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Generalization of Cassini ovals

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I'm working on a paper that describes black hole mergers. Most of the figures resemble Cassini ovals, except for the last figure... do you know of a way to make one of the ovals larger than the other?

 

The paper is at http://vixra.org/abs/1701.0614

 

Thanks for any help that you can provide.

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Figure 11: A unit mass black hole merging with a black hole of mass = 1000

The asymmetry in figure 11 is due to different black hole masses, as seen in formula 1 on the first page: increasing the Mi mass shifts the corresponding contribution to f towards larger ri, which in this physical model corresponds to more massive black holes having larger event horizon boundaries.

Render examples with less extreme M1/M2 ratios to understand better

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Figure 11: A unit mass black hole merging with a black hole of mass = 1000

The asymmetry in figure 11 is due to different black hole masses, as seen in formula 1 on the first page: increasing the Mi mass shifts the corresponding contribution to f towards larger ri, which in this physical model corresponds to more massive black holes having larger event horizon boundaries.

Render examples with less extreme M1/M2 ratios to understand better

 

 

Sounds good. Thanks for taking the time to reply :)

 

I figured out that it is a generalization of Cassini ovals where the torus in question is lopsided like with a ring cyclide.

 

Check the paper again... I uploaded a new version.

Edited by sjhalayka

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