File:Kerr-Flaechen.gif

Summary[edit]

DescriptionKerr-Flaechen.gif	Deutsch: Ergosphären, Ereignishorizonte und die Ringsingularität eines rotierenden schwarzen Lochs. a ist der Spinparameter und läuft von 0 bei keiner Rotation bis 1 bei maximaler Rotation. English: Ergospheres, Event horizons and the ring singularity of a rotating black hole. a is the spin parameter, which is 0 for no rotation and 1 for maximal rotation.
Date	20 June 2017
Source	Own work
Author	Yukterez (Simon Tyran, Vienna)
Other versions

Licensing[edit]

I, the copyright holder of this work, hereby publish it under the following license:

This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.

You are free:

• to share – to copy, distribute and transmit the work
• to remix – to adapt the work

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• share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.

https://creativecommons.org/licenses/by-sa/4.0CC BY-SA 4.0 Creative Commons Attribution-Share Alike 4.0 truetrue

Code[edit]

rE=1+Sqrt[1-a^2 Cos[θ]^2]; RE[A_]:={Sqrt[rE^2+A^2] Sin[θ]Cos[φ],Sqrt[rE^2+A^2] Sin[θ]Sin[φ],rE Cos[θ]}; (* äußere Ergosphäre *)
rG=1-Sqrt[1-a^2 Cos[θ]^2]; RG[A_]:={Sqrt[rG^2+A^2] Sin[θ]Cos[φ],Sqrt[rG^2+A^2] Sin[θ]Sin[φ],rG Cos[θ]}; (* innere Ergosphäre *)
rA=1+Sqrt[1-a^2]; RA[A_]:={Sqrt[rA^2+A^2] Sin[θ]Cos[φ],Sqrt[rA^2+A^2] Sin[θ]Sin[φ],rA Cos[θ]};           (* äußerer Horizont *)
rI=1-Sqrt[1-a^2]; RI[A_]:={Sqrt[rI^2+A^2] Sin[θ]Cos[φ],Sqrt[rI^2+A^2] Sin[θ]Sin[φ],rI Cos[θ]};           (* innerer Horizont *)
p[f_, c_]:=ParametricPlot3D[f, {φ, 0, 2 π}, {θ, 0, π}, PlotStyle -> Directive[c, Opacity[0.15]]]             (* Plotfunktion *)
Do[Print[Show[p[RE[a], Blue], p[RA[a], Cyan], p[RI[a], Orange], p[RG[a], Red]], {a,0,1,0.1}]]           (* Kerr-Schild x,y,z *)
Do[Print[Show[p[RE[0], Blue], p[RA[0], Cyan], p[RI[0], Orange], p[RG[0], Red]], {a,0,1,0.1}]]       (* Boyer-Lindquist r,θ,Ф *)

Comparison[edit]

• Boyer-Lindquist: doi:10.1139/p81-086 Nigel Sharp: On embeddings of the Kerr geometry; page 3, figure 3]
• Kerr-Schild: Matt Visser: The Kerr spacetime, A brief introduction; page 35, figure 3
• Source: kerr.yukterez.net / kerr.newman.yukterez.net