File:Kerr-Flächen.png: Difference between revisions

• Animation einschalten

DescriptionKerr-Flächen.png	Deutsch: Ergosphären, Ereignishorizonte und Ringsingularität eines rotierenden schwarzen Lochs - Animation einschalten
Date	20 June 2017
Source	Own work
Author	Yukterez (Simon Tyran, Vienna)
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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+A^2] Sin[θ]Cos[φ],Sqrt[rI+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 *)

• Boyer-Lindquist: 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

• de.wikipedia.org/wiki/Kerr-Metrik
• en.wikipedia.org/wiki/Ring_singularity