin-polarization. A comparison of this density with that obtained from the Mössbauer isomer shift measurement has been made. An estimate of Δ〈r²〉, the change in mean square nuclear charge radius between the two levels involved in theγ transition, has been made and compared with those obtained by other workers.

The stationary solutions given by Amenedo and Manko generated from known solutions of Laplace’s equation as seed have been generalised to include the electromagnetic field. Further, the exterior solution of an axially symmetric rotating body with higher multipole moments and a solution corresponding to a Kerr object embedded in a gravitational field are given. We also give a method for constructing stationary vacuum solutions from static magnetovac solutions and vice versa and discuss a specific application of this method.

The structure of the stationary metrics [1], generated from Laplace’s solutions as seed, is investigated. The expressions for the equatorial and polar circumferences, the surface area of the event horizon, location of singular points and the Gaussian curvatures of the metrics [1] are derived and their variations with the field parameter α₀ are studied. The multipole moments are calculated with the help of coordinate invariant Geroch-Hansen technique. These investigations expose some interesting properties of the metrics, some of which are known in the literature and some deserve a new interpretation.

One-soliton solutions of axially symmetric vacuum Einstein field equations are presented in this paper. Two sets of Laplace’s solutions are used as seed and it is shown that the derived solutions reduce to some already known solutions when the constants are properly adjusted. An analysis of the solutions in terms of the Ernst potential is also presented. It is found that the solutions do not reduce to the Euclidean form at spatial infinity. However, in the static limit, Weyl solutions are obtained for half integral ∂-values.