Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2008-08-28
JHEP 0810:017,2008
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
19 pages, 4 figures. v2: changed statement about thermodynamical equilibrium in section 3; minor changes; added references. v3
Scientific paper
10.1088/1126-6708/2008/10/017
The double-Kerr solution is generated using both a Backlund transformation and the Belinskii-Zakharov inverse-scattering technique. We build a dictionary between the parametrisations naturally obtained in the two methods and show their equivalence. We then focus on the asymptotically flat double-Kerr system obeying the axis condition which is Z_2^\phi invariant; for this system there is an exact formula for the force between the two black holes, in terms of their physical quantities and the coordinate distance. We then show that 1) the angular velocity of the two black holes decreases from the usual Kerr value at infinite distance to zero in the touching limit; 2) the extremal limit of the two black holes is given by |J|=cM^2, where c depends on the distance and varies from one to infinity as the distance decreases; 3) for sufficiently large angular momentum the temperature of the black holes attains a maximum at a certain finite coordinate distance. All of these results are interpreted in terms of the dragging effects of the system.
Herdeiro Carlos A. R.
Rebelo Carmen
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