The interaction force between rotating black holes at equilibrium

Varzugin, G. G.

doi:10.1007/bf02557144

Cited by 24 publications

(55 citation statements)

References 6 publications

(8 reference statements)

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“…1) and a single Schwarzschild black hole (at ¼ 2M). Indeed, in the latter limit, the temperature (14) yields that of a single Schwarzschild black hole with mass 2M, and the total area of the two black holes A 1 þ A 2 (13) yields that of a single black hole with mass 2M. However, in general, this is not the case, because the BZ vectors of the solitons at z ¼ a 2 ¼ a 3 do not become trivial, cf.…”

Section: A Counterrotating Double Kerrmentioning

confidence: 96%

“…This case was first considered in [14] and studied in detail in [5]. The solution is obtained by a four-soliton transformation, at z ¼ a 1 (antisoliton), z ¼ a 2 (soliton), z ¼ a 3 (antisoliton), and z ¼ a 4 (soliton), respectively, with BZ vectors ð1; 2a 1 bÞ; ð1; 2a 2 cÞ; ð1; 2a 3 cÞ; and ð1; 2a 4 bÞ;…”

Section: A Counterrotating Double Kerrmentioning

confidence: 99%

“…Note that it has the same asymptotic behavior, at infinity and in the merging limit, as the corresponding function in the counterrotating case, cf. (13) and (14). The force between the two black holes, for fixed mass and physical distance, is displayed in Fig.…”

Section: B Corotating Double Kerrmentioning

confidence: 99%

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Dynamical and thermodynamical aspects of interacting Kerr black holes

2009

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We consider the asymptotically flat double-Kerr solution for two equal mass black holes with either the same or opposite angular momentum and with a massless strut between them. For fixed angular momentum and mass, the angular velocity of two corotating Kerr black holes decreases as they approach one another, from the Kerr value at infinite separation to the value of a single Kerr black hole with twice the mass and the angular momentum at the horizons merging limit. We show that the ratio J=M 2 for extremal corotating Kerr black holes varies from unity at infinite separation to two at the merging limit. These results are interpreted in terms of rotational dragging and compared with the case of counterrotating Kerr black holes. We then analyze the merging of ergoregions. In the corotating case the merger point occurs at an angle of =2, in agreement with recent general arguments. In the counterrotating case the ergoregions never merge. We study the horizon geometry for both cases as a function of the distance and provide embedding diagrams. Finally, we study the thermodynamical evolution of the corotating doubleKerr system, showing that, in the canonical ensemble, it is thermodynamically stable for fast spinning black holes. As for single Kerr black holes the stable and unstable phases are separated by a second order phase transition. We show that for large fixed angular momentum two Kerr black holes reach a minimum distance, before horizon merging has occurred, where the thermodynamical approximation breaks down. We also consider the microcanonical ensemble to study the maximal energy that can be extracted from the double-Kerr system as a function of the separation between the black holes.

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Section: A Counterrotating Double Kerrmentioning

confidence: 96%

Section: A Counterrotating Double Kerrmentioning

confidence: 99%

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Dynamical and thermodynamical aspects of interacting Kerr black holes

2009

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“…(31), is a generalization of the one for the vacuum case [12]. Furthermore, in the vacuum solution, the interaction force related with the strut in-between does not provide any information on the spin-spin interaction, as it happens in the identical case [22].…”

Section: Derivation Of the Black Hole Horizonsmentioning

confidence: 94%

Asymmetric black dyonic holes

2015

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A 6-parametric asymptotically flat exact solution, describing a two-body system of asymmetric black dyons, is studied. The system consists of two unequal counterrotating Kerr-Newman black holes, endowed with electric and magnetic charges which are equal but opposite in sign, separated by a massless strut. The Smarr formula is generalized in order to take into account their contribution to the mass. The expressions for the horizon half-length parameters σ 1 and σ 2 , as functions of the Komar parameters and of the coordinate distance, are displayed, and the thermodynamic properties of the twobody system are studied. Furthermore, the seven physical parameters satisfy a simple algebraic relation which can be understood as a dynamical scenario, in which the physical properties of one body are affected by the ones of the other body.

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“…Later on, a paper of Varzugin [3] appeared in which the interaction of two counter-rotating Kerr black-hole constituents was analyzed within the framework of the boundary Riemann-Hilbert problem, however, without an attempt to reconstruct the corresponding vacuum solution. Two interesting results of the paper [3] are worth mentioning: (i) Varzugin demonstrated that the interaction force in the "antisymmetric" configuration of Kerr black holes is the same as in the double-Schwarzschild solution, i.e.,…”

Section: Introductionmentioning

confidence: 99%