Hydrodynamics and global structure of rotating Schwarzschild black holes

TL;DR

This paper investigates the hydrodynamics and global structure of rotating Schwarzschild black holes, deriving equations of motion, analyzing effective potentials numerically, and constructing higher-dimensional embeddings of the spacetime.

Contribution

It introduces a detailed analysis of fluid dynamics and global embeddings in rotating Schwarzschild black holes, extending understanding of their physical and geometric properties.

Findings

Derived radial equations of motion with effective potentials.

Numerical analysis of particle effective potentials based on angular velocity, energy, and angular momentum.

Constructed higher-dimensional global embeddings inside and outside the event horizon.

Abstract

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