Why naked singularities may not be a problem:
A problem about spinning Black Holes that have been making scientists uncomfortable is that of naked singularities. Black holes can spin so fast that it may be possible to see into the singularity. More on that here.
However, I have a hypothesis that may solve the existing problem of naked singularities.
The size of the Event Horizon:
The size of the Event Horizon is equal to the Black Hole’s Schwarzschild radius, or
with M as the mass, G as the Gravitational Constant, and c as the speed of light. This yields the radius of the Event Horizon.
The spin factor:
As I have discussed here, the speed of spin of a Black Hole can decrease the ISCO (Innermost Stable Circular Orbit) around a Black Hole, making objects able to have a stable orbit closer to the Black Hole. This spin, however, can increase to such an extent, that the ISCO will be smaller than the Event Horizon, and thus light can escape from it and we could see the singularity.
Where goes where:
Before going into why naked singularities may not be a problem, we need to understand how light travels inside a Black Hole.
In the above-given picture, I show how light travels inside a Black Hole, Lets get over the various points. We have the light's velocity, c, and the Black Hole’s gravitational pull, the escape velocity v.
Black- The dotted line represents the direction it was traveling. The black light was traveling as a tangent on the event horizon, touching point A. As it hits the event horizon, c=v, so it can neither escape, nor go into the singularity, orbiting the singularity endlessly.
Red- The red light was traveling directly towards the singularity. It experiences no extra force until it touches the singularity and orbits it infinitely.
Cyan and Green- Both the lights go directly into the event horizon, but not into the singularity. Thus, they bend and orbit the singularity many times before merging into the singularity.
We observe that all the light that enters the Event horizon, goes on and merges into the singularity. The singularity does not emit anything. I repeat, The singularity does not emit anything.
Problem solved?
And since the singularity does not emit anything, there is nothing to escape. So, there is no way we can ‘see’ the singularity. The problem of naked singularities is solved, isn't it? Actually, not quite.
Take a look at this diagram:
Here, the cyan light has not reached the singularity yet. If suddenly, for some external causes, the Black Hole may start spinning faster, the ISCO may shrink into a radius smaller than the displacement between A and the singularity. The photons will suddenly be in a stable orbit, and will escape into space. This can also be considered as a bit of a naked singularity.
This falsifies the fact that nothing can escape once it enters the event horizon. How about this scenario? Will the cyan light escape?
Changes to the equation:
This brings me to one of the main parts of my hypotheses. Actually, the cyan light won’t escape. This is because the radius of the event horizon also depends on the Black Hole’s spin. In other words,
The radius of a Black Hole’s Event Horizon is inversely proportional to its spin velocity.
If that’s the case, you can imagine the Event horizon as a hollow sphere, with the cyan light trapped inside it. Even if the Event Horizon shrinks faster than the cyan light can reach the singularity, the Event Horizon will drag the cyan light with it.
At the center:
Though I have finished with my hypothesis, I feel like I would like to illustrate a point. All the light that merges into the singularity, what happens to them?
Well, photons are massless particles. If their speed is <c they can’t exist, as their net energy would be 0 (in par with E = mc²). Therefore, they need to keep traveling at c. Therefore they just orbit the singularity forever (remember, in spinning Black Holes, we have a ringularity), without any hope to escape. To bring the ISCO down to this orbit, the angular momentum of the Black Hole has to be >c, which is impossible.
Conclusion:
Before judging any of my writing, please remember this is written by a 14-year-old kid who is basically self-taught in astronomical physics. If you find any problem in my above-mentioned hypothesis, please leave a response down below and I’ll try to make the amends.
-Rak Laptudirm
