<p>First, let's clarify that there are unphysical, coordinate dependent singularities and there are physical, coordinate independent singularities. An event horizon is an unphysical singularity, while the <a href="https://en.wikipedia.org/wiki/Ring_singularity" rel="nofollow noreferrer">ring singularity</a> of the Kerr metric is a physical singularity.</p>
<blockquote>
<p>Since toroidal planet are hypothetically possible, albeit very unlikely to actually exist, can we extend this idea to black holes? Would these unstable bodies work at least on paper?</p>
</blockquote>
<p>Yes, this is a mathematically sound concept. Axisymmetric black hole solutions (i.e. Kerr) that are toroidal near the ring singularity was first pointed out by <a href="https://aip.scitation.org/doi/10.1063/1.522763" rel="nofollow noreferrer">Kip Thorne in 1975</a> (available for free <a href="https://authors.library.caltech.edu/10778/" rel="nofollow noreferrer">here</a>). The event horizon can be toroidal, not the physical singularity itself. These toroidal horizons are <a href="https://journals.aps.org/prd/abstract/10.1103/PhysRevD.52.6982" rel="nofollow noreferrer">not necessarily</a> in violation of cosmic censorship. But one must be careful as it can apparently lead one to slip into <a href="https://ui.adsabs.harvard.edu/abs/2000MNRAS.316..856S/abstract/" rel="nofollow noreferrer">quackery</a>. More recently, <a href="https://arxiv.org/abs/gr-qc/9710123" rel="nofollow noreferrer">new solutions</a> have been found of rotating toroidal black holes.</p>
<p>Although there is no observational evidence to support this idea, it was <a href="https://arxiv.org/abs/1606.00436" rel="nofollow noreferrer">recently reported in a numerical relativity simulation</a> that the event horizon of a binary black hole merger can be temporarily toroidal, as was predicted earlier, and which does not violate <a href="https://en.wikipedia.org/wiki/Topological_censorship" rel="nofollow noreferrer">topological censorship</a>. This is very interesting, as it implies that a toroidal black hole horizon may be observable.</p>

CC BY-SA 4.0
2022-03-04T15:50:42.590Z
I was curious about your quackery link, but it appears to be broken.
Lee Mosher
CC BY-SA 4.0
2022-03-04T18:46:35.820Z
@LeeMosher I've added an updated link
Daddy Kropotkin
CC BY-SA 4.0
2022-02-26T18:24:55.690Z
2022-03-05T12:40:59.640Z
2022-03-05T12:40:59.640Z
Daddy Kropotkin
<p>Since <a href="https://en.wikipedia.org/wiki/Toroidal_planet" rel="nofollow noreferrer">toroidal planet</a> are hypothetically possible, albeit very unlikely to actually exist, can we extend this idea to black holes? Would these unstable bodies work atleast on paper?</p>

CC BY-SA 4.0
2022-02-25T15:49:39.797Z
Not gonna answer because maybe someone has some insight that I don’t, but first impressions are that since a singularity is a point source, it can’t be extended and it defines the event horizon, so I just can’t conceive of a geometry where that would work, because where would the singularity go you know?
Justin T
CC BY-SA 4.0
2022-02-25T16:55:16.837Z
@JustinT Well singularities don't have to be a point source. For instance, you can have a [ringularity](https://en.wikipedia.org/wiki/Ring_singularity)
H2Forge
CC BY-SA 4.0
2022-02-26T11:07:18.853Z
I don't know what you mean by "work at least on paper".  A quick web search does return info on models like this.
StephenG - Help Ukraine
<black-hole><general-relativity>
Are toroidal black holes hypothetically possible?
H2Forge
# Are toroidal black holes hypothetically possible?

(Asked by: username_0 on 2022-02-25)

Since [toroidal planet](https://en.wikipedia.org/wiki/Toroidal_planet) are hypothetically possible, albeit very unlikely to actually exist, can we extend this idea to black holes? Would these unstable bodies work atleast on paper?

**Tags:** black-hole, general-relativity
> **Comments:**
> **username_1**: Not gonna answer because maybe someone has some insight that I don’t, but first impressions are that since a singularity is a point source, it can’t be extended and it defines the event horizon, so I just can’t conceive of a geometry where that would work, because where would the singularity go you know?  
> **username_0**: @JustinT Well singularities don't have to be a point source. For instance, you can have a [ringularity](https://en.wikipedia.org/wiki/Ring_singularity)  
> **username_2**: I don't know what you mean by "work at least on paper".  A quick web search does return info on models like this.  

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## 1 answers

### Answer by username_3 on 2022-02-26. Score: 2 | Accepted answer

First, let's clarify that there are unphysical, coordinate dependent singularities and there are physical, coordinate independent singularities. An event horizon is an unphysical singularity, while the [ring singularity](https://en.wikipedia.org/wiki/Ring_singularity) of the Kerr metric is a physical singularity.

> Since toroidal planet are hypothetically possible, albeit very unlikely to actually exist, can we extend this idea to black holes? Would these unstable bodies work at least on paper?

Yes, this is a mathematically sound concept. Axisymmetric black hole solutions (i.e. Kerr) that are toroidal near the ring singularity was first pointed out by [Kip Thorne in 1975](https://aip.scitation.org/doi/10.1063/1.522763) (available for free [here](https://authors.library.caltech.edu/10778/)). The event horizon can be toroidal, not the physical singularity itself. These toroidal horizons are [not necessarily](https://journals.aps.org/prd/abstract/10.1103/PhysRevD.52.6982) in violation of cosmic censorship. But one must be careful as it can apparently lead one to slip into [quackery](https://ui.adsabs.harvard.edu/abs/2000MNRAS.316..856S/abstract/). More recently, [new solutions](https://arxiv.org/abs/gr-qc/9710123) have been found of rotating toroidal black holes.

Although there is no observational evidence to support this idea, it was [recently reported in a numerical relativity simulation](https://arxiv.org/abs/1606.00436) that the event horizon of a binary black hole merger can be temporarily toroidal, as was predicted earlier, and which does not violate [topological censorship](https://en.wikipedia.org/wiki/Topological_censorship). This is very interesting, as it implies that a toroidal black hole horizon may be observable.

> **Comments:**
> **username_4**: I was curious about your quackery link, but it appears to be broken.  
> **username_3**: @LeeMosher I've added an updated link  

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