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.
References
- 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"
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