A Visible Infinite

Naked Singularity

Now, comes the time when we talk about the “naked” singularity. What does it mean and why is it so important? Let's find out.

Till now, we have been talking about black holes, more specifically, the Schwarzschild black hole or the non-spinning, non-changing, electrically uncharged one. The ideal or the simplest case. More complicated objects, like the spinning black holes, do not have a simple event horizon.

A spinning black hole

But, before I get into this I would like to define naked singularity for you. You are very aware from our previous discussion on black holes that gravitational singularity is not directly observable, it is hidden behind an event horizon (the point of no return). So, what happens to a body that reaches this singularity after falling into a black hole remains a mystery due to these shields. But, what if there was no event horizon? The singularity would be directly visible and we can easily observe the fate of objects being compressed to infinite density! Such a singularity is called a naked singularity.

So, now the question is how are these formed? What is the importance of their existence? And, most importantly do they even exist? Are they just theoretical or some fundamental law of nature keeps guarding them? And if they do exist why haven’t we discovered one yet?

We will deal with all of these questions serially.

How are naked singularities formed?

How are these formed or how is it even possible to have a gravitational singularity with no event horizon?

Let's imagine a situation. Suppose, we start spinning the world. I mean it is actually spinning, but we spin it really, really fast. If we spin it fast enough, people would fly outwards from the surface. In other words, we can partially “cancel” gravity.

We can apply the same logic to a spinning black hole, and we will find similar effects. The faster it spins, the smaller the event horizon gets. From concepts drawn from rotating black holes, it is shown that a singularity, spinning rapidly, can become a ring-shaped object. This results in two event horizons, as well as an Ergosphere, which draws closer together as the spin of the singularity increases. When the outer and the inner horizons merge, they shrink towards the rotating singularity and eventually expose it to the rest of the Universe. A singularity rotating fast enough might be created by the collapse of the dust or by a supernova of a fast-spinning star. But, to our disappointment when it comes to practicality, we can't spin a black hole fast enough to make the event horizon disappear entirely!

Anatomy of a rotating black hole

What is the importance of their existence? And if they do exist why haven’t we discovered one yet? Or is nature guarding its secret closely?

As I have already mentioned earlier, a naked singularity allows us to directly observe the fate of an object which is being compressed to literally infinite density! Its discovery will also cause some foundational problems for general relativity because general relativity cannot make predictions about the future evolution of space-time near a singularity.

But, the primary question remains, do they really exist?

They have not been observed or detected to date. And the cosmic censorship hypothesis, says that a naked singularity cannot arise in our universe from realistic initial conditions. A singularity will always be in our future or our past.  To elaborate; this means we would never be alive to actually witness the singularity even if we fall into a black hole. We would be torn apart by its gravitational pull (spaghettification) and our conscious self would simply not exist. It’s our remains that would still manage to reach the singularity but we obviously won’t get any information from that! The singularity would always exist in the future for us. This is the weak cosmic censorship hypothesis. Similarly, the big bang singularity exists in our past and we don’t have any clue about it either. This is the strong cosmic censorship hypothesis. Predictability loses its power at a singularity. Or to quote Stephen Hawking, “Nature abhors a naked singularity”.

Hawking designed this t-shirt after losing a bet to his fellow scholars

But, the story doesn't end here; looking at other suggestions, we find that if loop quantum gravity is correct, the naked singularities could exist in nature implying cosmic censorship hypothesis does not hold. Some numerical calculations hint at its possibility.

Disappearing event horizons exist in the Kerr metric, which is a spinning black hole in a vacuum. Specifically, if angular momentum is high enough, the event horizons could disappear. Disappearing event horizons can also be seen with the Reissner-Nordstrom geometry of a charged black hole. You should not ponder so much on the technical terms here as they are out of the scope of this blog.

We don’t know if naked singularities really exist or not. But its discovery would certainly open a new door for physicists.

So, that was all for now. Hope you found the article informative. Will see you soon. 

Danke!