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### What are black holes

According to special theory of relativity, the maximum velocity that can exist is the velocity of light
c=3X108 m/s
Now we also Know that escape velocity which is the velocity needed for an object to become essentially free of the gravitational effect of another object is given
$v=\sqrt{\frac{2\mathrm{GM}}{R}}$
or
${v}^{2}=\frac{2\mathrm{GM}}{R}$
We may speculate on the mass and radius of a steller body that has an escape velocity of c.
Then
${c}^{2}=\frac{2\mathrm{GM}}{R}$
or
$R=\frac{2\mathrm{GM}}{{c}^{2}}$
This quantity R is called the Schwarzschild Radius and is usually designated by RS
Substituting the values of G and c,we have
RS=1.485 X10-2 M
The above equation gives us the relation between M and RS. It states that A body of Mass M in kg and radius RS in m or smaller produces such a strong gravtitional at its surface that no particle on its surface can escape.This even applied to electromagnetic radiation ( photons) including light.
So Even light cannot escape from such planet or body. That is the reason such body bodies are termed as Black holes
The most common way for a black hole to form is probably in a supernova, an exploding star. When a star with about 25 times the mass of the Sun ends its life, it explodes. The outer part of the star screams outward at high speed, but the inner part of the star, its core, collapses down. If there is enough mass, the gravity of the collapsing core will compress it so much that it can become a black hole. When it’s all over, the black hole will have a few times the mass of the Sun. This is called a “stellar-mass black hole”, what many astronomers think of as a “regular” black hole.

### Fictitous Force and Free falling Elevator

A non inertial Frame of Refrence is the frame of refrence which is having acceleration(a0) Example Free Falling elevator
Newtons law are valid in inertial frame of refrence only. We cannot apply them as it is in non inertial frame of refrence as it left out the acceleration of the object because of the frame of refrence.
Let me provide simple example to illustrate this.
You are moving in car which is accelerating. From your frame of refrence,a block on the road would be accelerating in opposite direction.
Now if we apply newton's law, we will find acceleration to be zero as no net force is acting. But the block has acceleration from car frame of refrence.
So to fix this issue,we will add one fictitous quantity in the Newton law equation like
F+F0=Ma
Where F0 is the fictitous force and it is in opposite direction of accleration frame
F0=-Ma0
Where ais the acceleration of Non inertial frame of refrence
Now let me further illustrate this with example of free falling elevator
A free falling elevator is an non inertial frame of refrence.The acceleration of the elevator as defined from the observer on the ground will be
g=-gk
Where k is the unit vector along vertical axis in the upward direction
Let us take an unattached object of mass M in the elevator.
From the frame of refrence of free falling elevator,Two forces are acting on the mass
Fictitous Force due to non inertail frame of refrence
Ffic=MgIt is opposite to the acceleration of the elevator
Gravitional Force on the Mass
FG=-Mgk
So the total Force on the body from elevator frame of refrence
FT=Ffic+FG=0
Which mean body is unacclerated in the elevator frame of refrence. The body will appear to be suspended in the air ,if it has no initial relative velocity to the elevator
Few more important things about Fictitous force
• Fictitous force are called pseudo force.
• It simple represent the effect of the acceleration of the non inertial frame of refrence
• They dont have any physical significance
• Whenever we work the problem in non inertial frame of refrence,always make sure to include fictitous force in the newton law