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shminux comments on Questions for shminux - Less Wrong
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No, it's the same velocity regardless of direction, because the escape velocity is determined by the potential energy, which is just a number for each point and is direction-independent.
From here, you can escape the system planet Earth-SupermassiveBlackHole in almost every direction easy. But not even the light will escape this system if it goes from here toward the SMBH.
From the same point, much different escape velocities, dependent of the escape direction.
What do I miss?
Just like classically light gets consumed by the ground if you aim it wrong, in GR light gets consumed by the black hole if it gets close enough to the horizon (1.5x the horizon radius for a non-rotating black hole). If you aim it better, it misses the black hole and escapes to infinity.
Yes. And a rock flown 1000 km per second will not escape in one direction, it will escape in other.