Stars generate energy and fuse lighter elements into heavier ones through nuclear fusion. The majority of stars produce energy by fusing hydrogen into helium. More massive stars can continue to fuse helium into carbon, carbon into oxygen, oxygen into silicon and silicon into iron. Once iron is produced, it signals the last step in any stable nuclear fusion reaction because the creation of elements heavier than iron consume more energy than can be produced. In general, most stars are not massive enough to fuse carbon and other heavier elements. These stars die off as stellar remnants known as white dwarfs which gradually cool over eons and settle as black dwarfs. The present universe is way too young for black dwarfs to exist. Stars massive enough to fuse carbon and other heavier elements typically explode as supernovae.
Currently, the universe is estimated to be 13.8 billion years old. The last stars in the universe are expected to fizzle out ~1014 years from now and the largest supermassive black holes are expected to evaporate completely via Hawking Radiation ~10100 years from now. From this time period onwards, most of the ordinary matter in the universe is predicted to be in the form of black dwarfs, brown dwarfs and free-floating planets. With no free hydrogen to from new stars, objects simply float around in a dark and empty universe. Nevertheless, quantum mechanics can still cause a number of interesting phenomena to occur.
If a ball is thrown at a wall, it would always hit the wall and bounce back. However, according to quantum mechanics, there is a very small chance the ball could hit the wall and pass right through it. This process is called quantum tunnelling and it can allow lighter elements to spontaneously fuse into heavier elements at zero temperature. Even though the probability of even a single event like this is incredibly small, over a sufficiently long period of time, an event with an infinitesimal probability of happening is bound to eventually happen.
Initially, a stellar remnant such as a black dwarf is mostly made of elements such as hydrogen, helium, carbon and oxygen. Given enough time, nuclear fusion via quantum tunnelling will cause all matter to fuse into iron. Likewise, elements heavier than iron should also decay into iron by nuclear fission and alpha particle emission. Technically, it is accurate to say that over sufficiently long timescales, a stellar remnant such as a black dwarf is still generating energy through nuclear processes via quantum tunnelling. An iron star is produced once all matter has been converted into iron. Such an object is basically a cold sphere consisting almost entirely of pure iron. The timescale required for ordinary matter in the universe to fuse into iron via quantum tunnelling is estimated to be ~101500 years. From here on out, all black dwarfs, brown dwarfs and free-floating planets would have turned into cold spheres of iron.
While an iron star can no longer undergo any form of nuclear fusion or fission, it is by no means in its state of lowest energy. Over an immensely longer timescale, an iron star could collapse via quantum tunnelling into a dense sphere of neutrons or a black hole. The timescale estimated for an iron star to collapse into a ball of neutrons is 10^1076 years (1 followed by 1076 zeroes) and the timescale for collapse into a black hole is 10^1026 years (1 followed by 1026 zeroes).
The collapse of an iron star into a neutron star would produce a huge outburst of energy over a very short period of time. Whether such an outburst constitutes a supernova explosion remains uncertain. Nevertheless, if a supernova does occur, a fraction of the iron is expected to be reconverted back into elements both heavier and lighter than iron. Some of the ejecta could fall back and form a disk of material around the newly born neutron star where planets could form out from the disk’s material. This is not impossible to conceive since planets are known to exist around neutron stars in the present universe.
Conditions favourable for carbon-based life might even be present on some of these planets since they contain elements both heavier and lighter than iron. Heavy elements such as uranium and thorium are radioactive while light elements such as hydrogen, carbon and oxygen are necessary for life. A planet formed out from the debris of such a supernova can produce its own internal heat for many billions of years by radioactive decay. As a result, it is possible to imagine a planet with a frozen icy surface and beneath it is an ocean of water kept liquid by heat from radioactive decay. It sure is intriguing to consider that carbon-based life could exist in a future so incomprehensibly distant that it might just as well be separated from the present universe by an eternity. Although life might exist for billions of years on such a planet, it is still no more than a fleeting instant in a future without end.
It should be understood that predictions regarding the far future of the universe should not be taken with certainty because our currently understanding of the universe is by no means sufficient for such predictions and new knowledge is added all the time. Finally, the possible existence of iron stars assumes that protons are stable and do not decay. This is a reasonable assumption because experiments thus far have not shown any evidence that protons decay.
Dyson, Freeman J., “Time Without End: Physics and Biology in an Open Universe”, Reviews of Modein Physics, Vol. 51, No. 3, July 1979