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Register a new userThermodynamics of two aligned Kerr black holes
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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 $ell$ is defined by the formula $ell=Lexp(gamma_0)$, where $L$ is the coordinate length of the strut, and $gamma_0$ is the value of the metric function $gamma$ on the strut.
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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-Nordstrom 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 $ell=Lexp(gamma_0)$, $L$ being the coordinate length of the strut and $gamma_0$ the value of the metric function $gamma$ 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.
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.
Using the covariant phase space formalism, we compute the conserved charges for a solution, describing an accelerating and electrically charged Reissner-Nordstrom black hole. The metric is regular provided that the acceleration is driven by an external electric field, in spite of the usual string of the standard C-metric. The Smarr formula and the first law of black hole thermodynamics are fulfilled. The resulting mass has the same form of the Christodoulou-Ruffini mass formula. On the basis of these results, we can extrapolate the mass and thermodynamics of the rotating C-metric, which describes a Kerr-Newman-(A)dS black hole accelerated by a pulling string.
The open question of whether a Kerr black hole can become tidally deformed or not has profound implications for fundamental physics and gravitational-wave astronomy. We consider a Kerr black hole embedded in a weak and slowly varying, but otherwise arbitrary, multipolar tidal environment. By solving the static Teukolsky equation for the gauge-invariant Weyl scalar $psi_0$, and by reconstructing the corresponding metric perturbation in an ingoing radiation gauge, for a general harmonic index $ell$, we compute the linear response of a Kerr black hole to the tidal field. This linear response vanishes identically for a Schwarzschild black hole and for an axisymmetric perturbation of a spinning black hole. For a nonaxisymmetric perturbation of a spinning black hole, however, the linear response does not vanish, and it contributes to the Geroch-Hansen multipole moments of the perturbed Kerr geometry. As an application, we compute explicitly the rotational black hole tidal Love numbers that couple the induced quadrupole moments to the quadrupolar tidal fields, to linear order in the black hole spin, and we introduce the corresponding notion of tidal Love tensor. Finally, we show that those induced quadrupole moments are closely related to the well-known physical phenomenon of tidal torquing of a spinning body interacting with a tidal gravitational environment.
Ongoing observations in the strong-field regime are in optimal agreement with general relativity, although current errors still leave room for small deviations from Einsteins theory. Here we summarise our recent results on superradiance of scalar and electromagnetic test fields in Kerr-like spacetimes, focusing mainly on the Konoplya--Zhidenko metric. We observe that, while for large deformations with respect to the Kerr case superradiance is suppressed, it can be nonetheless enhanced for small deformations. We also study the superradiant instability caused by massive scalar fields, and we provide a first estimate of the effect of the deformation on the instability timescale.
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