This page is intended to be a complementary resource to my master’s thesis on the “Study of Global Vortical Null Geodesics in Kerr Spacetime“. For this purpose, the animations we created in the context of the thesis are presented and shortly discussed here (because videos are hard to print on paper).
The first video shows on the left side the inner throat (parametrised by the impact parameters α, β) as seen by an observer far away from a Kerr black hole in the negative-r-region (at ro=-∞, θo=π/4, ψo=0). The rotational parameter of the black hole is set to a/m=0.99. In the movie we consider centred rings insided the inner throat with a distance to the inner throat boundary as seen in the bottom right corner.
For each point on these rings, we calculated the starting angles θs and ψs for a source at rs=+∞, i.e. the observer views the sky at positive infinity from their position at negative infinty. These angles are plotted in the right plot as polar coordinates (θs cos(ψs), θs sin(ψs)), i.e. the distance to the origin is θs while the angle around the origin (in the counterclockwise direction) is ψs. Therefore, the right plot is the projection of the northern hemisphere onto a two-dimensional surface. The blue circle with radius π/2 corresponds to the equatorial plane.
What can be seen is that the field of view rotates in the anticlockwise direction as the rings on the left approach the inner throat boundary, meaning that large portions of the sky are visible (even though they may not be resolvable for the observer). However, this field of view always keeps a certain distance to the equatorial plane (grey region).
The second video shows the view of an observer with radial coordinate ro=-∞ and θo=π/4, orbiting around the black hole (a/m=0.99), i.e. increasing their azimuthal angle ψo, and looking through the disk spanned by the ring singularity (left).
The source in the video is comprised of four colours and covers the whole sky at rs=+∞, as can be seen in the polar plot on the right. The division is as follows: yellow 0<ψs<π/2, red π/2<ψs<π, blue π<ψs<3π/2, green 3π/2<ψs<2π. The grey dots in the right plot correspond to the field of view of the observer defined by the values of θs and ψs at rs=+∞, which were calculated for 149,000 pairs of impact parameters (α,β) inside the inner throat.
The video starts at ψo=0, increasing by π/50 from frame to frame, until it ends at ψo=99π/50. Due to the spacetime being 2π-periodic in the azimuthal direction, the video loops around and starts anew, corresponding to one whole revolution of the observer around the black hole.
Redshifting effects due to the motion of the observer are disregarded, resulting in individual stationary snapshots of the field of view of the observer along their orbit around the black hole.
It can be seen quite nicely that the middle of the inner throat magnifes the restricted field of view of the sky at rs = +∞ as the transitions of the colours happen rather quickly. At the same time, the regions in the vicinity of the inner throat boundary cramp together large parts of the sky at positive infnity, thus showing multiple colours at once throughout the whole revolution of the observer around the black hole.