Relation between the sol, mass, gravity, and black holes

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Jeaaas
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I'm a fan. Not a physicist or astronomer.. But this question is bothering me. If the mass of an object increases to infinity as it approaches the speed of light, does that also create infinite gravity at the object?

And if so, if we consider the gas swirling around the black hole is very near the speed of light, wouldn't the mass of the gas be infinite? And therefore the gravity of the gas would be infinite. So. Does the inside of the black hole have infinite gravity or does just appear so because the gas at the edge has infinite gravity?
 
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Near the speed of light is not the same as at the speed of light. Since all objects with mass cannot go at the speed of light, their masses never become infinite.

Black hole gravity is not infinite. It is large enough so that the escape velocity is greater than the speed of light, so nothing can escape.