Axisymmetry

In the Kerr metric, which describes rotating black holes, the polar angle (θ) and azimuthal angle (φ) define positions in curved spacetime using Boyer-Lindquist coordinates.

The polar angle θ spans from 0 to π and measures position relative to the black hole’s spin axis—θ = π/2 marks the equatorial plane where frame-dragging is strongest.

The azimuthal angle φ, ranging from 0 to 2π, describes rotation around the black hole’s axis, influencing the path of particles and light due to axial symmetry and frame-dragging.

These angular coordinates are essential in modeling geodesics, disk structures, and photon orbits, especially in relativistic ray-tracing simulations of black hole environments.