[thedoc (OP)]

Josh Ansell asked the Naked Scientists:
   
Love the show, it's really interesting and so are the kitchen sciences. My secondary specializes in science so sometimes we do the kitchen science experiments.

My question is: a neutron star is a collapsed star and a black hole is a collapsed red giant what happens when a neutron star collapses, and what happens is a black hole collapses?

What do you think?

[evan_au]

Physicists think that no physical material can withstand the intense gravitational pull of a black hole, and so all matter entering the black hole must collapse into a gravitational singularity, inside the black hole.
See: https://en.wikipedia.org/wiki/Gravitational_singularity

When a neutron star collapses (due to sucking more matter of a nearby star, or if it merges with with another neutron star), it is expected to form a black hole.
However, some physicists think that there may be other states of matter, which have a higher density than neutrons, but which are able to withstand even more intense gravity than a neutron star without collapsing all the way into a black hole.
See: https://en.wikipedia.org/wiki/Exotic_star

[yor_on]

A black hole is a singularity, we don't know its inside, we can't prove its form, we can guess though. But it's already as 'compressed' as it can be. It's like asking what happens if you 'push' 'c'. Will it go faster?

[Navraj Sikand]

Black holes do not collapse they die due to Hawking radiation

[syhprum]

Black holes will not start to die until the temperature of the CMBR drops below their surface temperature which is in the mili Kelvin range most are absorbing energy.

[Janus]

Josh Ansell asked the Naked Scientists:
   
Love the show, it's really interesting and so are the kitchen sciences. My secondary specializes in science so sometimes we do the kitchen science experiments.

My question is: a neutron star is a collapsed star and a black hole is a collapsed red giant what happens when a neutron star collapses, and what happens is a black hole collapses?

What do you think?

Some stars, like our own Sun, become white dwarfs at the end of their life cycle.  These are essentially the cooling embers of a once active star.    However, There is a limit as to how massive a white dwarf can be. This limit, known as the Chandrasekhar limit is ~1.4 solar masses.   After that, the star cannot no longer support its mass by electron degeneracy pressure and the star would collapse into a Neutron star.   
Neutron stars also have a maximum mass. The Tolman–Oppenheimer–Volkoff limit, for cold, non-rotating neutron stars has been recently estimated to be 2.17 solar masses. 

If a white dwarf were to collect enough additional material it would collapse into a neutron star, and if a neutron star were to collect enough material it would collapse into a black hole.
These are not the usual methods by which neutron star or black hole are produced.  Both are produced by the collapse of stars at the end of their life cycle (just like white dwarfs.   What decides the end fate is how much mass is left after the collapse.  Our own star will blow off a good part of its mass before what is left shrinks to a white dwarf.  Stars much more massive than our own die by supernova, blowing off a large part of their mass.  Whether a neutron star or black hole is left behind depends on how massive the remnant is.  The more massive the original star was, the more likely it is to form a black hole.
All moderate to large mass stars that reach  either white dwarf, neutron star or black hole stages pass through a red giant stage first.   Red dwarf stars on the other hand never pass through a red giant stage. They just continue to burn fuel until they finally reach a blue dwarf stage. This takes trillions of years and no red dwarf has yet reached its end stage during the lifetime of the universe.