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dark stars | John Michell bio | John Michell paper

The Eighteenth-Century "Dark Star"

A dark star was a theoretical object that obeyed the laws of Newtonian mechanics, and had a surface escape velocity that equalled or exceeded the speed of light. A crude calculation would tell us that light emitted at the surface of a dark star should be trapped by the star’s gravity, but dark stars also supported indirect radiation effects – light (and matter) leaving the star's surface could escape a little way beyond the horizon before gravity turned it around and pulled it back in, and during that brief visit, these emissions had a chance of colliding with other passing particles and generating secondary signals outside the horizon, or even being knocked completely free. These indirect-radiation effects due to visiting particles generate effects that appear to have counterparts under quantum mechanics, that are usually blamed on virtual particles.

This "indirect radiation" mechanism doesn't exist under Einstein's geeneral theory of relativity. Under GR1915's observerspace conventions, since a photon emitted at or below r= 2M can't reach a distant observer (without help), it's considered never to have left the region bounded by the r = 2M surface at all.  Under GR, this special surface (the event horizon) permanently screens off the contents of a black hole from the outside universe. The GR1915 counterpart of the dark star is not merely dark, its zero-emisisons make it utterly black, and since the outside observer can no longer sense any specifics about the event horizon's contents, it no longer appears as a conventional body, but as something like an informational "hole" (giving us the GR1915 phrase, "black hole").

The case of indirect radiation from a (hypothetical) dark star now seems to be accepted as a legitimate class of Hawking radiation (as an example of indirect radiation through an acoustic horizon), albeit in a non-GR1915 context. Current wisdom (circa 2008) seems to be that this is sheer coincidence and has no deeper significance ... but so far, the results of the "archaic" calculations don't seem to be distinguishable from their more modern QM counterparts – if you were to decide that GR1915 was wrong, and that Newtonian optics (with a few updates) was right, then you'd seem to get get "good" QM-compatible answers. Since quantum gravity researchers are now using acoustic metrics to model Hawking radiation across a gravitational horizon, dark stars give us a quick way of visualising the expected predictions of quantum gravity, without actually knowing anything about quantum gravity. 

Although the Newtonian physics that generated the "dark star" description was obviously incomplete, its results demonstrate that Hawking radiation doesn't have to be QM-specific.

Dark star history

John Michell and dark stars

In 1783, John Michell wrote a long letter to Henry Cavendish describing the properties that we'd expect of stars with a high surface gravity. Michell's letter was then 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 wouldn't 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 measure the surface gravity of distant stars that were outside this limit by measuring 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 then cited Isaac Newton as saying that blue light was less energetic than red (Newton had thought that more massive particles were associated with "bigger" wavelengths), which put Michell’s predicted spectral shifts in the wrong direction. It's difficult to tell whether Michell’s careful citing of Newton’s position on this reflected a lack of conviction on Michell’s part over whether the mighty Newton was correct, or whether it just represented academic thoroughness. 
If Michell had been able to use the correct proportional relationship between the energy and frequency of light, then he'd have been faced with the same apparent paradox that confronted Einstein in 1911: that if someone observing a weaker-gravity object saw that object to have a gravitational blueshift, the only way they could see an increased frequency persisting indefinitely would be if the weaker-gravity object was ageing more quickly, and if the local rate of timeflow was a function of background gravitational field intensity. 

Laplace and dark stars

A few years later, Pierre-Simon Laplace also considered the idea of gravitationally-cloaked stars in his book, “System du Monde”, apparently independently of Michell. Laplace's mention of the concept was fleeting, and was apparently removed from later editions of his book. However, since Michell's work (in England) got hit rather harder by the political fallout (and ensuing coverup) associated with the Newtonian Catastrophe than Laplace's (in revolutionary France), citations of Laplace's work survived more easily, and until comparatively recently, the concept of the dark star was generally attributed to Laplace rather than to Michell. 

In Brief ...

  • Dark stars are “dirty” and they “smell” – they support an 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.

  • GR1915's black holes are clean and smell-free. They have no proper sustainable atmosphere (although they may have accretion disks) and they thermselves emit no radiation at all (although hot infalling accreted matter around them may radiate strongly).

  • QM’s description of black holes differs from GR’s – according to QM black holes are again “dirty” and “smelly” ... but it's not yet agreed exactly what a QM black hole ought to smell of. Since dark stars and quantum-mechanical black holes both obey the same basic statistical laws of thermodynamics and information theory, it's not immediately obvious how we would tell these two sets of predictions ... pre-GR1915, and post-GR1915 ... apart. 

Recent work on QM and black hole theory has tended to recreate characteristics that existed in the "Newtonian" descriptions, but were absent in the GR1915 version, for instance, post-2005 it has been increasingly recognised that the information encoded in Hawking radiation must relate to information that previously fell into a black hole: the characteristics of the emissions from the hole depend on the hole's contents.

  • Simon Schaffer, "John Michell and black holes" Journal for the History of Astronomy 10 42-43 (1979)
  • Gary Gibbons, "The man who invented black holes [his work emerges out of the dark after two centuries]" New Scientist, 28 June pp.1101 (1979)
  • J Eisenstaedt, "De L'influence de la gravitation sur la propagation de la lumière en théorie Newtonienne. L'archéologie des trous noirs" Arch. Hist. Exact Sci. 42 315-386 (1991) 
  • Werner Israel, "Dark stars: The evolution of an idea", pages 199-276 of:
    Hawking and Israel (eds), Three hundred years of gravitation (1987) 
  • Kip S. Thorne, Black holes and time warps: Einstein's outrageous legacy (1994) Chapter 3 "Black holes discovered and rejected"
  • Eric Baird, Relativity in Curved Spacetime (2007) Chapter 11 "Dark Stars and Black Holes"

This article is a modified version of the article originally submitted by the author to Wikipedia, as "Dark_star"