Black Holes and Singularities
Is there really a singularity at the centre of a black hole?
If matter is to be concentrated to a point inside a black hole, a neutron at absolute zero must be in some way compressible and several neutrons must be able to exist in the same place. I know of no direct evidence for either.There could be a critical mass when the radius of a cold spherical neutron star is equal to the event horizon. This is about 100 times the mass of the Sun at 2×1032kg.
It can be shown that the maximum rate of spin for a cold neutron star before losing matter by centrifugal force is 109 revolutions per second. The matter is lost from parts of greatest radius and the rotation speeds up as the star shrinks until it becomes a line of neutrons. The gravitational force at the end of the line is only 1.87×10-52N: much too small for any further collapse: again avoiding a singularity.
The force towards the centre on a neutron inside the neutron star is
which is finite, and falls to zero at the centre; so again there is no singularity: where ro is the radius of the neutron star.
I therefore conclude that there is no singularity at the centre of a black hole; on three counts.
J F Fleming 16 November 2010