Collision: Destruction or Creation

   We still know how giant and strong these black holes are. This was all for about a single black hole, but now imagine what would happen if a black hole collided with another black hole of about the same mass. What will be the result of this destruction? Will it be a very huge big bang or the creation of a new beast? So, let’s find out what will happen.

Binary black holes.

     A binary black hole system is a pair of black holes revolving around a particular point that is its epicenter. So, is the collision of all the black holes the same? The answer is no, as when different sizes of black holes collide with each other, the resultant energy released is different. That is, the collision of two stellar black holes will result in a different amount of energy being released than the collision of two supermassive black holes. So, there are different types of collisions. One type of collision is the collision of two stellar black holes formed by the revolution of the remains of two heavily dense stars revolving around a particular point. Then there is the collision of two galaxies that results in the collision of two super massive black holes. So, all these black holes before colliding revolve around each other, and this system is coined as the binary black hole system.

 Process of collision.

    Imagine two black holes of nearly 80 solar masses each. That is the mass of 80 suns densely packed together into an area that is the size of Japan. Then what would happen is the formation of a black hole. Now, imagine two black holes, the second one similar to the first one we discussed earlier, approaching each other. What will happen? Earlier, when it was not observed, it was very difficult to locate a black hole precisely where it was and how far it was from us, because the black hole does not give any signs of its existence due to its terrible gravitational force. But when two black holes collide, an immense amount of energy in the form of gravitational waves is released in the space and time whose energy has been calculated by the use of general relativity. It is said that the collision of two black holes results in the strongest and largest production of gravitational waves. These are the only quantities that remain the same in all dimensions, so it is easy to detect them. As the gravitational waves are released, the orbit of a black hole decays, and the period of the orbit also decreases. This whole phenomenon is known as an inspiral. Once it happens, the back holes start to merge into each other, and finally a single black hole is formed. In this process, as two black holes combine, the total mass of the black hole is not the same as the addition of the masses of two black holes, as at the time of collision, a huge amount of energy is released in the form of gravitational waves. So some amount of mass is converted into energy in the form of gravitational waves and released.

So, what ones happened is….

    On the 14th of September 2015, approximately 1.4 billion light-years from Earth, two black holes spiraled around each other and, after some time, collided, creating waves in the fabric of space-time. These waves, known as gravitational waves, arrived at Earth and were observed and announced by Virgo and LIGO in February 2016. The readings given by LIGO were approximately and more accurately correct and were accurate to the general relativity prediction of two massive bodies spiraling inwards towards each other, having asses approximately equal to 36 and 29 solar masses, which finally emerged into a single black hole. The signal that was detected was named GW150914, which says, Gravitational waves noticed on September 14, 2015. It was the first time an observation of the merging or collision of black holes was observed and put forward with proof. This gave a clear response that the collision of stellar black holes still occurs in this age and era. Earlier, gravitational waves had only been inferred indirectly, via their effect on the timing of pulsars in binary star systems. The news of the first direct observation was spread around the world as a remarkable achievement for many reasons. Many efforts have been made in the last fifty-five years to show the existence of such waves, and the waves are so small that Albert Einstein himself never thought that they could ever be detected. But, this gave the boost to the scientists and researchers that they needed for a long time to discover many more things about them, and the day is not so far when we could actually go near this beast.

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Entropy of Black hole

Introducing thermodynamics to Black holes.

Entropy is the term which when we read about it leads us to the path towards thermodynamics. In the early 1800s, researchers and scientists started studying heat, temperature, and the behaviour of gases, which later evolved into thermodynamics. According to thermodynamics and the famous three laws of thermodynamics, it says that:

• The zeroth law states that if two bodies are each in thermal equilibrium with a third body, then the first two bodies are also in thermal equilibrium with each other.
• The first law states that the total energy of an isolated system always remains constant. It can only transform from one state to another but never be destroyed.
• The second law states that the change in the entropy of the entire universe can never be negative.
• The third law states that the entropy of a system at absolute zero is a well-defined constant.

So, considering all this above, many controversies and paradoxes arise when we try to apply them to black holes. As black holes have mass, rotation, and temperature, it is obvious for them to have entropy, so as the second law states that (the total energy of an isolated system always remains constant, it can only transform from one state to another but never be destroyed). The energy of a black hole should always remain constant, but if you could throw an object (with a considerable amount of entropy) into a black hole, the entropy would simply go away. It would vanish nowhere. In other words, the entropy of the system would get smaller and smaller, which would violate the second law of thermodynamics. Considering another situation is that the classical black hole has a temperature of absolute zero. This means you could take a bucket full of hot water and throw it into a black hole, which would essentially be cooling an object to absolute zero. It is a violation of the third law of thermodynamics.

Bekenstein-Hawking entropy :

 Bekenstein-Hawking entropy, also known as black hole entropy, is the amount of entropy that a black hole must have in order to obey thermodynamic laws as interpreted by observers outside the black hole. A black hole can be formed in many ways . After it settles down, space and time outside are described by only M and J. The radiation it emits is essentially thermal. It can’t depend on the information inside without violating causality or locality. 

There are several ways to justify the entropy of a black hole.

• Considering the loss of signal with a body outside the black hole, when a body enters into a black hole, it is the same as the loss of information, and in ordinary physics, entropy is the measure of the loss of information. Hence, entropy can be defined for a black hole.
• A black hole is usually formed from the collapse of matter under its own gravity or radiation. Both the terms which relate to the formation of a black hole, i.e., matter and radiation, are associated with entropy. However, the black hole’s matter inside is unknown to the observer outside the black hole. Thus, a thermodynamic layout of the collapse from that observer's point of view cannot be based on the entropy of that matter or radiation (the key roles in the formation of a black hole) because these are unobservable. Associating entropy with the black hole provides a handle on thermodynamics.

 

Formulation for a concrete formula for entropy…

There is a need for a concrete formulation to describe the entropy of a black hole, but from the above discussion it is clear that only the observable parameters can be considered for the formulation of black holes. So the major observable parameters were mass, angular momentum, and electric charge. So, taking the area theorem into consideration, all these parameters come into the same combination as that which represents the surface area of a black hole. The area theorem states that the surface area of a black hole can’t decrease; it can only increase in black hole transformation. So, the final formulation provided as a solution to all these is

                                                   

Where,

             A represents the surface area of black hole.

             G Newton's gravity constant.

             h the Planck-Dirac constant (h/(2π)).

             c speed of light.

   For, Schwarzschild or spherically symmetric black hole the horizon's radius is 

So,                      

                                     A=16π(GM/c2)2

Hence, the considerable efforts to make all the parameters fit to make a defined formulation to find the entropy of black was possible, but still, much more research is going on to find more reasonable formulations in the present and future.

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