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In physics, a black hole is an object that, due to its large mass, has a surface escape velocity that equals or exceeds the speed of light. Because Newton's law of gravitation shows that an object will only become a black hole when it has an extremely large mass, the only objects known that can possibly attain such a high mass as to become a black hole are the stars in the universe.
Because the escape velocity equals or exceeds the speed of light, a pulse of light that is emitted from the surface of a black hole would not be able to escape from the gravitational pull and will therefore be trapped by the back hole's gravity. No pulse of light would therefore be able to leave the object. This means that (if the black hole is a star) the light from such a star would not reach us, and the black hole would be invisible. This is why the name "black hole" is used.
Black holes are still hypothetical objects, because gravitational trapping of light has not yet been observed.
In 1783 John Michell, a geologist , wrote a letter to Henry Cavendish outlining the theory of black holes. This letter was published by The Royal Society in their 1784 volume. Michell calculated that when the escape velocity at the surface of a star was equal to or greater than lightspeed, the generated light would be gravitationally trapped, so that the star would not be visible to a distant astronomer.
Michell also had a brilliant idea for proving the existence of black holes despite their invisibility: he suggested that since a certain proportion of double-star systems might be expected to contain at least one black hole, we could search for and catalogue cases where only a single star circulating in an orbit was visible. The invisible companion (towards which the visible star is attracted by gravity, which causes the orbiting) is then a likely candidate for a black hole.
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 (this is the so-called gravitational redshift).
In 1796, the mathematician Pierre-Simon Laplace promoted the same idea in the first and second editions of his book Exposition du système du Monde, apparently independently of Michell.
It would be an error to think that black holes are a consequence of Einstein's general theory and that the original black holes of Michell and Laplace are not "real" black holes.
The black holes which follow from Einstein's theory are not real because Einstein's theory is based on the idea that at the surface of a black hole, time itself stands still, which is clearly impossible. Hawking himself calculated that the surface of a black hole leaks Hawking radiation (electron-positron pairs) which slowly drains a black hole of mass.
When from the surface of a large spherical body (like the earth, the sun or a star) a projectile is balistically fired perpendicar to the surface and away from it, the projectile will generally fall back to the surface because of the gravitational pull. But if the initial velocity of the projectile exceeds a certain velocity, called the escape velocity, the projectile will not return to the surface. Using Newton's law of gravitation and Newton's laws of motion the escape velocity can be shown to be given by the following equation:
- vesc = (2G M/R)1/2
- vesc is the escape velocity
- G is the gravtitational constant (approximately equal to 6.7 × 10-11 N m2 kg-2)
- M is the mass of the body from which the projectile is fired
- R is the radius of the body from which the projectile is fired
At the surface of the earth, the above equation can be used to show. that the escape velocity is approximately 11 m/s.
Another interesting consequence of the above equation for escape velocity is that it can be used to calculate some basic properties of black holes. For a black hole the escape velocity is larger than the speed of light. It follows that, for a black hole:
- Rblack hole < 2GMblack hole/c2
- c is the speed of light (which is approximately 3.0 × 108 m/s.
- G is the gravtitational constant (approximately equal to 6.7 × 10-11 N m2 kg-2)
- Mblack hole is the mass of the black hole
- Rblack hole is the radius of the black hole
Hence, theoretically, a body can become a black hole by compressing it into a sphere of which the radius is given by the above equation for Rblack hole.
- The mass of the earth is 5.98 × 1024 kg. The earth would become a black hole if it would be compressed to a sphere with a radius of less than 1 cm. Because the actual radius of the earth is 6.37×108 cm, this would require the earth to shrink by a factor of approximately 600 million. Clearly, it is impossible to transform the earth into a black hole.
- The mass of the sun is 1.98 × 1030 kg. The sun would become a black hole if it would be compressed to a sphere with a radius of less than 3 km. Because the actual radius of the sun is 6.96×105 km, this would require the sun to shrink by a factor of approximately 200,000.
- Generally, only the stars in the universe are massive enough to become black holes. The larger the star the more easily it can become a black hole. Some stars may even be so massive that no compression is required to turn them into a black hole: those stars are already a black hole.
Observational evidence for black holes
There are some indications that the centre of our galaxy has a black hole. Figure 2 shows an animation of the motion of stars near a possible black hole at the centre of our galaxy. This animation, which is the result of observations made in the period from 1992 to 2006, shows that stars are attracted by an (optically) invisible centre of attraction. The invisibility of this centre of attraction may be caused by gravitational trapping of light as explained in the above theory section. That would mean that it is a black hole as theorized by Michell and Laplace based on Newton's theory.
The orbits shown in Figure 2 are Keplerian orbits and calculations (based on Keplerian orbits, i.e. based on Newton's theory) indicate that the centre of attraction has a mass of about 4.4 million solar masses..
That the orbits in Figure 2 are accurately described using Newton's theory, is an indication that if there is a black hole, this black hole is not an Einsteinistic black hole. For example, Figure 2 shows that there is no "slowing of time" near the black hole as predicted by Einstein's theory. Also, Figure 2 shows no signs of perihelion precession (see also the article Gerber's equation for more information) which is predicted by Einstein's theory, because one of the orbits describes a closed ellipse which is only possible when there is no perihelion precession. Additional observations over longer periods of time will be needed to more accurately estimate the amount of perihelion precession.
- John Michell "On the means of discovering the distance, magnitude etc. of the fixed stars" Philosophical Transactions of the Royal Society (1784) 35–57, & Tab III
- 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)
- In chapter 6, "Black holes", Stephen Hawking writes: "John Michell, wrote a paper in 1783 in the Philosophical Transactions of the Royal Society of London in which he pointed out that a star that was sufficiently massive and compact would have such a strong gravitational field that light could not escape: any light emitted from the surface of the star would be dragged back by the star’s gravitational attraction before it could get very far. Michell suggested that there might be a large number of stars like this. Although we would not be able to see them because the light from them would not reach us, we would still feel their gravitational attraction. Such objects are what we now call black holes, because that is what they are: black voids in space."
- M. Alonso and E.J. Finn (1867) Fundamental University Physics, Volume 1, Mechanics page 406.
- It is noted that this calculation can be performed without knowing the mass of the earth or the gravitational constant separately, because Newtons law of gravitation can be used at the surface of the earth to find that their product is given by GM = gR2. where g is the gravitational acceleration at the surface of the earth (which can be easily measured). The radius of the earth is more difficult to measure, but this problem was solved by the ancient Greeks, see the main article on Ancient Greek astronomy.
- See for the text under figure 1.2 (a very similar figure to the one depicted here) in: Ramesh Narayan and Jeffrey E. McClintock (2014) Observational Evidence for Black Holes, http://arxiv.org/pdf/1312.6698v2.pdf (accessed July 2015)