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I think the planets would remain in orbit but orbits would be modified as suggested in this URL http://www.fourmilab.ch/gravitation/orbits/
I agree when the appropriate parameters had been put into the formula in the the URL that I reccomended the differences would be tiny
I must come back to the question of rotation, if rotation is of any relevance we have now replaced our Sun rotating at about once every 28 days with a black hole rotating in milli seconds if not micro seconds (who knows?) does this affect the planets if so to what degree?.I recant whether we should use Newton or Einstein it is not affected by this transition to a black hole we should have used Einstein all the time
My arithmetic may be wrong but it seems to me that every thing cancels out so that the rotational period is reduced by the same ratio as the radius is reduced this works out OK if I take a star of 10^6 Km radius rotating at once every 28 days and have it collapse to a neutron star of radius 10Km the rotation period would be 41 milli seconds This seems about right, the surface speed would be a reasonable 1530Km per second.
About what happend if the sun would suddenly become a black hole, I don't think planets would be sucked in, but I think probably a strong gravitational wave would be released from the sun, affecting the planets in some way (still not known from me).
Don't know about gravity waves, but I'd imagine you'd get a shock wave as the Sun first went supernova as its core collapsed.
Surely if there was no significant change in mass (as has been assumed) there would of been no pulse of gravitational energy.