Global embeddings and hydrodynamic properties of Kerr black hole

Abstract

In the presence of a rotating Kerr black hole, we investigate hydrodynamics of the massive particles and massless photons, to construct relations among number density, pressure and internal energy density of the massive particles and photons around the rotating Kerr black hole and to study an accretion onto the black hole. On equatorial plane of the Kerr black hole, we investigate the bound orbits of the massive particles and photons around the black hole to produce their radial, azimuthal and precession frequencies. With these frequencies we study the black holes GRO~J1655-40 and 4U~1543-47, to explicitly obtain the radial, azimuthal and precession frequencies of the massive particles in the flow of perfect fluid. We next consider the massive particles in the stable circular orbit of radius of $1.0~ly$ around the supernovas SN 1979C, SN 1987A and SN 2213-1745 in the Kerr curved spacetime, and around the potential supermassive Schwarzschild black holes M87, NGC 3115, NGC 4594, NGC 3377, NGC 4258, M31, M32 and Galatic center, to estimate their radial and azimuthal frequencies, which are shown to be the same results as those in no precession motion. The photon unstable orbit is also discussed in terms of the impact parameter of the photon trajectory. Finally, on the equatorial plane of the Kerr black hole, we construct the global flat embedding structures possessing (9+3) dimensionalities outside and inside the event horizon of the rotating Kerr black hole. Moreover, on the plane we investigate the warp products of the Kerr spacetime.