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V. S. Manko

Publications and source records attributed to V. S. Manko.

At least 19 recordsLinked to original sources
arXiv2024

On the simplest static and stationary vacuum quadrupolar metrics

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 $δ$-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-Perjés relativistic multipole moments.

gr-qc↗
arXiv2023

Exterior field of neutron stars: The singularity structure of vacuum and electrovac solutions

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 $φ$ 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.

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arXiv2023

Dyonic black holes: The theory of two electromagnetic potentials

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-Nordström 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 $φ$-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-Nordström 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.

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arXiv2023

Dyonic black holes: The theory of two electromagnetic potentials. II

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 $φ$-components of the dual potential $B_μ$, the magnetic potential $Φ_m$ which, similar to the known electric potential $Φ_e$, 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.

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arXiv2021

The temperature and free energy of multi-black hole systems

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 $κ_i$ 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.

gr-qc↗
arXiv2020

Equatorially symmetric configurations of two Kerr-Newman black holes

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.

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arXiv2020

Thermodynamics of two aligned Kerr-Newman black holes

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-Nordström 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 $\ell=L\exp(γ_0)$, $L$ being the coordinate length of the strut and $γ_0$ the value of the metric function $γ$ 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.

gr-qc↗
arXiv2020

Thermodynamics of two aligned Kerr black holes

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 $\ell=L\exp(γ_0)$, where $L$ is the coordinate length of the strut, and $γ_0$ is the value of the metric function $γ$ on the strut.

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arXiv2020

Comments on two papers of Clément and Gal'tsov

We comment on physical inconsistences of the Clément-Gal'tsov approach to Smarr's mass formula in the presence of magnetic charge. We also point out that the results of Clément and Gal'tsov involving the NUT parameter are essentially based on the known study (dating back to 2006) of the Demiański-Newman solutions which was not cited by them.

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arXiv2019

Metric of a rotating charged magnetized sphere

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-Perjés relativistic moments.

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arXiv2019

Binary systems of recoiling extreme Kerr black holes

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.

gr-qc↗
arXiv2019

Smarr formula for black holes endowed with both electric and magnetic charges

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 $\bar{\cal Q}Φ^H_{ext}$, where ${\cal Q}$ is the complex charge and $Φ^H_{ext}$ the complex extension of the electric potential.

gr-qc↗
arXiv2019

Black hole-naked singularity dualism and the repulsion of two Kerr black holes due to spin-spin interaction

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.

gr-qc↗
arXiv2018

Metric for two arbitrary Kerr sources

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.

gr-qc↗
arXiv2017

Simple metric for a magnetized, spinning, deformed mass

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.

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arXiv2017

Hierarchy of Universal Relations for Neutron Stars in Terms of Multipole Moments

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.

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arXiv2017

Metric for two equal Kerr black holes

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.

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