How to become a Black Hole

In order to become a black hole a mass needs to be very compressed. So much so that the entire mass fits inside a sphere with a radius called the Schwarzschild radius. This radius depends on the mass. The more mass, the bigger the radius. So in order to become a black hole you either need to have a lot of mass (like a super massive star) or you need to be very small. Let's see how small we have to be.

The Schwarzschild radius is given as

rs=2GMc2

with G the gravitational constant approx. 6.674 10^-11 m^3kg^-1 s^-2 and c the speed of light 299,792,458 m/s. Using those units the resulting radius will be in meters.

G = 6674 * 10**-11
c = 299792458

def schwarzschild(M, G=G, c=c):
    return 2*G*M / c**2  

I weigh about 75kg and am about 1.70m tall. When I put my mass into the equation I'll get my Schwarzschild radius which I can compare to my current height.

mymass = 75

myheight = 1.7

myradius = schwarzschild(mymass)

​print("My Schwarzschild radius: ", myradius, "m")

print("Ratio compared to my height: ", myheight/myradius) 

My Schwarzschild radius:  1.1138739711152773e-22 m
Ratio compared to my height:  1.526204978376376e+22

In order to get a better understand of what that means we look at the size of a hydrogen atom. There are two sizes that we can look at, the covelant radius, which measures the size of the atom that forms the covalent bond, and the van der waal radius, which measures the size of the atom with regards to how close it gets to other atoms. Both are measured in picometres (10^-12m)

picom = 10**-12

covalent = 31 * picom

van_der_waal = 1.2 * picom

print("Ratio of my rs to a hydrogen covelant radius:", (covalent/myradius))

print("Ratio of my rs to a hydrogen van der waal radius:", van_der_waal/myradius) 

Ratio of my rs to a hydrogen covelant radius: 278307966645.1038
Ratio of my rs to a hydrogen van der waal radius: 10773211612.068537 

Looks like even if I was the size of a hydrogen atom I'd still be far too large to become a black hole. And if I could get that small even the event horizon telescope could not take a picture of me :P