Schwarzchild Radius

Not Reviewed
Equation / Last modified by EdwardOmbui on 2015/09/16 12:29
Schwarzchild Radius
Variable Instructions Datatype
Mass of Star Enter the mass in your chosen units Decimal (kg)
Type
Equation
Category
vCommons
Contents
1 variables
Rating
ID
MichaelBartmess.Schwarzchild Radius
UUID
98df02ac-219a-11e4-b7aa-bc764e2038f2

The Schwarzchild Radius, `R_S`, is the radius defining the maximum size of a star necessary to create a black hole.  In other words, a mass must collapse to a size having a radius smaller than this radius to become a black hole.

Any mass with a radius less than the Schwarzchild Radius will have an escape velocity greater than the speed of light, so even light cannot escape it's gravitational grasp.  The Schwarzchild Radius also defines the sphere sometimes referred to as the Event Horizon.  Since light cannot escape from a black hole, a Star of this dimension has a spherical surface inside of which we cannot see events occurring.

Input to this equation is M, the mass of the star.

Black Hole

Notes

Current theory suggests that a burned-out star of approximately three times the Sun's mass will collapse under its own gravity and form a black hole.  This equation then suggests that such a star, once collapsed, would have an event horizon of less than 6 miles (less than 9 kilometers).

So, what then would be the approximate density of such a three-solar mass black hole?  Greater than `2E18 kg/m^3`.  That's more than 100,000,000,000,000 times denser than gold.