The Physics behind the Schwarzschild Radius

            First of all, the equation for which Schwarzschild solved Einstein's equations of General Relativity is as follows,

            This equation shows that the Schwarzschild Radius, or rs, is equal to twice the Gravitiational constant (G=6.67x10^-11 N(m/kg)^2) multiplied by the mass of
    the object, and divided by the speed of light (c=3x10^8 m/s) squared. As the Schwarzschild Radius relies only on an objects mass, every object has an associated     Schwarzschild Radius.
            So, lets find a few Schwarzschild Radius' that are easy to relate to,

An average human has a mass of about 70kg, so by entering that into the equation for the Schwarzschild radius, we get:

Which is equal to 1.04x10^-25 meters. or .1 yoctometer.

For the Earth, the equation would be:

So the Schwarzschild Radius of the Earth is ~.009 meters.

At 9mm, we really shouldn't be worried about the Earth collapsing into a black hole. So, using the equation for the Schwarzschild radius, its pretty easy to see that it requires a lot of mass to have a realistic point that an object can be compressed to so as to create a gravitational singularity. As another example, the Schwarzschild radius of the sun is around 3 kilometers. This should also show just how incredibly dense an object becomes for it to collapse under the force of its own gravity.

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