A dark star is a theoretical object compatible with Newtonian mechanics that, due to its large mass, has a surface escape velocity that equals or exceeds the speed of light. Whether light is affected by gravity under Newtonian mechanics is unclear but if it were accelerated the same way as projectiles, any light emitted at the surface of a dark star would be trapped by the star's gravity, rendering it dark, hence the name. Dark stars are analogous to black holes in general relativity.
During 1783 geologist John Michell wrote a letter to Henry Cavendish outlining the expected properties of dark stars, 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's idea for calculating the number of such "invisible" stars anticipated 20th century 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 a 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, 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 just academic thoroughness.
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, independently of Michell. Because of the development of the wave theory of light, Laplace may have removed it from later editions as light became to be thought of as a massless wave, and therefore not influenced by gravity and as a group, physicists dropped the idea although the German physicist, mathematician, and astronomer Johann Georg von Soldner continued with Newton's corpuscular theory of light as late as 1804.
Indirect radiation
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 while outside the critical surface, can interact with other matter, or be accelerated free from the star through such interactions. A dark star, therefore, has a rarefied atmosphere of "visiting particles", and this ghostly halo of matter and light can radiate, albeit weakly. Also as Faster than light speeds are possible in Newtonian mechanics, it is possible for particles to escape.
