# Event horizon vs high gravitational field: How is it light can escape a gravity greater than the speed of light

Calculated event horizon using Schwarzchild radius for 10 Earth mass primordial black hole and get a diameter of 17.7336cm. Using spherical gravity calculation of g=GM/r^2, I get gravity at 1 meter of 3.984 x 10^15m/s^2. Given speed of light is c=299,792,458m/sec, how is it that light can escape the gravity outside of the event horizon? As a non-physicist, understanding has been light is trapped by gravity yet surface gravity of a supermassive black hole is much less than that of a primordial black hole even at multiples of the primordial black holes radius.

• What is the relationship between the local value of $g$ and the escape velocity? Commented Oct 11, 2020 at 1:41

You are supposed to calculate the escape velocity at the event horizon, which will (just by chance) come the same if you consider Newtonian gravity or general relativity. For the Scwarzschild metric, the escape velocity comes out to be $$c$$, and even if you consider the escape velocity due to Newtonian gravity, it will come out to be $$c$$.
Gravity "$$g$$" has units of ms$$^{-2}$$. You cannot compare this with the speed of light that has units of ms$$^{-1}$$