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Hi,
Since there is not yet a unified theory of everything take your pick on whether you want to talk about gravitons (quantum mechanics) or curved spacetime (general relativity).
When a sun becomes a black hole the event horizon is far below the original surface of the star. Gravity is not infinite at the event horizon and in fact at a distance from the singularity of the original surface the gravity would be as or a bit less than before. Gravity or spacetime around a mass is only dependant on the mass and the black hole has less mass than the original star because to form a black hole the original star blew up and lost a lot of mass.
The curvature of spacetime or gravity only becomes infinite if you get very close to the black hole singularity. This is because all the mass is concentrated at a point and you can get very close to it.
Before a star becomes a black hole there is a gravitational field which in GR is eqivalent to a particular curvature of spacetime. Once the black hole forms this curvature does not change. If you think it does then you need to say what force you think it is that somehow smooths out the original curvature of spacetime once a black hole forms.
Cheers
Paul
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