Hydrodynamics and global embeddings of Taub-NUT spacetime

Abstract

On Taub-NUT spacetime, we investigate the hydrodynamic properties of perfect fluid spiraling inward toward the spacetime along a conical surface. On the equatorial plane of the Taub-NUT spacetime, we derive the radial equations of motion with effective potentials and the Euler equation for steady-state axisymmetric fluid. Higher dimensional global embeddings are constructed inside and outside the event horizons of the Taub-NUT spacetime. We also study the effective potentials of particles on the Taub-NUT spacetime in terms of the gravitational magnetic monopole strength of the source, the total energy, and the angular momentum per unit rest mass of the particle.