black holes's singularities

[papernuke]

I just thought of this
if black holes are created when super-massive stars collapse onto themselves to create singularities, then how can the singularity's gravitational force be so massive if it was created from the same mass that the super-massive star was.
the gravitational pull from that a singularity has would be impossible because by the conservation of matter, the singularity must have the same gravitational attraction as the super-massive star, since no mass was added or lost, so the gravity must have remained constant.
and if the gravitational pull were the same, then the singularity would not be a black hole because light would be able to escape from it, simply how light can escape from the super-massive star.

[wendy]

The black hole is considerably smaller than the star that produced it.

Consider the sun. The diameter of the sun is roughly 864000 miles. At the surface, the force of gravity is small, that light freely escapes. Where the sun to collapse to a black hole or a neutron star, gravity would be unchanged, and the planets would still orbit it, providing they survive any event that accompanies the collapse (usually a super-nova, but the devil's in the details).

The schwarzchild radius of the sun is the diameter of the black hole: literally, the radius where the escape velocity is the speed of light. For the sun, this is roughly one mile. The actual mass of the sun in this radius is very tiny, about 1e-18 of the total solar mass, so light escapes even here.

When a star looses the outwards pressure that prevents it collapsing, then gravity takes over, and the star crumbles under its own weight. For stars less than 1.4 solar masses, the diameter is larger than the schwarzchild radius, the result is a neutron star. For larger stars, the gravity takes it past this point, eventually falling into an ever-denser state. A black hole forms.

Mass is indeed not lost, but what happens when a black hole or neutron star forms, is that there's a lot more space before the surface is met, or more accurately, there is more matter much closer to a point on the surface, and gravity is indeed more. In a super-massive star, the distances are much larger, and the escape velocity is much smaller.

[papernuke]

ok, I understand now.
also, how could the diameter of a black hole's event horizon be calculated?

[wendy]

http://en.wikipedia.org/wiki/Schwarzschild_radius R=2Gm/c² For metrics, ye get roughly m/25c³, when m is in kgs and c in mtr's/s.

This is the formula that determines the diameter of a black hole, of mass m.

Note that this is the diameter of the black hole: the surface where the escape velocity is c, not the size of the object causing it. A black hole might be caused by a pinpoint sized thing, yet the radius of the black hole might be several miles across. It's just that you're "still in the air" when the escape velocity exceeds the speed of light.