A dark star was the Newtonian predecessor of the modern black hole – it was an object whose surface gravity was so strong that not even light could escape it.
Einstein's General Theory of Relativity incorporated modifications to NM relationships introduced by the special relativity, and as a result the physics of these objects is different: according to GR, these objects show more extreme behaviour, and are not just "dark" stars, but black holes.
Differences between a dark star and a black hole
Dark stars and black holes both have a surface escape velocity equal or greater than lightspeed, and a critical radius of r<=2M.
However, the dark star is capable of emitting indirect radiation - outward-aimed light and matter can leave the r=2M surface briefly before being recaptured, and whilst outside the critical surface, can interact with other matter, or be accelerated free from the star by a chance encounter with other matter. A dark star therefore has a rarefied atmosphere of “visiting particles”, and this ghostly halo of matter and light can radiate, albeit weakly.
This "classical Hawking radiation" mechanism does not exist under C20th general relativity. Under GR, a photon emitted at or below r=2M never manages to leave the region bounded by the r=2M surface at all. Under GR, this special surface is called the event horizon, and it permanently screens off the contents of a black hole from the outside universe.
Quantum mechanics, black holes, and dark stars
In the early 1970s, Jakob Bekenstein argued that the surface area of a black hole’s event horizon relates to its entropy, which in turn suggested that perhaps black holes perhaps ought to have a nonzero temperature, the implication being that they then ought to radiate. At about the same time, Borisovich Zel’dovich argued that according to QM’s general arguments, a spinning black hole (a Kerr black hole ) ought to somehow be capable of throwing off radiation – the tidal forces associated with frame-dragging should shear apart some of the quantum fluctuations around the spinning hole, so that the surrounding region sprayed radiation away like a muddy tyre on a spinning bicycle wheel. This argument could then be extended: we could argue from the general principle of relativity that if an observer was orbiting a “standard” black hole, the visible effects should be somewhat similar to a non-rotating observer suspended above a rotating hole. It’s not quite that straightforward, but if you swoop down and skim above the horizon of a non-rotating hole, something very like Zel’dovich’s radiation really ought to be hitting your spaceship’s front window. And, of course, tidal effects were also a feature of non-spinning gravity sources.
In 1974 Stephen Hawking boldly published (In a letter to Nature, "Black hole explosions") a general conclusion that all black holes had to radiate, and that if they were not adequately fed, they would end up radiating away all their massenergy until they disappeared altogether. The effect then became generally known as Hawking radiation.
The new description of the phenomenology of a “QM” black hole is very reminiscent of the old dark star descriptions. Both normally have a low (but non-zero) external temperature, and both might naively be expected by a distant observer to seem to be emitting no radiation at all, but get close, and the visiting particles (dark star) or virtual particles (Hawking radiation) will register on your detectors, (under QM, the “virtual” particles are said to become “real” when they interact with the observer).
With a dark star, there is also a statistical likelihood of some “visiting particles” being bumped out of the star’s atmosphere and escaping from time to time, and with a QM black hole there is a similar statistical probability of virtual particles outside the horizon being converted into real particles and escaping.
Dark Star History
John Michell and Dark Stars
In 1783 John Michell wrote a long letter to Henry Cavendish outlining the expected properties of dark stars, published by The Royal Society in their 1784 volume. Michell calculated that when a surface whose escape velocity was equal or greater than lightspeed generated light, that light would be gravitationally trapped, so that the star would not be visible to a distant astronomer.
Michell’s idea for calculating the number of such “invisible” stars anticipated C20th astronomers' work: he suggested that since a certain proportion of double-star systems might be expected to contain at least one “dark” star, we could search for and catalogue as many double-star systems as possible, and identify cases where only a single circling star was visible. This would then provide some sort of statistical baseline for calculating the amount of other unseen stellar matter that might exist in addition to the visible stars.
Dark stars and gravitational shifts
Michell also suggested that future astronomers might be able to identify the surface gravity of a distant star by seeing how far the star’s light was shifted to the weaker end of the spectrum, a precursor of Einstein’s 1911 gravity-shift argument. However, Michell cited Newton as saying that blue light was less energetic than red (Newton thought that more massive particles were associated with bigger wavelengths), so Michell's predicted spectral shifts were in the wrong direction. It is difficult to tell whether Michell’s careful citing of Newton’s position on this may have reflected a lack of conviction on Michell's part over whether Newton was correct, or whether it was just academic thoroughness.
If Michell had been given the correct (proportional) relationship between energy and frequency, he would have been tantalisingly close to being able to predict the existence of gravitational time dilation, perhaps one of the greatest missed opportunities in gravitational physics.
Laplace and Dark Stars
Newton’s mistakenly inverted relationship between energy and wavelength reinforced the apparent validity of some other inverted relationships given in his book Optiks, including the relationship between gravity and the time taken for light to cross a region (Shapiro effect), and a corresponding relationship between lightspeeds in rarer and denser optical media. Newton had said that lightspeed should be faster in glass than air, and when it was demonstrated that the reverse was true in the early C19th, the existence of Newtonian "light corpuscles", and the validity of calculations based on them, were widely considered to have been disproved. Subsequent C19th theory had more emphasis on the idea of light as a wave in a medium, whose properties did not necessarily have to be compatible with Newtonian principles or calculations.
Pierre-Simon Laplace’s mention of dark stars was remembered, but embarrassment in England over Newton having "gotten light wrong" led to a discreet veil being lowered over the contents of Optiks (which went out of print) and also over Michell's paper, which effectively became "lost" from the citation chain until its rediscovery in the 1970’s – Optiks was only resurrected and brought back into print when it was recognised that Newton had arguably pioneered the pilot wave and wave/particle duality approaches now appeared in quantum mechanics, but although Einstein had now reinvented the idea that gravity affected light (1911), and quantum mechanics had reinvented the “light corpuscle” as a “photon”, Michell’s paper was still considered wrong-headed, because by now we all knew that black holes were very different to dark stars.
C20th scientific biographies before 1970 tend to list Michell because of his work on the theory of earthquakes or his relationship with the Cavendish experiment rather than his work on the theory of dark stars. After Hawking’s paper generated a flurry of interest, Michell’s paper was rediscovered and he began to be championed as "The man who invented black holes".
Dark stars are "dirty" and they "smell" – they have a rarefied atmosphere ("dirt") and they emit EM radiation and particulate matter ("smell"). A dark star will smell of whatever it was that you originally fed it.
GR black holes are clean and smell-free. They have no proper sustainable atmosphere (although they may have accretion disks) and they emit no radiation at all (although hot accreted infalling matter around them may radiate strongly).
QM’s description of black holes is different to GR’s – they are "dirty" and "smelly", but although it is agreed that they have about the same amount of dirt and smell as dark stars, it is not yet agreed whether the dirt is “old” or “new”, or exactly what a QM black hole ought to smell of (see: black hole information paradox).
- "Black Holes and time warps: Einstein's outrageous legacy" by Kip S Thorne (1994) covers most of this material, especially Chapter 3: "Black holes discovered and rejected". It probably has the clearest easily-accessable account in print of how dark stars went in and out of favour. Very clear writing, references, and even a few nice drawings.
- Modern editions of "Optiks" have a foreword discussing its long period out of print and its eventual rehabilitation. Optiks includes the faulty association between big particles and big wavelengths.
- The issue of the "discreet veil" drawn by C18th physicists over much of Newton's Optiks-related work is difficult to find references for (because it's still not usually discussed in polite company), but the history is discussed in a footnote in the multi-volume "Mathematical papers", edited by D.T. Whiteside.