Light escaping a black hole

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Orodruin
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You are essentially doing the equivalent of trying to measure distances on the Earths surface with a ruler and a Mercator projection map. In both cases, you are mistaking a coordinate distance with an actual distance and drawing faulty conclusions from it.
 
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isn't this a space-time diagram that's been shifted from a flat-space scenario to a curved space scenario with the addition of the gravitational mass?

No. Doing that is physically impossible; it would violate conservation of energy (more precisely, it would violate the condition that the covariant divergence of the stress-energy tensor must be zero).

I'm just looking at the diagram and what is happening during the light-cone tipping and it seems to indicate that near the event horizon the velocity of a light pulse is greater toward the massive body than it is away from it.

One can choose coordinates in which the coordinate velocity of light is larger towards the massive body and smaller away from it. (Note that these coordinates are not standard Schwarzschild coordinates; in those coordinates the coordinate velocity of light in both directions is the same, and it gets smaller as the horizon is approached. The coordinates in which the light cones appear to "tip" as shown in the video are either Painleve or Eddington-Finkelstein coordinates.) But that is just a coordinate velocity; it has no physical meaning. No observer will actually measure light to have that velocity.
 

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