# Black holes with a naked singularity?

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bbbl67
Yes, I understand that this is all kind of hypothetical, there have been no black holes discovered with a naked singularity. A black hole which is spinning beyond the speed of light is said to expand its event horizon to drop below the speed of light again. When it does that, it creates a donut-shaped, toroidal EVH, and that leads to its singularity being exposed to the outside universe. How would time work inside such a thing? Time inside a black hole is said lead towards the singularity, but how would anything head towards the singularity if the singularity is outside the EVH?

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Yes, I understand that this is all kind of hypothetical, there have been no black holes discovered with a naked singularity. A black hole which is spinning beyond the speed of light is said to expand its event horizon to drop below the speed of light again. When it does that, it creates a donut-shaped, toroidal EVH, and that leads to its singularity being exposed to the outside universe. How would time work inside such a thing? Time inside a black hole is said lead towards the singularity, but how would anything head towards the singularity if the singularity is outside the EVH?
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Angular velocity increases when you contract a rotating object. No particle involved in the collapse would need to ever move faster than the speed of light.

The sequence of events listed is a calculation sequence not a series of events in real time and real space.

bbbl67
Angular velocity increases when you contract a rotating object. No particle involved in the collapse would need to ever move faster than the speed of light.

The sequence of events listed is a calculation sequence not a series of events in real time and real space.
But how does time work inside a black hole with a naked singularity?

But how does time work inside a black hole with a naked singularity?

A naked singularity is not inside a black hole. :P

I am not sure about this. I would suspect that frame dragging causes motion in the direction of spin. Time dilation from increased velocity can compete with gravitational time dilation. Approaching a normal black hole you move toward the singularity which is also toward the event horizon. With the naked singularity you still accelerate but get spin accelerated too. Should be some motion toward the tangent.

Mentor
A black hole which is spinning beyond the speed of light is said to expand its event horizon to drop below the speed of light again.

Where are you getting this from? Please give a reference. It doesn't look like any valid black hole model that I am aware of.

Mentor
how does time work inside a black hole with a naked singularity?

There is no such thing. A naked singularity is a singularity that is not inside a horizon.

Gold Member
Yes, I understand that this is all kind of hypothetical, there have been no black holes discovered with a naked singularity. A black hole which is spinning beyond the speed of light is said to expand its event horizon to drop below the speed of light again. When it does that, it creates a donut-shaped, toroidal EVH, and that leads to its singularity being exposed to the outside universe. How would time work inside such a thing? Time inside a black hole is said lead towards the singularity, but how would anything head towards the singularity if the singularity is outside the EVH?

Without going into a great detail, to clarify, the Kerr black hole has two horizons, the outer and inner (sometimes referred to as the Cauchy) where the coordinate radii of these horizons are defined by $r_+=M +\sqrt(M^2-a^2)$ and $r_-=M -\sqrt(M^2-a^2)$ respectively (where $M$ is mass and $a$ is spin) where normally $a/M<1$ (in geometric units). At $r>r_+$, worldlines are timelike; between $r_+-r_-$, worldlines are spacelike (as in a conventional Schwarzschild bh) and at $r<r_-$, worldlines return to timelike again. In the hypothetical maximal case, where $a=M$, $r_+$ and $r_-$ 'meet' and the ring singularity within $r_-$ becomes visible. There's a few issues with this. $a/M=1$ results in the Killing surface gravity becoming zero which violates the third law of black hole thermodynamics. Secondly the idea that a bh spin can be increased by throwing in objects with angular momentum is counteracted by the fact that M would also increase and thirdly, the inner (Cauchy) horizon is predicted to be unstable and the boundary of predictability. Also a naked singularity violates cosmic censorship. Below are links to some images that show the various stages -

http://inspirehep.net/record/1351202/plots (approx. two-thirds of the way down)

https://indico.cern.ch/event/93835/contributions/1280941/attachments/1103981/1575044/Primorsko_1.pdf (page 4, note: only the boundary of the ergoregion shown)

It might also be worth looking at charged (Reissner-Nordström) black holes where the horizons are defined by $r_\pm=M \pm\sqrt(M^2-Q^2)$ and Kerr-Newman (charge and spin) black holes where the horizons are defined by $r_\pm=M \pm\sqrt(M^2-a^2-Q^2)$ where similar principles apply.

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