CHAPTER 3: GENERAL RELATIVISTIC IN BLACK HOLE

  

  The Black holes solutions are made by some huge non-physical assumptions. According to 2nd law of thermodynamics if a body is contracting some radiations have to pass through it for contracting. It not only has a contraction but also it has some resistance like viscosity, heat radiation, heat flow, etc . Stephen hawking, Roger Penrose gave solutions by assuming that the black holes only have gravitational collapse. And from that they assumed that there is a trapped surface around the black hole from which nothing can escape. For a rotating black hole the photon sphere gets converted into a ring. The image of a so called blackhole can be the shadow of any object ( for e.g. if we keep the tennis ball or any spherical object in front of sun's rays the shadow is created). 

 

  In Einstein's special  theory of relativity as shown in the image (ve=v) if we put the value of v>c then mathematically the time(t^1) can't exist because there will be negative in the square root which diverges us to imaginary axis. And if we put v=c then the t^1 becomes infinite. As mentioned in the previous chapter time and space interchange their values and signs. If we take the x,y,z coordinates in a straight line in pythagoras theorem as shown in the image and if some object is travelling faster than light then that object can see the things earlier than other person and also time will be slow for that person and he can see future and in a sense the decrement in speed of time will be proportional to the future time (i.e. for example he can go 1hr in future for some small increase in v, 2 hrs for big increase and so on...). In the image ds is the space-time curvature. This is a science fiction and in that there comes many paradoxes which can't be solved.

 However in quantum mechanics if we assume that value of h/4pie equal to 1 then we all can see that all effects of quantum mechanics. But the value of h/4pie is very much small approximately 10^-34 something. Therefore we can't see that things happening with our naked eyes. We can just calculate the probability of that position of that electron. For understanding the accurate position of that electron we must know the waves that are emitted by the person ( i.e. think that a person is walking in a path, we can't assume its exact path the maximum thing that we can do is calculate the probability, but that person knows where he is going. The waves are created after every millisecond in our body and environment and according to that waves it commands to our brain and we follow that exact path and that waves are also emitted in the surrounding from which the electron chooses its path and according to that waves that physical object works, but the biggest and most important difference is that we can the things that we can see and that object also works with our calculation but the electrons don't because the commander for that electrons are the waves that are generated by any object in the universe). But we can't calculate the waves that are generated by every object in the universe, so therefore if we detect the waves that are generated in a bounded we can predict the path more accurately than today's

technique, because today we calculate the probability by just using wavefunction. And therefore in quantum level all the laws get violated but not in the real world that we see like the so called blackholes. 

Stephen hawking also gave  theory of hawking radiation to strengthen the paradigm of black hole. And the theory got accepted because the radiation is due to relativistic quantum effects which is true for every object because every object emits radiation in quantum level. Highlight the point that the laws are only violated in quantum level and not in the real world ( reason mentioned above).

CHAPTER 2: HYPOTHETICAL BEHAVIOUR OF BLACKHOLE

  Stars usually have two forces due to which they contract and expand. There are some limitations of expansion and contraction, meaning after a certain mass they cannot expand. Because after a certain mass the force of contraction becomes much larger than expansion. The force of contraction is due to gravity and the force of expansion is due to radiation pressure.

  If the mass of a neutron star is more than 3 solar masses then gravitational force wins over repulsion due to radiation pressure . And also any star's radius in space cannot be smaller than Schwarzschild radius. The formula for Schwarzschild radius is 2GM/c^2 in which M is the mass of the object and c is speed of light in vacuum. It has a certain limit of expansion and contraction. The density of neutron star is very much higher than the Sun, approximately 100 trillion times more than the Sun. Therefore Schwarzschild radius for a neutron star is much higher than the Sun.

 Gravitational shift of an object are the waves that are emitted by an object as it moves away from  gravitational field. As it moves away, the color appears reddish and at only a few distance from which it stars moving away it appears blue. As it moves away the frequency of the wave decreases and the wavelength increases. And as the object is moving away, photon starts losing its energy due to which the reddish color appears. The value of gravitational shift is much smaller. For the Sun whose Schwarzschild Radius is approximately 3 km, the gravitational redshift is only about one millionth.

 If the photon particles are emitting from a spherical star of Radius R1  and it reaches at some receiver (assume on the Earth)  and the Radius at which the radiation is approaching is R2 and the escape velocity of that object is same as that of Earth. And the emitting wavelength is (lambda)1 and receiving wavelength is (lambda)2 and the gravitational redshift is z, then z is defined by change in wavelength/ initial wavelength. Assume the Schwarzschild radius to be RS. The Schwarzschild radius of black hole is 2M (by setting G=c=1). They came to be known as Schwarzschild black hole, derivation is written in image:

 Factor for the time part A=(1-2M/R1) and for radial part B = -(1-2M/R1)^-1. Therefore at R1=2M time becomes 0 and radial distance becomes -infinity and for R1<2M the signatures are changed and inside the blackhole time becomes space and space becomes time. At the event horizon z=infinity and in this case light cannot escape from event horizon and it should appear black. For a black hole mimicker, R1=2M(1+e),z=1/e^1/2 which is a huge value of z but not infinite and for black hole, e=0 which is not possible. This proves that light can escape from a blackhole mimicker it just bends due to intense gravity which is valid in mathematics and also follows Einstein's theory of relativity. The event horizon is assumed to be the origin and therefore R1=0 (at event horizon). This point has infinite density and pressure and it is a gravitational singularity where space-time curvature is infinite. Therefore the blackhole paradigm doesn't follow Einstein's theory of relativity.