Abstract
Massive bosons in the vicinity of Kerr–Newman black holes can form pure bound states when their phase angular velocity fulfills the synchronization condition, i.e. at the threshold of superradiance. The presence of these stationary clouds at the linear level is intimately linked to the existence of Kerr black holes with synchronized hair at the nonlinear level. These configurations are very similar to the atomic orbitals of the electron in a hydrogen atom. They can be labeled by four quantum numbers: [Formula: see text], the number of nodes in the radial direction; [Formula: see text], the orbital angular momentum; [Formula: see text], the total angular momentum; and [Formula: see text], the azimuthal total angular momentum. These synchronized configurations are solely allowed for particular values of the black holes mass, angular momentum and electric charge. Such quantization results in an existence surface in the three-dimensional parameter space of Kerr–Newman black holes. The phenomenology of stationary scalar clouds has been widely addressed over the last years. However, there is a gap in the literature concerning their vector cousins. Following the separability of the Proca equation in Kerr(–Newman) spacetime, this paper explores and compares scalar and vector stationary clouds around Kerr and Kerr–Newman black holes, extending previous research.
Highlights
PACS numbers: 1. Introduction Energy extraction from Kerr black holes was first devised in 1969 by Penrose,[1] who conceived a gedankenexperiment whereby a particle disintegrates within the ergo– region of a Kerr black hole into two other particles in such a way that the black hole loses energy
The state of affairs does not change much when looking at synchronised states around Kerr–Newman black holes
This paper aimed at providing a comparative analysis of stationary scalar and vector clouds around Kerr and Kerr–Newman black holes
Summary
Energy extraction from Kerr black holes was first devised in 1969 by Penrose,[1] who conceived a gedankenexperiment whereby a particle disintegrates within the ergo– region of a Kerr black hole into two other particles in such a way that the black hole loses energy. The endpoint is a classical boson condensate – colloquially referred to as cloud or hair – which is stationary with respect to the slowed-down black hole.[10,11,12] These equilibrium configurations are solutions of Einstein’s gravity minimally coupled to complex massive bosons, first unveiled for scalar bosons[13] and extended to vector bosons.[14] Kerr black holes with synchronised hair evade well-known uniqueness theorems15 – which state that asymptotically-flat stationary black holes in scalar– or vector–(electro–)vacuum general relativity are necessarily Kerr(–Newman) black holes16–18 – and defy the no-hair conjecture – acoording to which the gravitational collapse in the presence of any type of matter-energy must give birth to a Kerr(– Newman) black hole .
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