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.