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Properties of the distorted Kerr black hole
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abstract
We investigate the properties of the ergoregion and the location of the curvature singularities for the Kerr black hole distorted by the gravitational field of external sources. The particular cases of quadrupole and octupole distortion are studied in detail. We also investigate the scalar curvature invariants of the horizon and compare their behaviour with the case of the isolated Kerr black hole. In a certain region of the parameter space the ergoregion consists of a compact region encompassing the horizon and a disconnected part extending to infinity. The curvature singularities in the domain of outer communication, when they exist, are always located on the boundary of the ergoregion. We present arguments that they do not lie on the compact ergosurface. For quadrupole distortion the compact ergoregion size is negatively correlated with the horizon angular momentum when the external sources are varied. For octupole distortion infinitely many ergoregion configurations can exist for a certain horizon angular momentum. For some special cases we can have $J^2/M^4 > 1$ and yet avoid the naked singularity.
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Cited by 1 Pith paper
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The Vanishing of the Non-linear Static Love Number of Kerr Black Holes and the Role of Symmetries
Using the Ernst formalism, the paper argues that the static quadrupole tidal Love number of a Kerr black hole vanishes at full nonlinear order, because a decaying tidal mode would create a naked curvature singularity ...
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