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Wrote 10^10^26 and 10^10^76 in original long hand exponential form to keep consistency with the rest of the article.
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Sorry about the 10^146 mistake. I was tired then. I found the correct value of 1.7x 10^106 + 10^40. It equals 2.077358491x 10^106 so I rounded because I know how Wikipedia is about rounding.'
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Given our assumption on the half-life of the proton, protons (and bound [[neutron]]s as well)<ref name=dying>A dying universe: the long-term fate and evolution of astrophysical objects, Fred C. Adams and Gregory Laughlin, ''Reviews of Modern Physics'' '''69''', #2 (April 1997), pp. 337–372. {{bibcode|1997RvMP...69..337A}}. {{doi|10.1103/RevModPhys.69.337}} {{arxiv|astro-ph|9701131}}.</ref><sup>,&nbsp;§IVA</sup> will have undergone roughly 1,000 half-lives by the time the universe is 10<sup>40</sup> years old. To put this into perspective, there are an estimated 10<sup>80</sup> protons currently in the Universe.<ref>[http://www.nap.edu/html/oneuniverse/frontiers_solution_17.html Solution, exercise 17], ''One Universe: At Home in the Cosmos'', Neil de Grasse Tyson, Charles Tsun-Chu Liu, and Robert Irion, Washington, D.C.: Joseph Henry Press, 2000. ISBN 0-309-06488-0.</ref> This means that the number of nucleons will be slashed in half 1,000 times by the time the universe is 10<sup>40</sup> years old. Hence, there will be roughly ½<sup>1,000</sup> (approximately 10<sup>–301</sup>) as many nucleons remaining as there are today; that is, ''zero'' [[nucleons]] remaining in the Universe at the end of the Degenerate Age. Effectively, all baryonic matter has been changed into [[photons]] and [[leptons]].
Given our assumption on the half-life of the proton, protons (and bound [[neutron]]s as well)<ref name=dying>A dying universe: the long-term fate and evolution of astrophysical objects, Fred C. Adams and Gregory Laughlin, ''Reviews of Modern Physics'' '''69''', #2 (April 1997), pp. 337–372. {{bibcode|1997RvMP...69..337A}}. {{doi|10.1103/RevModPhys.69.337}} {{arxiv|astro-ph|9701131}}.</ref><sup>,&nbsp;§IVA</sup> will have undergone roughly 1,000 half-lives by the time the universe is 10<sup>40</sup> years old. To put this into perspective, there are an estimated 10<sup>80</sup> protons currently in the Universe.<ref>[http://www.nap.edu/html/oneuniverse/frontiers_solution_17.html Solution, exercise 17], ''One Universe: At Home in the Cosmos'', Neil de Grasse Tyson, Charles Tsun-Chu Liu, and Robert Irion, Washington, D.C.: Joseph Henry Press, 2000. ISBN 0-309-06488-0.</ref> This means that the number of nucleons will be slashed in half 1,000 times by the time the universe is 10<sup>40</sup> years old. Hence, there will be roughly ½<sup>1,000</sup> (approximately 10<sup>–301</sup>) as many nucleons remaining as there are today; that is, ''zero'' [[nucleons]] remaining in the Universe at the end of the Degenerate Age. Effectively, all baryonic matter has been changed into [[photons]] and [[leptons]].


=== The Black Hole Era, from 10<sup>40</sup> years to 1.7×10<sup>106</sup> years from now===
=== The Black Hole Era, from 10<sup>40</sup> years to 2.077×10<sup>106</sup> years from now===
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Black holes will continue to form for another 10<sup>40</sup> years. Black holes will be able to form as long as there is baryonic matter in the Universe. As time goes on, Black holes will continue to get larger as they suck up more matter.
Black holes will continue to form for another 10<sup>40</sup> years. Black holes will be able to form as long as there is baryonic matter in the Universe. As time goes on, Black holes will continue to get larger as they suck up more matter.


Even though all of the protons in the Universe have decayed in the Black Hole Era, there can still be light in the Universe when a black hole ends its life. This is because, as the mass of a black hole decreases, the amount of radiation it emits increases. During the last few seconds of its life, an evaporating black hole emits a burst of light, X-rays, and gamma rays. This means that during the Black Hole Era the Universe will occasionally be filled with some light when a black hole ends its life. So the Universe will contain light for another 1.7x10^106 years. After 1.7 x 10^106 years all of the light in the Universe will be permanently gone as the last supermassive black hole ends its life. The Universe will then become permanently dark and devoid of all matter. The Universe will remain dark and devoid of all matter forever, because in 1.7x 10^106 years, there will be nothing left to create matter or light in the Universe. At this moment in time the Universe will enter its final Era which is called the Dark Era. Once the Universe enters the Dark Era it will remain in that Era forever.
Even though all of the protons in the Universe have decayed in the Black Hole Era, there can still be light in the Universe when a black hole ends its life. This is because, as the mass of a black hole decreases, the amount of radiation it emits increases. During the last few seconds of its life, an evaporating black hole emits a burst of light, X-rays, and gamma rays. This means that during the Black Hole Era the Universe will occasionally be filled with some light when a black hole ends its life. So the Universe will contain light for another 2.077x10^106 years. After 2.077 x 10^106 years all of the light in the Universe will be permanently gone as the last supermassive black hole ends its life. The Universe will then become permanently dark and devoid of all matter. The Universe will remain dark and devoid of all matter forever, because in 2.077x 10^106 years, there will be nothing left to create matter or light in the Universe. At this moment in time the Universe will enter its final Era which is called the Dark Era. Once the Universe enters the Dark Era it will remain in that Era forever.





Revision as of 04:24, 12 July 2008

The heat death is a possible final state of the universe, in which it has "run down" to a state of no thermodynamic free energy to sustain motion or life. In physical terms, it has reached maximum entropy (because of this, the term "entropy" has often been confused with Heat Death, to the point of entropy being labeled as the "force killing the universe"). The hypothesis of a universal heat death stems from the 1850s ideas of William Thomson (Lord Kelvin) who extrapolated the theory of heat views of mechanical energy loss in nature, as embodied in the first two laws of thermodynamics, to universal operation. See also 1 E19 s and more for more information regarding the heat death.

Origins of the idea

The idea of heat death stems from the second law of thermodynamics, which states that entropy tends to increase in an isolated system. If the universe lasts for a sufficient time, it will asymptotically approach a state where all energy is evenly distributed. In other words, in nature there is a tendency to the dissipation (energy loss) of mechanical energy (motion); hence, by extrapolation, there exists the view that the mechanical movement of the universe will run down in time due to the second law. The idea of heat death was first proposed in loose terms beginning in 1851 by William Thomson, who theorized further on the mechanical energy loss views of Sadi Carnot (1824), James Joule (1843), and Rudolf Clausius (1850). Thomson’s views were then elaborated on more definitively over the next decade by Hermann von Helmholtz and William Rankine.

History

The idea of heat death of the universe derives from discussion of the application of the first two laws of thermodynamics to universal processes. Specifically, in 1851 William Thomson outlined the view, as based on recent experiments on the dynamical theory of heat, that “heat is not a substance, but a dynamical form of mechanical effect, we perceive that there must be an equivalence between mechanical work and heat, as between cause and effect.” [1]

William Thomson (Lord Kelvin) - originated the idea of universal heat death in 1852.

In 1852, Thomson published his “On a Universal Tendency in Nature to the Dissipation of Mechanical Energy” in which he outlined the rudiments of the second law of thermodynamics summarized by the view that mechanical motion and the energy used to create that motion will tend to dissipate or run down, naturally.[2] The ideas in this paper, in relation to their application to the age of the sun and the dynamics of the universal operation, attracted the likes of William Rankine and Hermann von Helmholtz. The three of them were said to have exchanged ideas on this subject.[3] In 1862, Thomson published the article “On the age of the sun’s heat” in which he reiterated his fundamental beliefs in the indestructibility of energy (the first law) and the universal dissipation of energy (the second law), leading to diffusion of heat, cessation of motion, and exhaustion of potential energy through the material universe while clarifying his view of the consequences for the universe as a whole. The key paragraph is:[4]

The result would inevitably be a state of universal rest and death, if the universe were finite and left to obey existing laws. But it is impossible to conceive a limit to the extent of matter in the universe; and therefore science points rather to an endless progress, through an endless space, of action involving the transformation of potential energy into palpable motion and hence into heat, than to a single finite mechanism, running down like a clock, and stopping for ever.

In the years to follow both Thomson’s 1852 and the 1865 papers, Helmholtz and Rankine both credited Thomson with the idea, but read further into his papers by publishing views stating that Thomson argued that the universe will end in a “heat death” (Helmholtz) which will be the “end of all physical phenomena” (Rankine).[3][5]

Temperature of the universe

In a "heat death", the temperature of the entire universe would be very close to absolute zero. Heat death is, however, not quite the same as "cold death", or the "Big Freeze", in which the universe simply becomes too cold to sustain life due to continued expansion, though the result is quite similar.[6] For a "heat death" to occur, proton decay must take place.

Current status

Inflationary cosmology suggests that in the early universe, before cosmic expansion, energy was uniformly distributed,[7] and thus the universe was in a state superficially similar to heat death. However, the two states are in fact very different: in the early universe, gravity was a very important force, and in a gravitational system, if energy is uniformly distributed, entropy is quite low, compared to a state in which most matter has collapsed into black holes. Thus, such a state is not in thermal equilibrium, and in fact there is no thermal equilibrium for such a system, as it is thermodynamically unstable.[8][9] However, in the heat death scenario, the energy density is so low that the system can be thought of as non-gravitational, such that a state in which energy is uniformly distributed is a thermal equilibrium state, i.e., the state of maximal entropy.

The final state of the universe depends on the assumptions made about its ultimate fate, and these assumptions have varied considerably over the late 20th century and early 21st century. In a "closed" universe that undergoes recollapse, a heat death is expected to occur, with the universe approaching arbitrarily high temperature and maximal entropy as the end of the collapse approaches. In an "open" or "flat" universe that continues expanding indefinitely, a heat death is also expected to occur, with the universe cooling to approach absolute zero temperature and approaching a state of maximal entropy over a very long time period. There is dispute over whether or not an expanding universe can approach maximal entropy; it has been proposed that in an expanding universe, the value of maximum entropy increases faster than the universe gains entropy, causing the universe to move progressively further away from heat death.[citation needed] Finally, some models of dark energy cause the universe to expand in ways that result in some amount of usable energy always being available, preventing the universe from ever reaching a state of maximum entropy.[citation needed] The expectation of the scientific community as of 2007 is that the universe will continue expanding indefinitely.[citation needed]

Timeline for heat death

The Primordial Era, from the Big Bang to 155 million years after the Big Bang

The Primordial Era is the first Era of the Universe. There are no galaxies or stars in the Primordial Era. In this era, the Big Bang, the subsequent inflation, and Big Bang nucleosynthesis are thought to have taken place. Toward the end of this age, the recombination of electrons with nuclei made the universe transparent for the first time.

The Stelliferous Era, from 155 million years to 1014 (100 trillion) years after the Big Bang

This era, which we are currently inhabiting, is the time in which stars are formed from collapsing clouds of gas. About 155 million years after the Big Bang, the first star formed. After its formation, a star will begin to fuse some of its gas. Stars whose mass is very low will eventually exhaust all their fusible hydrogen and then become helium white dwarfs.[10] Stars of low to medium mass will expel some of their mass as a planetary nebula and eventually become a white dwarf; more massive stars will explode in a core-collapse supernova, leaving behind neutron stars or black holes.[11] In any case, although some of the star's matter may be returned to the interstellar medium, a degenerate remnant will be left behind whose mass is not returned to the interstellar medium. Therefore, the supply of gas available for star formation is steadily being exhausted.

The Milky Way Galaxy and the Andromeda Galaxy merge into one galaxy: 3 billon years from now

The Andromeda Galaxy is currently approximately 2.5 million light years away from our galaxy, the Milky Way Galaxy, and is moving towards it at approximately 120 kilometers per second. Approximately three billion years from now, or approximately 1.7×1010 (17 billion) years after the Big Bang, the Milky Way and the Andromeda Galaxy may collide with one another and merge into one large galaxy. Because it is not known precisely how fast the Andromeda Galaxy is moving transverse to us, it is not certain that the collision will happen.[12]

Coalescence of Local Group: 1011 (100 billion) to 1012 (1 trillion) years

The galaxies in the Local Group, the cluster of galaxies which includes the Milky Way and the Andromeda Galaxy, are gravitationally bound to each other. It is expected that between 1011 (100 billion) and 1012 (1 trillion) years from now, their orbits will decay and the entire Local Group will merge into one large galaxy.[13], §IIIA.

Galaxies outside the Local Group are no longer detectable in any way: 2×1012 (2 trillion) years

Assuming that dark energy continues to make the Universe expand at an accelerating rate, 2×1012 (2 trillion) years from now, all galaxies outside the Local Group will be red-shifted to such an extent that they are no longer detectable in any way.[14] Since the Local Group will have merged into one galaxy by then, this will be the only galaxy detectable by observers in our location.

The Degenerate Era, from 1014 (100 trillion) to 1040 years from now

Star formation ceases: 100 Trillion (1014) years

In 100 trillion years stellar formation will stop. At this point no more stars will be created in the Universe. The longest living stars in the Universe are Red dwarfs which have a lifetime of up to 100 trillion years. Red dwarfs will be the last stars left in the Univerese when they finally burn out in 200 trillion years. Once stellar formation ceases it will take another 100 trillion years before the last star burns out and dies because the smallest red dwarfs have a lifetime of 100 trillion years. The hydrogen fuel that stars use for fusion will be depleted in 200 trillion years, 100 trillion years after stellar formation ceases. Once the hydrogen fuel of large stars are depleted they will go supernova and become black holes. Once the hydrogen fuel of small stars are depleted they will become planetary nebula and later they will become white dwarfs. These white dwarfs will then turn into black dwarfs trillions of years later. The amount of time required for a white dwarf to become a black dwarf depends on the star. Once all of the stars deplete their hydrogen fuel they become cool and extremely dim. Formerly luminous bodies like stars cool and dim, eventually reaching the same temperature as the Universe's microwave background radiation.

The last stars in the Universe burn out and die: 200 Trillion (2x1014) years

The last stars in the Universe, the smallest Red dwarfs will burn out and die in 200 trillion years, about 100 trillion years after stellar formation ceases. The Universe will become extremely dark in 200 trillion years when the last star burns out. Even though all of the stars will burn out in 200 trillion years there can still be occasional light in the Universe. One of the ways that light can exist in the Universe beyond 200 trillion years in the future is if two white dwarfs with a combined mass of more than about 1.4 solar masses happen to merge, the resulting object undergoes runaway thermonuclear fusion. The result is a Type Ia supernova. Very, very rarely, the darkness of the Degenerate Age is dispelled for a few weeks while a supernova explodes. Another way that light can exist in the Universe beyond 200 trillion years is if brown dwarfs collide with each other. Occasionally, brown dwarfs collide with each other and form a new red dwarf star which can survive for upto 100 trillion years. When brown dwarfs collide with each other to form a new red dwarf star they can supply light for upto 100 trillion years whereas two white dwarfs colliding with each other supply a burst of light for only a few weeks. An advanced civilization 200 trillion years in the future would probably be able to manipulate the obits of stars and planets. This advanced civilization would probably be able to push brown dwarfs into each other for another 10^40 years. Thus the Universe could be filled with light from sextillions of stars for another 10^40 years until protons decay.

Planets fall or are flung from orbits: 1015 years

Over time, the orbits of planets will decay due to gravitational radiation, or planets will be ejected from their local systems by gravitational perturbations caused by encounters with another stellar remnant.[13], §IIIF, Table I.

White dwarfs and Black dwarfs fall or are flung from orbits: 1018 years

The same scattering effect happens to the white dwarfs and black dwarfs and their remnants within galaxies, leaving mostly scattered stellar debris and supermassive black holes.

Brown dwarfs, White dwarfs, and Black Dwarfs drift out of their galaxies: 1019 to 1020 years

Once the brown dwarfs , white dwarfs, and black dwarfs are flung from their orbits they drift off into space. In space the brown dwarfs, white dwarfs and black dwarfs encounter each other. The less massive objects tends to gain kinetic energy while the heavier objects lose it. As these encounters continue, most objects will gain enough energy to escape the galaxy, leaving a small fraction (approximately 1%) which fall into the central supermassive black hole. This process is expected to take from 1019 to 1020 years.[13], §IIIA;[16], pp. 85–87[13], §IIIA;[15], pp. 85–87

The supermassive black holes are all that remains of galaxies once all protons decay, but even these giants are not immortal.

Protons start to decay: >1032 years

The subsequent evolution of the universe depends on the existence and rate of proton decay. Experimental evidence shows that if the proton is unstable, it has a half-life of at least 1032 years.[16] If a Grand Unified Theory is correct, then there are theoretical reasons to believe that the half-life of the proton is under 1041 years.[13], §IVA. If not, the proton is still expected to decay, for example via processes involving virtual black holes, with a half-life of under 10200 years.[13], §IVF For the sake of definiteness, we assume in the rest of the timeline that the proton half-life is approximately 1037 years.[13], §IVA. Shorter or longer proton half-lives will accelerate or retard the process.

Half of all protons and neutrons decay: 1037 years

Given the above assumption on the half-life of the proton, one-half of all baryonic matter has now been converted into gamma radiation and leptons through proton decay.

All protons and neutrons decay: 1040 years

Given our assumption on the half-life of the proton, protons (and bound neutrons as well)[13], §IVA will have undergone roughly 1,000 half-lives by the time the universe is 1040 years old. To put this into perspective, there are an estimated 1080 protons currently in the Universe.[17] This means that the number of nucleons will be slashed in half 1,000 times by the time the universe is 1040 years old. Hence, there will be roughly ½1,000 (approximately 10–301) as many nucleons remaining as there are today; that is, zero nucleons remaining in the Universe at the end of the Degenerate Age. Effectively, all baryonic matter has been changed into photons and leptons.

The Black Hole Era, from 1040 years to 2.077×10106 years from now

Black hole estimated lifetimes[18]
Mass Lifetime
Mass of the Moon 1.1×1044 years
Mass of the Earth 6×1049 years
1 M 2.2×1066 years
10 M 2.2×1069 years
100 M 2.2×1072 years
1,000 M 2.2×1075 years
10,000 M 2.2×1078 years
100,000 M 2.2×1081 years
106 (1 million) M 2.2×1084 years
107 (10 million) M 2.2×1087 years
108 (100 million) M 2.2×1090 years
109 (1 billion) M 2.2×1093 years
1010 (10 billion) M 2.2×1096 years
1011 (100 billiion) M 2.2×1099 years
2×1011 (200 billion) M 1.7×10100years
1012 (1 trillion) M 2.2×10102 years
2×1012 (2 trillion) M 1.7×10103 years
1013 (10 trillion) M 2.2×10105 years
2×1013 (20 trillion) M 1.7×10106 years

Black holes now dominate the Universe. They will slowly evaporate via Hawking radiation. A black hole with a mass of around 1 solar mass will vanish in around 2.2×1066 years. As the lifetime of a black hole is proportional to the cube of its mass, larger black holes take longer to decay. The largest supermassive black holes, with a mass around 2×1013 (20 trillion) solar masses, will vanish in around 1.7×10106 years. Over most of a black hole's lifetime, the radiation emitted is predicted to be mostly in the form of neutrinos, with approximately 17% of the radiated energy in photons and 2% in gravitons.[18]

Black holes will continue to form for another 1040 years. Black holes will be able to form as long as there is baryonic matter in the Universe. As time goes on, Black holes will continue to get larger as they suck up more matter.

Even though all of the protons in the Universe have decayed in the Black Hole Era, there can still be light in the Universe when a black hole ends its life. This is because, as the mass of a black hole decreases, the amount of radiation it emits increases. During the last few seconds of its life, an evaporating black hole emits a burst of light, X-rays, and gamma rays. This means that during the Black Hole Era the Universe will occasionally be filled with some light when a black hole ends its life. So the Universe will contain light for another 2.077x10^106 years. After 2.077 x 10^106 years all of the light in the Universe will be permanently gone as the last supermassive black hole ends its life. The Universe will then become permanently dark and devoid of all matter. The Universe will remain dark and devoid of all matter forever, because in 2.077x 10^106 years, there will be nothing left to create matter or light in the Universe. At this moment in time the Universe will enter its final Era which is called the Dark Era. Once the Universe enters the Dark Era it will remain in that Era forever.


Ultimate fate

The lowly photon is now king of the Universe as the last of the supermassive black holes evaporate.

The Dark Era, 1.7×10106 years from now and beyond

After all the black holes have evaporated (and after all the ordinary matter made of protons has disintegrated, if protons are unstable), the universe will be nearly empty. Photons, neutrinos, electrons and positrons will fly from place to place, hardly ever encountering each other. It will be cold, and dark, and there is no known process which will ever change things.

By this era, with only very diffuse matter remaining, activity in the universe will have tailed off dramatically, with very low energy levels and very large time scales. Electrons and positrons drifting through space will encounter one another and occasionally form positronium atoms. These structures are unstable, however, and their constituent particles must eventually annihilate.[13], §VF3. Other low-level annihilation events will also take place, albeit very slowly.

The Universe now reaches an extremely low-energy state. What happens after this is speculative. It's possible that a Big Rip event may occur far off into the future. Also, the Universe may enter a second inflationary epoch, or, assuming that the current vacuum state is a false vacuum, the vacuum may decay into a lower-energy state.[13], §VE. Finally, the Universe may settle into this state forever, achieving true heat death.

Alternative Futures of the Universe

Freeman Dyson's "Time Without End: Physics and Biology in an Open Universe", 10^1500 to 10^(10^1100) Years

(10^1500) years – the estimated time until all matter decays to Fe56 (if the proton does not decay). See isotopes of iron. An alternative could be the following also according to Freeman Dyson's "Time without end: physics and biology in an open universe"

10^100000000000000000000000000 years – low estimate for the time until all matter collapses into black holes, assuming no proton decay 10^10000000000000000000000000000000000000000000000000000000000000000000000000000 years – high estimate for the time until all matter collapses into neutron stars or black holes, again assuming no proton decay.[1] This time assumes a statistical model subject to Poincaré recurrence. A much simplified way of thinking about this time is in a model where our universe's history repeats itself arbitrarily many times due to properties of statistical mechanics, this is the time scale when it will first be somewhat similar (for a reasonable choice of "similar") to its current state again.

10^(10^1100) years – scale of an estimated Poincaré recurrence time for the quantum state of a hypothetical box containing a black hole with the estimated mass of our entire universe.

Logarithmic scale

See also

References

  1. ^ Thomson, William. (1951). “On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule’s equivalent of a Thermal Unit, and M. Regnault’s Observations on Steam.” Excerpts. [§§1-14 & §§99-100], Transactions of the Royal Society of Edinburgh, March, 1851; and Philosophical Magazine IV. 1852, [from Mathematical and Physical Papers, vol. i, art. XLVIII, pp. 174]
  2. ^ Thomson, William (1952). “On a Universal Tendency in Nature to the Dissipation of Mechanical Energy” Proceedings of the Royal Society of Edinburgh for April 19, 1852, also Philosophical Magazine, Oct. 1852. [This version from Mathematical and Physical Papers, vol. i, art. 59, pp. 511.]
  3. ^ a b Smith, Crosbie & Wise, Matthew Norton. (1989). Energy and Empire: A Biographical Study of Lord Kelvin. (pg. 500). Cambridge University Press.
  4. ^ Thomson, William. (1862). “On the age of the sun’s heat”, Macmillan’s Mag., 5, 288-93; PL, 1, 394-68.
  5. ^ Physics Timeline (Helmholtz and Heat Death, 1854)
  6. ^ see http://www.physlink.com/Education/AskExperts/ae181.cfm for a more detailed explanation
  7. ^ "An introduction to cosmological inflation". proceedings of ICTP summer school in high-energy physics, 1998. Retrieved 2006-09-09. {{cite web}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
  8. ^ "Black holes and thermodynamics". Phys. Rev. D 13, 191–197 (1976). Retrieved 2006-09-09. {{cite web}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
  9. ^ "Thermodynamics of black holes in anti-de Sitter space". Comm. Math. Phys. 87, no. 4 (1982), 577–588. Retrieved 2006-09-09. {{cite web}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
  10. ^ The End of the Main Sequence, Gregory Laughlin, Peter Bodenheimer, and Fred C. Adams, The Astrophysical Journal, 482 (June 10, 1997), pp. 420–432. Bibcode:1997ApJ...482..420L. doi:10.1086/304125.
  11. ^ How Massive Single Stars End Their Life, A. Heger, C. L. Fryer, S. E. Woosley, N. Langer, and D. H. Hartmann, Astrophysical Journal 591, #1 (2003), pp. 288–300.
  12. ^ The Great Milky Way-Andromeda Collision, John Dubinski, Sky and Telescope, October 2006. Bibcode:2006S&T...112d..30D.
  13. ^ a b c d e f g h i A dying universe: the long-term fate and evolution of astrophysical objects, Fred C. Adams and Gregory Laughlin, Reviews of Modern Physics 69, #2 (April 1997), pp. 337–372. Bibcode:1997RvMP...69..337A. doi:10.1103/RevModPhys.69.337 arXiv:astro-ph/9701131.
  14. ^ Life, the Universe, and Nothing: Life and Death in an Ever-expanding Universe, Lawrence M. Krauss and Glenn D. Starkman, Astrophysical Journal, 531 (March 1, 2000), pp. 22–30. doi:10.1086/308434. Bibcode:2000ApJ...531...22K.
  15. ^ The Five Ages of the Universe, Fred Adams and Greg Laughlin, New York: The Free Press, 1999, ISBN 0-684-85422-8.
  16. ^ Theory: Decays, SLAC Virtual Visitor Center. Accessed on line June 28, 2008.
  17. ^ Solution, exercise 17, One Universe: At Home in the Cosmos, Neil de Grasse Tyson, Charles Tsun-Chu Liu, and Robert Irion, Washington, D.C.: Joseph Henry Press, 2000. ISBN 0-309-06488-0.
  18. ^ a b Particle emission rates from a black hole: Massless particles from an uncharged, nonrotating hole, Don N. Page, Physical Review D 13 (1976), pp. 198–206. doi:10.1103/PhysRevD.13.198. See in particular equation (27).

Further reading