When A Star Collapses Into A Black Hole, How Long Does It Take For The Star To Overcome Electron And Neutron Degeneracy Pressure? And How Long Do Those Transitions Themselves Take?

When a star collapses into a black hole, how long does it take for the star to overcome electron and neutron degeneracy pressure? And how long do those transitions themselves take?When all the hydrogen in a star is fused to helium the core contracts and core temperature increases. This increased core temperature and pressure causes helium to fuse into carbon via the triple alpha process.

This fusion releases more energy than fusing hydrogen to helium, causing an increase in radiation pressure. This increased radiation pressure pushes matter outwards, thus expanding the star. As the star expands its surface cools and becomes redder - a red giant is formed.

Large stars can go through many fusion cycles forming `shells` of heavier chemical elements around the core up to and including iron.

This is the approximate phase duration for a large 20-Solar mass star:

hydrogen ~ 10 million years

helium ~ 1 million years

carbon ~ 1000 years

oxygen ~ 1 year

silicon ~ 1 week

iron <1 day

Our sun isn t massive enough to be able to generate enough heat and pressure to fuse anything more than carbon - and it will take millions of years for it to go through that phase. But more massive stars can go further - and there are a great many stars far larger than our sun lurking in the cosmos. Large stars have disproportionately larger cores than smaller stars, therefore a much higher proportion of their mass is directly involved in the fusion process. This means they get through their available nuclear fuel much faster so their lifespan is shorter.

Once a large star starts fusing silicon at the centre, it enters its final stage. As the silicon fuses, the reaction is creating iron and nickel. However these won t fuse because this fusion reaction doesn t release energy since iron has the largest nuclear binding energy of all atomic nuclei. So you start getting a growing ball of iron at the core. Unlike all the previous phases of fusion, where the core was prevented from crushing inward due to the outward radiation pressure generated by the fusion reaction, the only thing supporting the iron core against further collapse is electron degeneracy pressure.

The Pauli exclusion principle states that no two fermions (in this case these fermions are electrons) with the same spin can occupy the same energy state in the same volume of space at the same time. When this is applied to the scale of stars, nature does not allow the unlimited compression of matter to extreme densities without matter itself suffering dramatic and catastrophic changes in its fundamental character. This is how the universe works, it is characterised by phase changes rather than continuously smooth transitions.

The growing iron core in the centre of the large star consists of electron degenerate matter. Thermonuclear fusion is no longer taking place so the electrons within the core now take on a more significant roll in the absence of any outward radiation pressure. The electrons are not specifically associated with any atomic nucleus but in fact there is a sea of electrons which keep each other at arms length due to the continual and rapid exchange of virtual photons. The more tightly they are compressed the more furious this exchange becomes and the faster the electrons move. However they can`t do this indefinitely, since electrons cannot travel faster than the speed of light. This is the limit, as soon as the electrons are forced to travel at the speed of light then electron degeneracy pressure has run its course and the core will collapse down to a neutron star - very quickly. Protons and electrons are forced together forming neutron matter via reverse Beta decay, collapsing a huge sphere of iron many thousands of miles in diameter, down to a newborn neutron star with diameter of the order 10 15 miles or so, in a matter of seconds. Above that the layers of carbon, oxygen and silicon start collapsing as well, because there s now a huge void where there used to be that iron core. All of this matter is now in free fall towards this compact sphere of neutrons and can reach 30 40% the speed of light. The impact on the ultra dense neutron core, plus the release of so much gravitational potential energy, is what powers the supernova explosion. Within the supernova the temperatures can reach billions of degrees allowing for the fusion and formation of trace amounts of chemical elements heavier than iron. Thus these supernova seed regions of galaxies for future solar system formation.

In the aftermath of the supernova, when the threshold of energy necessary to force the combining of electrons and protons to form neutrons (the electron degeneracy limit) has been passed, the core collapse continues until it is stopped by neutron degeneracy pressure. At this point it appears that the collapse will stop for stars with mass less than approximately three or four solar masses, and the resulting collection of neutrons is called a neutron star. The periodic emitters called pulsars are thought to be neutron stars.

Neutron degeneracy is a stellar application of the Pauli Exclusion Principle, as is electron degeneracy. No two neutrons can occupy identical states, even under the extreme pressure of a large collapsing star.

So to recap, with star masses less than 1.4 solar masses (the Chandrasekhar limit), the energy from the gravitational collapse is not sufficient to produce the neutrons of a neutron star, so the collapse is halted by electron degeneracy pressure to form white dwarf stars. Our sun will become a white dwarf star in around 5 billion years. White dwarfs are indefinitely stable and will gradually cool to form black dwarfs.

For larger stars, once the iron core reaches sufficient size and collapses, enough energy is available from the gravitational collapse to force the combination of electrons and protons to form neutrons. As the star contracts further, all the lowest neutron energy levels are filled and the neutrons are forced into higher and higher energy levels, filling the lowest unoccupied energy levels. This creates an effective pressure which prevents further gravitational collapse, forming a neutron star. The density of a neutron star is extreme - a teaspoon of material would have a mass of about 10 million tonnes, which creates an intense gravitational field with an escape velocity approximately 0.4 times the speed of light. It is generally accepted that neutron stars are complex layered objects with a central core composed of a quark gluon plasma. This is consistent with the best mathematical models.

However, for core masses greater than around 3 or 4 solar masses, even neutron degeneracy pressure can`t prevent further collapse and it continues toward the black hole state. Please note there is no strict upper limit on star masses. There are 20+ solar mass monsters are lurking in our galaxy and the billions of other galaxies in the universe. The key to when and how the star collapses is how rapidly the iron core forms, and the mass of material above it. Extremely high mass stars have short lives and undergo hypernova rather than supernova. These are the most energetic events in the cosmos.

With regard to defining a transition time for overcoming neutron degeneracy pressure, this would now be very difficult since time dilation effects are becoming important. It would depend which time we are talking about. Time runs slower near to any gravitational mass, and black holes are obviously the most extreme example of this. Inside the event horizon of the newly formed black hole time ceases to have any meaning

The speed of the collapse is determined by the star s gravitational field. The region where infalling matter would reach the speed of light is precisely the region that corresponds to the event horizon of the newly forming black hole. The time taken for the neutron degeneracy threshold to be passed would be less than a second if we could somehow witness the event from within the location. But this time would take far longer if we could view from our Earthly perspective since time passes much more slowly close to a large gravitational mass (the greater the gravitational field strength the slower time passes) such that at the event horizon of the newly formed black hole time would stop altogether. Matter falling toward the event horizon would appear to become increasingly red shifted and dimmer, but would never appear to completely fall into the hole. The same gravitational field that collapses the star also produces extreme, divergent time dilation. So to an outside observer, anything near the event horizon will appear to slow down and freeze (which is why black holes have been referred to as frozen stars .) So paradoxically perhaps, even as matter accelerates to nearly the speed of light, to an outside observer it appears to slow to a crawl and vanish from sight, since the same gravitational time dilation also redshifts any visible signal to invisibility .

It is also worth bearing in mind however, that as the black hole is forming its event horizon is growing. This means despite the fact that matter falling into the black hole experiences extreme time dilation, the black hole itself is engulfing matter at the same time due to its expanding event horizon. The rate at which this happens is determined by the mass of the original neutron star from which the black hole formed. These different interacting phenomena are why black holes are so complicated and elusive when we try to model them!

As the Universe ages indefinitely for us on Earth, an object falling into the black hole would experience a normal passage of time. This is the majesty of time dilation. To think about it a different way, if we were the one entering the event horizon of a black hole then we wouldn t notice time pass any differently. But if we could somehow survive the experience and then make it back to Earth, we would find the earth potentially millions or even billions of years older than when we left it!

General relativity has been successful in describing the macroscopic properties of black holes. However, at the microscopic level, it predicts that black holes have a singularity at their cores: a region where the gravitational field is infinitely strong. Within the picture of gravity presented by general relativity, such a singularity would destroy all information about the quantum states of matter falling into a black hole - properties such as Baryon number, Lepton number, charge and spin. Yet a fundamental principle of quantum mechanics is that information is preserved - a principle which gives rise to the conservation laws. The loss of information in a singularity is therefore entirely paradoxical and points to a fundamental incompatibility between general relativity and quantum mechanics. A long-standing hope has been that the application of a quantum theory of gravity to the descri ption of black holes would eventually resolve these contradictions.

In many ways the singularity is an admission of defeat. The laws of physics as we know break down inside the event horizon, nothing can escape, so we only need to concern ourselves with events at and outside the event horizon - Hawking radiation for example (emitted just outside the event horizon) actually causes isolated black holes to slowly evaporate through time, releasing their mass/energy back into the universe, meaning that black holes are still connected to the mechanics of the universe. That said the space inside the event horizon is also a reality. It must be made of something, maybe there is no such thing as a singularity - but in fact a state of matter currently beyond our comprehension.

To focus on the issue with a clearer mental picture, if we consider a (hypothetical) small black hole with the mass only that of the Earth. Then the Schwarzschild radius can be shown to be only 9mm. The event horizon is a sphere of only 18mm diameter but with the entire mass of earth contained inside this volume. It is almost beyond comprehension how so much matter could fit into so small a space.

In reality it is very unlikely small black holes such as this will be able to form, but it is useful for visualisation purposes. The mass of the sun is too low to create a black hole, but a one solar mass black hole would have a Schwarzschild radius of 2.96km. Compare this to a neutron degeneracy radius of the order 10km for a 1.4 solar mass neutron star, or to earth size for a solar mass white dwarf. With this in mind it becomes clear how extreme the compression of matter is inside the black hole. But it isn t sufficient to just side step the issue - stating that matter compresses down to the singularity where the curvature or spacetime becomes infinite. The singularity may not even be real.

It may turn out to be the case that quantisation of a special class of black holes (known as spherically symmetric black holes) is possible within a framework for quantum gravity known as Loop Quantum Gravity.

Theoretical analysis shows that a region of incredibly highly curved spacetime (where quantum effects of gravity can be manifest), rather than the mythical singularity, is what actually makes up the core of a black hole. While this promising and encouraging theory removes the singularity implied by classical general relativity, time for further research and modelling will be needed. This is to establish whether these results solve the problems associated with the information loss paradox and if the approach may be generalised to other classes of black holes.