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In the present paper we study the singularity structure of the exterior field of neutron stars with the aid of the four-parameter exact solution of the Einstein-Maxwell equations. The complete analysis of this problem in the generic case becomes possible due to the implementation of the novel analytical approach to the resolution of the singularity condition, and it shows the absence of the ring singularities off the symmetry axis in the positive mass case, as well as the possibility of the removal of the ring singularity by a strong magnetic field in the negative mass case. The solution takes an extraordinarily simple form in the equatorial plane, very similar to that of the Kerr solution, which makes it most suitable for astrophysical applications as the simplest model of a rotating magnetized deformed mass. It also provides a nontrivial example confirming a recent claim that the $\varphi$ component of the electromagnetic four-potential has features inconsistent with the intrinsic properties of the electrovac metric, while the magnetic field is represented correctly by the $t$ component of the dual electromagnetic four-potential., Comment: 21 pages, no figures

The results obtained in our previous paper are now extended to the case of stationary axially symmetric dyonic black boles within the theory of two electromagnetic potentials. We slightly enlarge the classical Ernst formalism by introducing, with the aid of the $t$- and $\varphi$-components of the dual potential $B_\mu$, the magnetic potential $\Phi_m$ which, similar to the known electric potential $\Phi_e$, also takes constant value on the black hole horizon. We analyze in detail the case of the dyonic Kerr-Newman black hole and show how the Komar mass must be evaluated correctly in this stationary dyonic model. In particular, we rigorously prove the validity of the standard Tomimatsu mass formula and point out that attempts to "improve" it made in recent years are explained by misunderstanding of the auxiliary role that singular potentials play in the description of magnetic charges. Our approach is symmetrical with respect to electric and magnetic charges and, like in the static case considered earlier, Dirac strings of all kind are excluded from the physical picture of the stationary black hole dyonic spacetimes., Comment: 14 pages, no figures

In the present paper we argue that the dyonic black hole spacetimes must be studied within the theory of two electromagnetic potentials, and we use the dyonic Reissner-Nordstr\"om solution to demonstrate that the field of the monopole magnetic charge is correctly described by the $t$-component of the dual electromagnetic potential. As a result, the Dirac string associated with the $\varphi$-component of the usual electromagnetic 4-potential becomes just a mathematical object, without any physical content, that arises in some calculations when one employs unsymmetrical representations of the electromagnetic field. We use three different, though equivalent, forms of the electromagnetic energy-momentum tensor to calculate the Komar mass of the Reissner-Nordstr\"om black hole, and in one case the Dirac string is linked to the magnetic charge, in another to the electric charge, while the third, symmetrical case, is string-free., Comment: 11 pages, no figures

In the present paper, we compute the Euclidean action of a generic system consisting of $N$ arbitrary Kerr-Newman black holes located on the symmetry axis and separated from each other by massless struts. This allows us to introduce the {\it Hawking average temperature} (HAT) $\hat T$ of the multi-black hole system via the condition of vanishing the entire set of terms involving the singular horizons due to periodic time, and the resulting formula for this temperature contains solely the surface gravities $\kappa_i$ and horizon areas $A^H_i$ of the black hole constituents. We also show that the corresponding expression for the {\it free energy} of the system defined by $\hat T$ is consistent with the first law of thermodynamics and Smarr mass relations., Comment: 23 pages, 1 figure

In this paper, we employ the general equatorially symmetric two-soliton solution of the Einstein-Maxwell equations for elaborating two physically meaningful configurations describing a pair of equal Kerr-Newman corotating black holes separated by a massless strut. The first configuration is characterized by opposite magnetic charges of its constituents, while in the second configuration the black holes carry equal electric and opposite magnetic charges, thus providing a nontrivial example of a binary dyonic black-hole system. The thermodynamic properties of these binary configurations are studied and the first law of thermodynamics taking correctly into account the magnetic field contribution is formulated for each case., Comment: 20 pages, 2 figures

Using the notion of thermodynamic length, the first law of thermodynamics is consistently derived for two binary configurations of equal Kerr-Newman black holes separated by a massless strut. Like in the electrostatic systems of two Reissner-Nordstr\"om black holes and stationary vacuum systems of two Kerr black holes considered earlier, the thermodynamic length $\ell$ turns out to be defined by the same simple formula $\ell=L\exp(\gamma_0)$, $L$ being the coordinate length of the strut and $\gamma_0$ the value of the metric function $\gamma$ on the strut, which permits the elaboration of $\ell$ in a concise analytic form. The expression of the free energy in the case of two generic Kerr-Newman black holes is also proposed., Comment: 13 pages, 2 figures

We investigate the first law of thermodynamics in the stationary axisymmetric configurations composed of two Kerr black holes separated by a massless strut. Our analysis employs the recent results obtained for the extended double-Kerr solution and for thermodynamics of the static single and binary black holes. We show that, similar to the electrostatic case, in the stationary binary systems the thermodynamic length $\ell$ is defined by the formula $\ell=L\exp(\gamma_0)$, where $L$ is the coordinate length of the strut, and $\gamma_0$ is the value of the metric function $\gamma$ on the strut., Comment: 14 pages, 3 figures; revised version accepted for publication in PRD

We comment on physical inconsistences of the Cl\'ement-Gal'tsov approach to Smarr's mass formula in the presence of magnetic charge. We also point out that the results of Cl\'ement and Gal'tsov involving the NUT parameter are essentially based on the known study (dating back to 2006) of the Demia\'nski-Newman solutions which was not cited by them., Comment: 4 pages, 1 figure

Stationary axisymmetric metric describing the exterior field of a rotating, charged sphere endowed with magnetic dipole moment is presented and discussed. It has a remarkably simple multipole structure defined by only four nonzero Hoenselaers-Perj\'es relativistic moments., Comment: 6 pages, no figures; a minor misprint in formulas (13) rectified

In the present paper we argue that a special case of the Bach-Weyl metric describing a static configuration of two Schwarzschild black holes gives rise, after extending its parameter space to complex values, to a very simple 2-parameter model for the gravitational field of a static deformed mass. We compare this model, which has no restrictions on the quadrupole parameter, with the well-known Zipoy-Voorhees $\delta$-metric and show in particular that the mass quadrupole moment in the latter solution cannot take arbitrary negative values. We subsequently add an arbitrary angular momentum to our static model and study some properties of the resulting 3-parameter stationary solitonic spacetime, which permits us to introduce the notion of the Fodor-Hoenselaers-Perj\'es relativistic multipole moments., Comment: 17 pages, no figures, typos in formulas (24) fixed

In the present paper the repulsion of two extreme Kerr black holes arising from their spin-spin interaction is analyzed within the framework of special subfamilies of the well-known Kinnersley-Chitre solution. The binary configurations of both equal and nonequal extreme repelling black holes are considered., Comment: 12 pages, 7 figures

The full metric describing a stationary axisymmetric system of two arbitrary Kerr sources, black holes or hyperextreme objects, located on the symmetry axis and kept apart in equilibrium by a massless strut is presented in a concise explicit form involving five physical parameters. The binary system composed of a Schwarzschild black hole and a Kerr source is a special case not covered by the general formulas, and we elaborate the metric for this physically interesting configuration too., Comment: 12 pages, 1 figure

We report about the possibility for interacting Kerr sources to exist in two different states - black holes or naked singularities - both states characterized by the same masses and angular momenta. Another surprising discovery reported by us is that in spite of the absence of balance between two Kerr black holes, the latter nevertheless can repel each other, which provides a good opportunity for experimental detection of the spin-spin repulsive force through the observation of astrophysical black-hole binaries., Comment: 5 pages, 2 figures: a misprint in formula (3) rectified; published version

We present and discuss a 4-parameter stationary axisymmetric solution of the Einstein-Maxwell equations able to describe the exterior field of a rotating magnetized deformed mass. The solution arises as a system of two overlapping corotating magnetized non-equal black holes or hyperextreme disks and we write it in a concise explicit form very suitable for concrete astrophysical applications. An interesting peculiar feature of this solution is that its first four electric multipole moments are zeros; it also has a non-trivial extreme limit which we elaborate completely in terms of four polynomial factors. We speculate that the formation of the binary configurations of this type, which is accompanied by a drastic change of the system's total angular momentum due to strong dragging effects, might be one of the mechanisms giving birth to relativistic jets in the galactic nuclei., Comment: 13 pages, 1 figure; minor changes, one reference added

It is argued that the main results of the paper of Gibbons and Volkov (Phys. Rev. D {\bf 96}, 024053 (2017)) come from erroneous interpretations of the surface $r=0$ in the Kerr and Kerr-(anti)de Sitter spacetimes., Comment: 5 pages, 3 figures; a remark on physical nonrealizability of cross-gluing on disks is added; submitted to Physical Review D

We show that the exact solution of Einstein's equations describing a system of two aligned identical Kerr black holes separated by a massless strut follows straightforwardly from the extended 2-soliton solution possessing equatorial symmetry, and we give its concise analytic representation in terms of physical parameters., Comment: 14 pages, 2 figures; new section added

Recent studies of the analytical and numerical models of neutron stars suggest that their exterior field can be described by only four arbitrary parameters of the 2-soliton solution of Einstein's equations. Assuming that this is the case, we show that there exists an infinite hierarchy of the universal relations for neutron stars in terms of multipole moments that arises as a series of the degeneration conditions for generic soliton solutions. Our analysis of the simplest of these relations shows that the no-hair conjecture for neutron stars proposed by Yagi {\it et al.} fails to be verified by the perfect fluid models, but we argue that the conjecture could still be true for the models involving anisotropic fluid., Comment: 5 pages, 2 tables; our earlier critics of the estimation of higher multiples in Ref. [13] is withdrawn

We demonstrate that the total energy of electromagnetic field in the Bardeen and Ay\'on-Beato-Garc\'ia singularity-free models is equal to the mass parameter $M$, being therefore independent of the charge parameter $Q$. Our result is fully congruent with the original idea of Born and Infeld to use nonlinear electrodynamics for proving the electromagnetic nature of mass., Comment: 10 pages, 3 figures

The 4-parameter exact solution presumably describing the exterior gravitational field of a generic neutron star is presented in a concise explicit form defined by only three potentials. In the equatorial plane, the metric functions of the solution are found to be given by particularly simple expressions that make them very suitable for the use in concrete applications. Following Pappas and Apostolatos, we perform a comparison of the multipole structure of the solution with the multipole moments of the known physically realistic Berti-Stergioulas numerical models of neutron stars to argue that the hyperextreme sectors of the solution are not less (but possibly even more) important for the correct description of rapidly rotating neutron stars than the subextreme sector involving exclusively the black-hole constituents. We have also worked out in explicit form an exact analog of the well-known Hartle-Thorne approximate metric., Comment: 14 pages, 1 figure

In this brief note we argue that a dyonic generalization of the Emparan-Teo dihole solution is described by a static diagonal metric and therefore, contrary to the claim made in a recent paper by Cabrera-Munguia et al., does not involve any "non-vanishing global angular momentum" and rotating charges., Comment: 4 pages, 1 figure; typos corrected, matches the published version

The present paper clarifies how to consistently take into account the contribution of magnetic charges in the generalized Smarr mass formula by using properly the Tomimatsu's representation of Komar integrals. It is shown in particular that in all three examples of the dyonic solutions considered by us, the sum of the two electromagnetic terms in Smarr's formula can be cast into the form $\bar{\cal Q}\Phi^H_{ext}$, where ${\cal Q}$ is the complex charge and $\Phi^H_{ext}$ the complex extension of the electric potential., Comment: 11 pages, 3 figures; references added, title changed; published version

We comment on the role of the Cartesian-type Kerr-Schild coordinates in developing a faulty maximal extension of the Kerr-Newman solution in the well-known paper of Carter., Comment: 4 pages, no figures

We show that a recent solution published by Cabrera-Munguia et al. is physically inconsistent since the quantity $\sigma$ it involves does not have a correct limit $R\to\infty$., Comment: 4 pages, 1 figure; last item of initial version removed at referee's request

Gaussian curvature of the two-surface r=0, t=const is calculated for the Kerr-de Sitter and Kerr-Newman-de Sitter solutions, yielding non-zero analytical expressions for both the cases. The results obtained, on the one hand, exclude the possibility for that surface to be a disk and, on the other hand, permit one to establish a correct geometrical interpretation of that surface for each of the two solutions., Comment: 11 pages, 4 figures

In this paper we present and analyze the simplest physically meaningful model for stationary black diholes - a binary configuration of counter-rotating Kerr-Newman black holes endowed with opposite electric charges - elaborated in a physical parametrization on the basis of one of the Ernst-Manko-Ruiz equatorially antisymmetric solutions of the Einstein-Maxwell equations. The model saturates the Gabach-Clement inequality for interacting black holes with struts, and in the absence of rotation it reduces to the Emparan-Teo electric dihole solution. The physical characteristics of each dihole constituent satisfy identically the well-known Smarr's mass formula., Comment: 19 pages, 3 figures; small changes taking into account referee's suggestions

The present paper aims at elaborating a completely physical representation for the general 4-parameter family of the extended double-Kerr spacetimes describing two spinning sources in gravitational equilibrium. This involved problem is solved in a concise analytical form by using the individual Komar masses and angular momenta as arbitrary parameters, and the simplest equatorially symmetric specialization of the general expressions obtained by us yields the physical representation for the well-known Dietz-Hoenselaers superextreme case of two balancing identical Kerr constituents. The existence of the physically meaningful "black hole-superextreme object" equilibrium configurations permitted by the general solution may be considered as a clear indication that the spin-spin repulsion force might actually be by far stronger than expected earlier, when only the balance between two superextreme Kerr sources was thought possible. We also present the explicit analytical formulas relating the equilibrium states in the double-Kerr and double-Reissner-Nordstr\"om configurations., Comment: 10 pages, 2 figures; references added

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 version

The Breton-Manko solution for two identical counter-rotating Kerr-Newman charged masses is rewritten in the physical parametrization involving Komar quantities. The new form of the solution turns out to be very convenient for verifying that the black-hole sector of the Bret\'on-Manko binary configuration saturates a recent geometric inequality for interacting black holes with struts discovered by Gabach Clement., Comment: 6 pages, 1 figure; minor improvement of presentation of functions B and G compared to published version

In this paper we argue that the well-known maximal extensions of the Kerr and Kerr-Newman spacetimes characterized by a specific gluing (on disks) of two asymptotically flat regions with ADM masses of opposite signs are physically inconsistent and actually non-analytic. We also discover a correct geometrical interpretation of the surface $r=0$, $t={\rm const}$ - a dicone in the case of the Kerr solution and a more sophisticated surface of non-zero Gaussian curvature in the case of the Kerr-Newman solution - which suggests that the problem of constructing the maximal analytic extensions for these stationary spacetimes is likely to be performed within the models with only one asymptotically flat region, in which case a smooth crossing of the ring singularity becomes possible, for instance, after carrying out an appropriate transformation of the radial coordinate., Comment: 9 pages, 6 figures; published version

The Kerr-Newman solution with negative mass is shown to develop a massless ring singularity off the symmetry axis. The singularity is located inside the region with closed timelike curves which has topology of a torus and lies outside the ergoregion. These characteristics are also shared by the charged Tomimatsu-Sato delta=2 solution with negative total mass to which in particular a simple form in terms of four polynomials is provided., Comment: 10 pages, 7 figures; hyperextreme case included, one reference added

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. Phys

Stationary axisymmetric systems of two extreme Kerr sources separated by a massless strut, which arise as subfamilies of the well-known Kinnersley-Chitre solution, are studied. We present explicit analytical formulas for the individual masses and angular momenta of the constituents and establish the range of the parameters for which such systems can be regarded as describing black holes. The mass-angular momentum relations and the interaction force in the black-hole configurations are also analyzed. Furthermore, we construct a charging generalization of the Kinnersley-Chitre metric and, as applications of the general formulas obtained, discuss two special cases describing a pair of identical co- and counterrotating extreme Kerr-Newman black holes kept apart by a conical singularity. From our analysis it follows in particular that the equality $m^2-a^2-e^2=0$ relating the mass, angular momentum per unit mass and electric charge of a single Kerr-Newman extreme black hole is no longer verified by the analogous extreme black-hole constituents in binary configurations., Comment: final version revised according to referee's suggestions

A concise form of the Kinnersley-Chitre five-parameter metric for a spinning mass is obtained by exploiting a remarkable similarity between the metric's factor structure and the analogous structure of the Tomimatsu-Sato solutions with even distortion parameter delta. The corresponding general subfamily of asymptotically flat spacetimes containing four arbitrary real parameters is considered, and all configurations describing two extreme Kerr sources separated by a strut are identified and briefly discussed., Comment: 11 pages, 4 figures, extended section 4, reference added, accepted for Prog. Theor. Phys

The general analysis of the relations between masses and angular momenta in the configurations composed of two balancing extremal Kerr particles is made on the basis of two exact solutions arising as extreme limits of the well-known double-Kerr spacetime. We show that the inequality M^2 >= |J| characteristic of an isolated Kerr black hole is verified by all the extremal components of the Tomimatsu and Dietz-Hoenselaers solutions. At the same time, the inequality can be violated by the total masses and total angular momenta of these binary systems, and we identify all the cases when such violation occurs., Comment: 11 pages, 4 figures

The integral equations involved in Alekseev's "monodromy transform" technique are shown to be simple combinations of Sibgatullin's integral equations and normalizing conditions. An additional complex conjugation introduced by Alekseev in the integrands makes his scheme mathematically inconsistent; besides, in the electrovac case all Alekseev's principal value integrals contain an intrinsic error which has never been identified before. We also explain how operates a non-trivial double-step algorithm devised by Alekseev for rewriting, by purely algebraic manipulations and in a different (more complicated) parameter set, any particular specialization of the known analytically extended N-soliton electrovac solution obtained in 1995 with the aid of Sibgatullin's method., Comment: 7 pages, no figures, section II extended

The general extreme limit of the double-Reissner-Nordstrom solution is worked out in explicit analytical form involving prolate spheroidal coordinates. We name it the combined Majumdar-Papapetrou-Bonnor field to underline the fact that it contains as particular cases the two-body specialization of the well-known Majumdar-Papapetrou solution and Bonnor's three-parameter electrostatic field. To the latter we give a precise physical interpretation as describing a pair of non-rotating extremal black holes with unequal masses and unequal opposite charges kept apart by a strut, the absolute values of charges exceeding the respective (positive) values of masses., Comment: 10 pages, 3 figures, title changed, the result extended, matching the published version

It is shown that the equilibrium configurations of two spherical masses carrying charges of opposite sign that are present in Bonnor's approximate model for two charged particles and also in the exact double-Reissner-Nordstrom solution are formed due to the additional electric field of the repulsive character induced in the black-hole constituent by its overcharged partner. A three-parameter family of such configurations is pointed out., Comment: 8 pages, 1 figure; formulas and references added, typos corrected

The equilibrium configurations between a Schwarzschild black hole and a hyperextreme Kerr object are shown to be described by a three-parameter subfamily of the extended double-Kerr solution. For this subfamily, its Ernst potential and corresponding metric functions, we provide a physical representation which employs as arbitrary parameters the individual Komar masses and relative coordinate distance between the sources. The calculation of horizon's local angular velocity induced in the Schwarzschild black hole by the Kerr constituent yields a simple expression inversely proportional to the square of the distance parameter., Comment: 6 pages, 1 figure; improved version

In this paper we show that an isolated Kerr black hole can be interpreted as arising from a pair of identical counter-rotating NUT objects placed on the symmetry axis at an appropriate distance from each other., Comment: 3 pages, no figures; published version

In this paper we consider a magnetic analog of the double-Reissner-Nordstrom solution and construct the corresponding magnetic potential A_\varphi in the explicit form. The behavior of the resulting solution under the Harrison transformation then naturally singles out the asymmetric black diholes - configurations composed of two non-extreme black holes possessing unequal masses, and charges equal in magnitude but opposite in sign - as its most general subclass for which equilibrium of the black-hole constituents can be achieved with the aid of the external magnetic (or electric) field. We also generalize the double-Reissner-Nordstrom solution to the dilaton gravity with arbitrary dilaton coupling, yielding as the result the 4-dimensional double-Gibbons-Maeda spacetime. The study of some physical properties of the solutions obtained leads, in particular, to very simple formulas for the areas of the horizons and surface gravities., Comment: 18 pages, 1 figure; title changed, typos corrected; a considerably extended version which includes the discussion of the magnetostatic case and the explicit formula for the magnetic potential

The full metric describing two counter-rotating identical Kerr black holes separated by a massless strut is derived in the explicit analytical form. It contains three arbitrary parameters which are the Komar mass M, Komar angular momentum per unit mass a of one of the black holes (the other has the same mass and equal but opposite angular momentum) and the coordinate distance R between the centers of the horizons. In the limit of extreme black holes, the metric becomes a special member of the Kinnersly-Chitre five-parameter family of vacuum solutions generalizing the Tomimatsu-Sato delta=2 spacetime, and we present the complete set of metrical fields defining this limit., Comment: 9 pages, 1 figure, typos corrected, a footnote on p.6 extended

We show that any magnetostatic axially symmetric solution of the Einstein-Maxwell equations can be endowed with a specific charged fluid source of the Polanco et al type via a simple procedure requiring the knowledge of exclusively the magnetostatic seed spacetime. Using this procedure we construct yet another exact solution for a massive magnetic dipole surrounded by a static charged fluid which is different from the Polanco et al metric., Comment: 5 pages, no figures, submitted to Physical Review D

The Emparan-Teo non-extremal black dihole solution is reparametrized using Komar quantities and the separation distance as arbitrary parameters. We show how the potential $A_3$ can be calculated for the magnetic analogs of this solution in the Einstein-Maxwell and Einstein-Maxwell-dilaton theories. We also demonstrate that, similar to the extreme case, the external magnetic field can remove the supporting strut in the non-extremal black dihole too., Comment: 9 pages, 1 figure

Two theorems are proved concerning how stationary axisymmetric electrovac spacetimes that are equatorially symmetric or equatorially antisymmetric can be characterized correctly in terms of the Ernst potentials $\E$ and $\Phi$ or in terms of axis-data., Comment: 8 pages

In this second paper devoted to the equatorial symmetry/antisymmetry of stationary axisymmetric electrovac spacetimes we show how two theorems proved in our previous paper (Ernst, Manko and Ruiz 2006 Class. Quantum Grav. 23, 4945) can be utilized to construct exact solutions that are equatorially symmetric or antisymmetric., Comment: 11 pages, minor changes to match the published version

A simple formula, invariant under the duality rotation \Phi -> exp(i\alpha) \Phi, is obtained for the Poynting vector within the framework of the Ernst formalism, and its application to the known exact solutions for a charged massive magnetic dipole is considered., Comment: 9 pages; submitted to Class. Quantum Grav

The analysis of singular regions in the NUT solutions carried out in the recent paper (Manko and Ruiz, 2005 Class. Quantum Grav. 22, p.3555) is now extended to the Demianski-Newman vacuum and electrovacuum spacetimes. We show that the effect which produces the NUT parameter in a more general situation remains essentially the same as in the purely NUT solutions: it introduces the semi-infinite singularities of infinite angular momenta and positive or negative masses depending on the interrelations between the parameters; the presence of the electromagnetic field additionally endows the singularities with electric and magnetic charges. The exact formulae describing the mass, charges and angular momentum distributions in the Demianski-Newman solutions are obtained and concise general expressions P_n=(m+i\nu)(ia)^n, Q_n=(q+ib)(ia)^n for the entire set of the respective Beig-Simon multipole moments are derived. These moments correspond to a unique choice of the integration constant in the expression of the metric function \omega which is different from the original choice made by Demianski and Newman., Comment: 22 pages, 5 figures; submitted to Classical and Quantum Gravity

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 Grav

We show that the well-known NUT solution can be correctly interpreted as describing the exterior field of two counter-rotating semi-infinite sources possessing negative masses and infinite angular momenta which are attached to the poles of a static finite rod of positive mass., Comment: 7 pages, 1 figure, submitted to Classical and Quantum Gravity

Erroneous statements on the mathematical and physical properties of the double-Kerr solution made in a recent paper (Class. Quantum Grav. 21 (2004) 2723) are commented., Comment: 5 pages, 1 figure; submitted to Classical and Quantum Gravity