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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.

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    $\begingroup$ What is the relationship between the local value of $g$ and the escape velocity? $\endgroup$
    – BowlOfRed
    Commented Oct 11, 2020 at 1:41

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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 $c$.

As a non-physicist, I think this would be sufficient, but if you are interested, you should try to learn both, Newtonian gravity, and General Relativity, then you might get a clearer picture.

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  • $\begingroup$ "just by chance"? That sounds like an incredible coincidence. Has no one ever tried to explain it and prove that it must be the same? If not, that sounds like an amazing paper waiting to be written. $\endgroup$ Commented Oct 16, 2020 at 0:57
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Gravity "$g$" has units of ms$^{-2}$. You cannot compare this with the speed of light that has units of ms$^{-1}$

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  • $\begingroup$ ms means millisecond, which is not what you mean. You need a thin space or a center dot. $\endgroup$
    – G. Smith
    Commented Oct 11, 2020 at 2:23
  • $\begingroup$ @G. Smith. Good one! It's usually me who is the typesetting critic. $\endgroup$
    – mike stone
    Commented Oct 11, 2020 at 23:42
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What I gather since posting my question is that gravity at the event horizon of a super massive black hole (BH) can be vastly less than that at the event horizon of a small primordial black hole (PBH) and yet still light cannot escape. The reason for this is that the event horizon is the point at which the curvature of space induced by the BH curves back upon itself - think of water emptying via a drain in our dimension; it spins about the drain in a descending vortex starting at a boundary where the water is captured in such a curve, curving back upon itself as it courses down into the drain. In the case of the PBH, the curve of spacetime is so sharp as to create a commensurately high gravity; but it is the curvature of spacetime that is capturing the light and all else. The supermassive BH generates a vastly broader distortion of spacetime with a much greater radius and thus a much more gentle curvature at the point where it curves back upon itself resulting in a commensurately lower gravity at the surface of its event horizon. Hence it is the point where the curvature of space has curved back upon itself that is inescapable, not gravity.

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