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!