What will be the gravitational pull of the Sun if the Sun contracts to a black hole, and would the Sun be a Schwarzschild black hole or not?
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Related: http://physics.stackexchange.com/q/130918/2451 and links therein. – Qmechanic Apr 10 '15 at 23:09
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At the distance of the Earth, the gravitational pull would be the same: its mass does not change just because it's concentrated in a small region of space, and the gravitational field of the black sun at that distance would therefore be unchanged.
Our friends at NASA have answered the question essentially the same way:
It would exert no more gravitational force on Earth or the other planets in the solar system than it does now. Why? Because it would contain no more matter than it does now and it would be no closer to the planets than it is now.
but they also state that the sun is not massive enough to end life as a black hole. The premise of your question is therefore unsound. "When the sun becomes a black hole" = never.
Of course if it did, we would not be around to care.
Floris
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As noted, the sun isn't on this path. But, the gravity from a black hole is not radically increased. If the sun became a black hole, its mass wouldn't change, and we would experience the same gravitational force. (I am not sure how close you have to get before you start to see the GR-type effects. But it's pretty close.)
zeldredge
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