Scalar spheroidal harmonics in five dimensional Kerr(A)dS (original) (raw)
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Annals of Physics, 2020
The Newman-Janis (NJ) method is a prescription to derive the Kerr space-time from the Schwarzschild metric. The BTZ, Kerr and five-dimensional Myers-Perry (MP) black hole solutions have already been generated by different versions of the NJ method. However, it is not known how to generate the metric of higher-dimensional (d > 6) rotating black holes by this method. In this paper, we propose the simplest algorithm for generation of the fivedimensional MP metric with two arbitrary angular momenta by using the Kerr-Schild form of the metric and quaternions. Then, we present another new twostep version of the NJ approach without using quaternions that generate the five-dimensional MP metric with equal angular momenta. Finally, the extension of the later procedure is explained for the higher odd-dimensional rotating black holes (d > 5) with equal angular momenta.
Construction and physical properties of Kerr black holes with scalar hair
Kerr black holes with scalar hair are solutions of the Einstein-Klein-Gordon field equations describing regular (on and outside an event horizon), asymptotically flat black holes with scalar hair [1]. These black holes interpolate continuously between the Kerr solution and rotating boson stars in D = 4 spacetime dimensions. Here we provide details on their construction, discussing properties of the ansatz, the field equations, the boundary conditions and the numerical strategy. Then, we present an overview of the parameter space of the solutions, and describe in detail the space-time structure of the black holes exterior geometry and of the scalar field for a sample of reference solutions. Phenomenological properties of potential astrophysical interest are also discussed, and the stability properties and possible generalizations are commented on. As supplementary material to this paper we make available numerical data files for the sample of reference solutions discussed, for public use. * herdeiro@ua.pt † eugen.radu@ua.pt