The superposition of two Kerr solutions

Krämer, Dietrich; Neugebauer, Gernot

doi:10.1016/0375-9601(80)90556-3

Cited by 199 publications

(188 citation statements)

References 7 publications

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“…The first exact solution for two extreme Kerr particles in equilibrium which we are going to consider is the Tomimatsu solution [7] which arises, within the framework of the double-Kerr solution [5], as a special limiting case of the balance conditions. The form of the Ernst potential defining this spacetime was given by Hoenselaers [3]:…”

Section: The Tomimatsu Solutionmentioning

confidence: 99%

“…Since the axisymmetric model considered in [1] does not permit the balance of its constituents, it looks desirable to supplement Dain and Ortiz's "numerical evidences" of the absence of regular equilibrium solutions for two extreme black holes obtained in the symmetric case, with the general analysis of the mass-angular momentum relations in the exact solutions for two extreme Kerr sources in equilibrium which arise within the framework of the well-known double-Kerr spacetime [5]. By performing such an analysis, one would be able to find out, on the one hand, whether the aforementioned inequality characterizing any single subextreme or extreme Kerr source is also valid for two balancing extreme Kerr sources, and, on the other hand, whether there exist equilibrium configurations with positive Komar masses [6] of both extremal constituents.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Erratum: Remarks on the mass-angular momentum relations for two extreme Kerr sources in equilibrium [Phys. Rev. D82, 124042 (2010)]

Cabrera‐Munguia¹,

Manko²,

Ruiz³

2011

Phys. Rev. D

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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.

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Section: The Tomimatsu Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Erratum: Remarks on the mass-angular momentum relations for two extreme Kerr sources in equilibrium [Phys. Rev. D82, 124042 (2010)]

Cabrera‐Munguia¹,

Manko²,

Ruiz³

2011

Phys. Rev. D

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“…The paradigmatic example is the double-Kerr solution, originally generated in [20] via a Bäcklund transformation. The complexity of this solution has led to different claims concerning the explicit form of these conditions (see, for instance [21,16,22]), although it is a consensual conclusion that the solution for two black holes must have singularities, in agreement with the spinning test particle analysis of [8].…”

Section: Jhep00(2007)000mentioning

confidence: 99%

A double Myers-Perry black hole in five dimensions

Herdeiro¹,

Rebelo²,

Zilhão³

et al. 2008

J. High Energy Phys.

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Using the inverse scattering method we construct a six-parameter family of exact, stationary, asymptotically flat solutions of the 4+1 dimensional vacuum Einstein equations, with U (1) 2 rotational symmetry. It describes the superposition of two MyersPerry black holes, each with a single angular momentum parameter, both in the same plane. The black holes live in a background geometry which is the Euclidean C-metric with an extra flat time direction. This background possesses conical singularities in two adjacent compact regions, each corresponding to a set of fixed points of one of the U (1) actions in the Cartan sub-algebra of SO(4). We discuss several aspects of the black holes geometry, including the conical singularities arising from force imbalance, and the torsion singularity arising from torque imbalance. The double Myers-Perry solution presented herein is considerably simpler than the four dimensional double Kerr solution and might be of interest in studying spin-spin interactions in five dimensional general relativity.

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“…Ernst (1994) showed that this solution could also be obtained from Kramer -Neugebauer's (1980) the Kerr quadrupole moment…”

mentioning

confidence: 90%

“…The solution for the Ernst function symmetric about the equatorial plane and with the specified behavior on the symmetry axis (28) then takes a fairly elegant form: (7) from Kramer and Neugebauer (1980) with "Van der Mond representation" of Ernst function. However, an attempt to directly determine the parameters of this solution from the data on the axis leads to cumbersome calculations even for n = 2.…”

Section: The External Gravitational Fields Of Sources With a Finite Smentioning

confidence: 99%

Energy release during disk accretion onto a rapidly rotating neutron star

2000

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.Abstract The energy release L s on the surface of a neutron star (NS) with a weak magnetic field and the energy release L d in the surrounding accretion disk depend on two independent parameters that determine its state (for example, mass M and cyclic rotation frequency f ) and is proportional to the accretion rate. We derive simple approximation formulas illustrating the dependence of the efficiency of energy release in an extended disk and in a boundary layer near the NS surface on the frequency and sense of rotation for various NS equations of state. Such formulas are obtained for the quadrupole moment of a NS, for a gap between its surface and a marginally stable orbit, for the rotation frequency in an equatorial Keplerian orbit and in the marginally stable circular orbit, and for the rate of NS spinup via disk accretion. In the case of NS and disk counterrotation, the energy release during accretion can reach 0.67Ṁc2 . The sense of NS rotation is a factor that strongly affects the observed ratio of nuclear energy release during bursts to gravitational energy release between bursts in X-ray bursters. The possible existence of binary systems with NS and disk counterrotation in the Galaxy is discussed. Based on the static criterion for stability, we present a method of constructing the dependence of gravitational mass M on Kerr rotation parameter j and on total baryon mass (rest mass) m for a rigidly rotating neutron star. We show that all global NS characteristics can be expressed in terms of the function M(j, m) and its derivatives. We determine parameters of the equatorial circular orbit and the marginally stable orbit by using M(j, m) and an exact solution of the Einstein equations in a vacuum, which includes the following three parameters: gravitational mass M, angular momentum J, and quadrupole moment Φ 2 . Depending on Φ 2 , this solution can also be interpreted as a solution that describes the field of either two Kerr black holes or two Kerr disks.

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The superposition of two Kerr solutions

Cited by 199 publications

References 7 publications

Erratum: Remarks on the mass-angular momentum relations for two extreme Kerr sources in equilibrium [Phys. Rev. D82, 124042 (2010)]

Erratum: Remarks on the mass-angular momentum relations for two extreme Kerr sources in equilibrium [Phys. Rev. D82, 124042 (2010)]

A double Myers-Perry black hole in five dimensions

Energy release during disk accretion onto a rapidly rotating neutron star

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