What is Gravitational Singularity?-The Infinite gravity

  A Gravitational Singularity or Space time singularity is a location in Spacetime where the gravitational field of a celestial body becomes infinite that does not depend on coordinate.  Something is singular when it is one, odd, not just any individual or single. A singularity is like the answer to a question for which there is no answer. 

We know that,
         r_s = 2GM/c²

^{c=speed of light} 

^{G=gravitational constant}

^{M=mass of the object}

 ^{r_s =Schwarzschild radius}

 ^{here c and G are constants.}

^{Now if a sphere shape mass M is squeezed then mass will be the same but its volume  gets smaller. If it is squeezing more then it will become tiny but stay as massive as before. All the molecules compressed close to each other until it reaches a critical size and that is the Schwarzschild radius-the radius of a sphere mass when all masses of the object are compressed within the sphere, the escape velocity from the surface of the sphere would equal the speed of light this means in order to escape the gravitational pull of the object have to move faster than speed of light but it is not possible because only light can travel in this speed.}

^{Now the radius of earth is 6371 km the Schwarzschild radius will be only 8 mm. How massive a sphere object is it does not matter because it will be divided by the square of velocity of light that is huge.}

                                                           Pic courtesy: www.wikipedia.org

   

     If the object's radius is less than Schwarzschild radius  i.e.r<rs 

then it becomes a black hole.
Schwarzschild metric has the form with signature coordinate (1,-1,-1,-1)
$}$
where,

• when dτ² is positive, τ is the proper time (time measured by a clock moving along the same world line with the test particle),
• c is the speed of light,
• t is the time coordinate (measured by a stationary clock located infinitely far from the massive body),
• r is the radial coordinate (measured as the circumference, divided by 2π, of a sphere centered around the massive body),
• θ is the colatitude (angle from north, in units of radians),
• φ is the longitude (also in radians), and
• r_s is the Schwarzschild radius of the massive body, a scale factor which is related to its mass M 

what happens if the object's radius is zero.i.e. r=0
we know Y=f(x), Y=1/x and if x→0 then Y→∞  if x=0 then Y=∞ 
rs /0 =∞ 
  so the equation will be the infinite, in the middle of a black hole r becomes zero so the gravitational field becomes infinite. So in the middle of a black hole is an example of gravitational Singularity.

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