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How can the speed and the mechanics of light be similar to the speed and the mechanics of gravity?

Most say that light cannot escape a black hole. Then gravity cannot escape a black hole either, so there would be no effects of gravity felt outside of this black hole.

Qmechanic
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If you're thinking in terms of waves, yes the mathematical formalism used in both cases are quite similar. Gravity does rid itself from the black hole, because the kind of wave (gravitational one) yielding gravitational radiation, what can be measured outside the event horizon. This gravitational irradiation moves on the speed of light.