The double-Kerr equilibrium configurations involving one extreme object

We demonstrate the existence of equilibrium states in the limiting cases of the double-Kerr solution when one of the constituents is an extreme object. In the `extreme-subextreme' case the negative mass of one of the constituents is required for the balance, whereas in the `extreme-superextreme' equilibrium configurations both Kerr particles may have positive masses. We also show that the well-known relation |J|=M^2 between the mass and angular momentum in the extreme single Kerr solution ceases to be a characteristic property of the extreme Kerr particle in a binary system.Comment: 12 pages, 3 figures, submitted to Class. Quantum Gra

On the physical interpretation of the delta=2 Tomimatsu-Sato solution

The physical properties of the Tomimatsu-Sato delta=2 spacetime are analyzed, with emphasis on the issues of the negative mass distribution in this spacetime and the origin of a massless ring singularity which are treated with the aid of an equatorially asymmetric two-body configuration arising within the framework of the analytically extended double-Kerr solution. As a by-product of this analysis it is proved analytically that the Kerr spacetime with negative mass always has a massless naked ring singularity off the symmetry axis accompanied by a region with closed timelike curves, and it is also pointed out that the Boyer-Lindquist coordinates in that case should be introduced in a different manner than in the case of the Kerr solution with positive mass.Comment: 13 pages, 6 figures, submitted to Prog. Theor. Phy

On the Properties of Exact Solutions Endowed with Negative Mass

It is shown that various pathological properties of spacetimes can be explained by the presence of negative mass, including the cases when the total mass of the solution is a positive quantity. As an illustration, we consider several well-known stationary axisymmetric vacuum and electrovac solutions of the Einstein-Maxwell equations. Our investigation naturally leads to a critique of the known maximal extensions of the Kerr and Kerr-Newman spacetimes which turn out to be neither analytic nor physically meaningful.Comment: 4 pages, no figures; published versio

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

Squeezed states of damped oscillator chain

The Caldirola-Kanai model of one-dimensional damped oscillator is extended to the chain of coupled parametric oscillators with damping. The correlated and squeezed states for the chain of coupled parametric oscillators with damping are constructed. Based on the concept of the integrals of motion, it is demonstrated how squeezing phenomenon arises due to parametric excitation