## Naked Singularities

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Yukterez
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### Naked Singularities

Although naked singularities propably do not exist in nature, General Relativity allows them so they are still of at least theoretical interest. The images and videos show the gravitational lensing of electrically overcharged Reissner Nordström, overextremal Kerr and also charged and spinning Kerr Newman singularities. The raytracing was done with the Yukterez Raytracer, which is written in Mathematica Syntax.

The total energy Mc² of the naked singularities on this page is the same in all examples, but its irreducible mass (ℳ), electric charge (℧) and angular momentum (a) components are split up differently. The following animation shows a naked singularity with different inclinations (0°=polar, 90°=equatorial).

Kerr Newman, M=1, a=1, ℧=1 → ℳ=½√(1+2i) - r=50GM/c², θ=0°..90°, FOV=120°×60° (click on the gif to load a higher resolution mp4):

Background: Milky Way panorama (ESO/Brunier), unlensed view with FOV=120°×60°:

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Yukterez
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### Naked Singularities

Images (a²+℧²=2², click to enlarge)

Reissner-Nordström: M=1, a=0, ℧=2 → ℳ=½+i√¾ - Observer: r=50GM/c², θ=egal (symmetric), FOV=120°×60°:

Kerr-Newman: M=1, a=√2, ℧=√2 → ℳ=∜(3/16)·(1+i) - Observer: r=50GM/c², θ=90° (equatorial view), FOV=120°×60°:

Kerr-Newman: M=1, a=√2, ℧=√2 → ℳ=∜(3/16)·(1+i) - Observer: r=50GM/c², θ=45° (inclined view), FOV=120°×60°:

Kerr-Newman: M=1, a=√2, ℧=√2 → ℳ=∜(3/16)·(1+i) - Observer: r=50GM/c², θ=1° (polar view), FOV=120°×60°:

Kerr: M=1, a=2, ℧=0 → ℳ=√¾+i/2 - Observer: r=50GM/c², θ=90° (equatorial view), FOV=120°×60°:

Kerr: M=1, a=2, ℧=0 → ℳ=√¾+i/2 - Observer: r=50GM/c², θ=45° (inclined view), FOV=120°×60°:

Kerr: M=1, a=2, ℧=0 → ℳ=√¾+i/2 - Observer: r=50GM/c², θ=1° (polar view), FOV=120°×60°:

Further reading and comparison: Waseda, p.14 & DeVries, p.20

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Yukterez
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### Naked Singularities

Videos: equatorial orbits, φ=0..360° (a²+℧²=1.01²)

Reissner Nordström, M=1, a=0, ℧=1.01 → ℳ=½+0.0708872i - r=20GM/c², θ=90°, FOV=154.8°×77.4°:

Kerr, M=1, a=1.01, ℧=0 → ℳ=0.708872+0.05i - r=20GM/c², θ=90°, FOV=154.8°×77.4°:

Kerr Newman, M=1, a²+℧²=1.01² → ℳ=0.61305+0.0578152i - r=20GM/c², θ=90°, FOV=154.8°×77.4°:

Full HD videos: raytracing.yukterez.net

Симон Тыран @ facebook || wikipedia || stackexchange || wolfram

Yukterez
Beiträge: 193
Registriert: Mi 21. Okt 2015, 02:16

### Naked Singularities

Horizons and ergosurfaces for different spin and charge parameters:

Surface plot in cartesian coordinates (these surfaces would not be directly visible):

Naked singularities would not have inner and outer horizons, but inner and outer ergosurfaces.
Units: G=M=c=K=1, Code: kerr.newman.yukterez.net and raytracing.yukterez.net

All work here as well as the 3rd party source material (the raw panorama photo) is published under the Creative Commons License. Simon Tyran (Yukterez), 2018

Симон Тыран @ facebook || wikipedia || stackexchange || wolfram