Event Horizon

S=k(4πR^2)/(2l)^2

This is Bekenstein–Hawking formula about black hole. 4πR^2 is event horizon which is the end of the universe. l is Planck length. It is about 1.616*10^-35(m).

They are symmetry. Entropy increases according to the length of black hole. It is chaotic.

v^2/2=GM/r

This is law of the conservation of energy. Kinetic energy is universal gravitation. If the horizon (r) were small, the gravity would increase. Therefore, the kinetic energy is faster to escape from the black hole. This is speed of light.

r=2GM/c^2

There is the horizon even in the speed of light. You can't escape from the black hole.

You need singularity for expansion of time and space.