Hydrodynamics and global structure of rotating Schwarzschild black holes

Abstract

Exploiting a rotating Schwarzschild black hole metric, we study the hydrodynamic properties of a perfect fluid whirling inward toward a black hole along a conical surface. On the equatorial plane of the rotating Schwarzschild black hole, we derive the radial equations of motion with effective potentials and the Euler equation for a steady-state axisymmetric fluid. Moreover, a numerical analysis is performed to figure out the effective potentials of. the particles on the rotating Schwarzschild manifolds in terms of the angular velocity, the total energy and the angular momentum per unit rest mass. Higher dimensional global embeddings are also constructed inside and outside the event horizon of the rotating Schwarzschild black hole.