Stationary Axially Symmetric Exterior Solutions in the Five Dimensional Representation of the Brans-Dicke-Jordan Theory of Gravitation

摘要

The Inverse Scattering Method of Belinsky and Zakharov is used to investigate axially symmetric stationary vacuum soliton solutions in the five-dimensional representation of the Brans-Dicke-Jordan theory of gravitation, where the scalar field of the theory is an element of a five-dimensional metric. The resulting equations for the space-time metric are similar to those of solitons in general relativity, while the scalar field generated is the product of a simple function of the co-ordinates and an already known scalar field solution. Kerr-like solutions are considered that reduce, in the absence of rotation, to the five-dimensional form of the well-known Weyl-Levi Civita axially symmetric static vacuum solution. Hence these metrics can be interpreted as the exterior gravitational fields of rotating non-spherical configurations in the Brans-Dicke-Jordan theory. With a proper choice of the parameters in the solutions, the deviation from spherical symmetry will be due only to the angular momentum of the system, as it is with the Kerr metric in general relativity. An explicit exact/solution is given. 19 refs. (Atomindex citation 17:063285)