We show that the exact solution of Einstein’s equations describing a binary system of aligned identical Kerr black holes separated by a massless strut follows straightforwardly from the extended ...2-soliton solution possessing equatorial symmetry. We give its concise analytic form in terms of physical parameters and then compare with our old solution of that problem obtained in canonical parametrization, demonstrating the equivalence of the two approaches. A surprising physical by-product of our analysis is the discovery that up to three different configurations of two corotating Kerr sources can have equal masses and equal angular momenta. We also introduce physical parametrization to the general six-parameter asymmetric configuration which permits to treat analytically the case of two nonequal corotating black holes.
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We present and discuss a 4-parameter stationary axisymmetric solution of the Einstein-Maxwell equations, which is able to describe the exterior field of a rotating magnetized deformed mass. The ...solution arises as a system of two overlapping corotating magnetized nonequal black holes or hyperextreme disks, and we write it in a concise explicit form that is very suitable for concrete applications. An interesting peculiar feature of this electrovac solution is that it does not develop massless ring singularities outside the stationary limit surface, its first four electric multipole moments being equal to zero; it also has a nontrivial extreme limit, which we elaborate completely in terms of four polynomial factors.
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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 are 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.
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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 two-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 three-parameter stationary solitonic spacetime, which permits us to introduce the notion of the Fodor-Hoenselaers-Perjés relativistic multipole moments.
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A concise form of the asymptotically flat metrics describing the simplest magnetic generalizations of the Kerr and Kerr-Newman spacetimes is presented. The explicit formulae for the corresponding ...electromagnetic potentials are also given, together with simple expressions of all metric functions in the equatorial plane. It is shown that the magnetic field changes the structure of the gravitational multipole moments of the vacuum Kerr solution.
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. As in ...the electrostatic systems of two Reissner-Nordström black holes and stationary vacuum systems of two Kerr black holes considered earlier, the thermodynamic length ℓ turns out to be defined by the same simple formula ℓ = L exp ( γ0), L being the coordinate length of the strut and γ0 the value of the metric function γ on the strut, which permits the elaboration of ℓ in a concise analytic form. The expression of the free energy in the case of two generic Kerr-Newman black holes is also proposed.
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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 ℓ is defined by the formula ℓ = L exp (γ0), where L is the coordinate length of the strut, and γ0 is the value of the metric function γ on the strut.
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Recent studies of the analytical and numerical models of neutron stars suggest that their exterior field can be well approximated by only four arbitrary parameters of the 2-soliton solution of ...Einstein's equations, which gives rise to the so-called no-hair conjecture for neutron stars proposed by Yagi et al. By assuming that the latter conjecture is correct, we show that there exists an infinite hierarchy of universal relations for neutron stars in terms of multipole moments that arises as a series of the degeneration conditions for generic soliton solutions. The analysis of the simplest of these relations involving the hexadecapole mass moment is able to reveal which of the known equations of state for the stellar interior are most consistent with the Yagi et al conjecture.
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