No. Escape velocity is a purely Newtonian concept and represents a limiting velocity. The escape velocity from the surface of the Earth is 11.2 kilometers/second, which means that if you gave a particle this velocity at the surface, it will be able to travel all the way to 'infinity' and arrive there with zero speed. It continuously decreases with distance from the Earth so that to 'escape' the gravitational field of the Earth at a distance of 20,000 kilometers, you only need a speed of about 6.5 kilometers/sec. If you launched rocket 1 from the Earth at 10 kilometers/second, it could make it all the way out to 20,000 kilometers, at which point it might fall back to the Earth, but not before it had time to launch a second rocket at a speed of 6.5 kilometers/sec which could make it all the way to 'infinity'.
Black holes are very different.
It is sometimes portrayed that black holes are so massive that their escape velocity is the speed of light. In Newtonian terms, this means that if you were 'inside' a black hole, light traveling at 300,000 kilometers/sec would not be able to escape to 'infinity'. BUT, as the rocket example above shows, light could get any number of kilometers away from a black hole before falling back into the black hole so there really would not be any definite size to such a 'Newtonian' black hole whose escape velocity was the speed of light. This, in fact, is not the correct relativistic model for a black hole. It is only relativity, and not Newtonian physics, that applies to defining what is going on in this situation. We have no conceptual 'choice' in the matter.
General relativity provides us with TWO coordinate systems to choose from; the system used by the 'freely falling' observer ( similar to the 'proper' coordinates used in special relativity) and the coordinate system used by a distant observer trying to deduce what is happening near or inside the black hole. We 'live' in this later coordinate system because we are not falling into the black hole. The problem is that ALL of the possible coordinate systems used by distant observers have a 'coordinate singularity' at the distance of the black hole's event horizon. All of them predict that at this location, light will suffer an infinite redshift, AND that the equation we use for establishing the differences in position between events in space-time will always yield 'infinity' as an answer. This is not a gradual process, but happens exactly when our radial distance from the black hole equals exactly the event horizon radius of R = 2GM/c^2. Now, as seen from the coordinate system of the in-falling observer, NOTHING HAPPENS at R=2GM/c^2. He/she simply falls through this distance and continues inside, but of course cannot pass back again through the event horizon. The definition of the horizon distance or R=2GM/c^2 has the speed of light 'c' in it, and identifies this radius as being relative to the maximum signaling speed permitted in space-time. If you could signal with tachyons, or other faster than light particles, the event horizon radius would be smaller still according to the square of their velocity.
The important thing is that the event horizon is not a solid surface, and the reason that light cannot escape is not the newtonian explanation of 'escape velocity' Instead it has to do with a very sudden change in how distant observers see space-time behaving near the event horizon from their coordinate system.
Copyright 1997 Dr. Sten Odenwald
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