Determining parameters of the Neugebauer family of vacuum spacetimes in terms of data specified on the symmetry axis

We express the complex potential E and the metrical fields omega and gamma of all stationary axisymmetric vacuum spacetimes that result from the application of two successive quadruple-Neugebauer (or two double-Harrison) transformations to Minkowski space in terms of data specified on the symmetry axis, which are in turn easily expressed in terms of multipole moments. Moreover, we suggest how, in future papers, we shall apply our approach to do the same thing for those vacuum solutions that arise from the application of more than two successive transformations, and for those electrovac solutions that have axis data similar to that of the vacuum solutions of the Neugebauer family. (References revised following response from referee.)Comment: 18 pages (REVTEX

Floquet operator as integral of motion

Nonstationary quantum systems have no energy levels. However, for time-dependent periodical quantum systems, the notion of quasi-energy levels has been introduced. The main point of the quasi-energy concept is to relate quasi-energies to eigenvalues of the Floquet operator or monodromy operators which is equal to the evolution operator of a quantum system taken at the moment coinciding with the period of the system. The purpose of this article is to relate the Floquet operator to integrals of the motion and to introduce a new operator which is the integral of motion and has the same quasi-energy spectrum that the Floquet operator has. We wish to discuss an explicit formula for this new integral of motion

How can exact and approximate solutions of Einstein's field equations be compared?

The problem of comparison of the stationary axisymmetric vacuum solutions obtained within the framework of exact and approximate approaches for the description of the same general relativistic systems is considered. We suggest two ways of carrying out such comparison: (i) through the calculation of the Ernst complex potential associated with the approximate solution whose form on the symmetry axis is subsequently used for the identification of the exact solution possessing the same multipole structure, and (ii) the generation of approximate solutions from exact ones by expanding the latter in series of powers of a small parameter. The central result of our paper is the derivation of the correct approximate analogues of the double-Kerr solution possessing the physically meaningful equilibrium configurations. We also show that the interpretation of an approximate solution originally attributed to it on the basis of some general physical suppositions may not coincide with its true nature established with the aid of a more accurate technique.Comment: 32 pages, 5 figure