Black hole leaks...

Hawking Radiation

Hey friends! It has been a long time since we connected. So here I am with a new article – the Hawking Radiation, theorized by Stephen Hawking in 1974 (Our small effort to remember him).

Stephen Hawking in space situation

Hawking Radiation! The phenomenon has been confusing physicists since its discovery. The process describes the death of a black hole or the process by which a black hole emits radiation. The very fact that radiations are coming from a black hole is in itself mind-blowing!

The thought came into existence after it was mathematically proved that black holes have entropy. The presence of entropy signified that it must have a temperature. And as we know from the laws of thermodynamics, it meant that it must be radiating energy and thus losing mass.

Hot things radiate

The equation that describes the entropy of a black hole is also an interesting one.

S = (Ac^3) / (4ħG)

Here,    S is the entropy

            A is the area of the event horizon.

This wonderful expression contains the three fundamental constants of nature: c, the speed of light; G, Newton’s constant of gravitation; and ħ, Planck’s constant. Wow!

This expression establishes the relation between gravity and thermodynamics.

As we can see from the equation, entropy is directly proportional to the area of the event horizon. As the area of the event horizon increases, the entropy of a black hole increases; it may happen when a black hole sucks more mass or when two black holes merge to form a single black hole.

The more the entropy lesser is the temperature. The larger a black hole is lesser would be its absolute temperature. The temperature and mass follow the following relation:

T = (ħc^3) / (8(pi)GMk)

Where T is the Hawking temperature, ħ is Planck’s constant, G is Newton’s constant of gravitation, M is the mass of the black hole and k is the Boltzmann constant.

The explanation to Hawking Radiation combines Relativity and Quantum Mechanics – The sciences of the very big and of the very small, respectively.

Quantum Mechanics, in a strange way as it is, talks about the creation of virtual particles in a vacuum. These particles pop up on themselves and immediately annihilate giving energy. These particles are matter-antimatter pairs. When matter and antimatter annihilate, they both vanish and give energy. The vacuum is not essentially empty. These new particles always keep on popping.

If this process takes place near the event horizon, chances are one of the particles, the one with negative energy will get sucked up and the other with positive energy will escape into the Universe as a real particle. As the negative mass gets inside the black hole it reduces some of its mass. For an observer seeing it from outside, the positive particle would appear as radiation and it would appear that the black hole is losing mass. Thus, the black hole will lose matter, particle by particle, and gradually evaporate with time.

Creation of virtual-real particle pairs

From the principle of conservation of mass, and relativity, we know that mass and energy are interconvertible. For a reminder, here is the equation:

E=mc²

This equation tells the energy possessed by an object of relative mass m, moving with the speed of light c, or the similar nature of mass and energy. The particles that are formed near the event horizon, are formed using the energy from a black hole’s gravitational potential energy. Thus, making it lose energy and eventually mass.

This happens incredibly slow at first. For a supermassive black hole, it is really insignificant. Reasons being: its large event horizon, high suction to emission ratio, and, as we have seen from the above equations temperature is inversely proportional to the mass of a black hole. The process gets faster as the black hole becomes smaller. The smallest of the black holes live for a fraction of a second only. (The scientists at the Large Hadron Collider hope on making one such ultra-tiny micro black hole in order to study Hawking Radiation.) When it arrives at the mass of a large asteroid, it is radiating at room temperature. When it has the mass of a mountain, it radiates with about the heat of our sun. And in the last seconds of its life, the black hole radiates away with the energy of billions of nuclear bombs in a huge explosion. The wavelength emitted is the same as the size of a black hole. As the size gets smaller, the wavelength also gets smaller. The largest of the black holes are the coldest and the smallest ones are the hottest.

But, this process is incredibly slow. The last of the largest of the black holes may take a googol year to evaporate (hundred zeroes after 1). This period is so long that when the last black hole radiates away, nobody will be around to witness it. The universe would have become uninhabitable long before then!

Hawking Radiation

A proper explanation to the Hawking Radiation needs a quantum theory of gravity, that is, the unification of gravitation and quantum mechanics – the two giants of modern physics. We are working towards it but haven’t achieved it yet. We do have better hopes for the future though.

So, this was all for today. Hope you found it informative. I will be back soon. Till then, thank you very much.

Bis später!

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!