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Mathematical Foundations of the Theory of Relativistic Stellar and Black Hole Configurations

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Gravitation in Astrophysics

Part of the book series: NATO ASI Series ((NSSB,volume 156))

Abstract

Late in the year 1783, Benjamin Franklin (then U.S. representative in France) wrote from Paris to his regular London scientific correspondent Sir Joseph Banks (then president of the Royal Society) that the most exciting recent development in France was the breakthrough in ballooning resulting from the use by Charles of hydrogen (as an alternative to the hot air technique that had just been tried out with only moderate success by the Montgolfiers). After the (manifestly reluctant) admission that “our friends on your side of the water” were more advanced in the competition to achieve practical flying, and the declaration that his own side nevertheless claimed credit for the fundamental research on which it was based (thinking particularly of the hydrogen bubbles blown by Cavendish, who had recently carried out the first serious study of the chemical and physical properties of the lightest element), Banks went on to reply (9th Dec. 1783) to the effect that the most interesting recent scientific event in London had been the presentation at the Royal Society of a “very curious paper” on the influence of gravity on light. In the paper in question, which was published soon after,1 John Michell (1724–1783) foreshadowed modern black hole theory by evaluating the critical radius given in modern notation as

$$r\, = \,{{2GM} \over {{c^2}}}$$
(1.1)

within which a body of mass M would become invisible because the Newtonian gravitational potential

$$\varphi \, = \, - \,{{GM} \over r}$$
(1.2)

would exceed the specific (Newtonian) kinetic energy 1/2 c 2 of a projectile moving with the speed c of light.

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  1. Groupe d’Astrophysique Relativiste - D.A.R.C., CNRS - Observatoire de Paris, 92195, Meudon Principal Cedex, France

    Brandon Carter

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  1. CNRS-Observatoire de Paris, Paris, France

    B. Carter

  2. University of California, Santa Barbara, California, USA

    J. B. Hartle

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Carter, B. (1987). Mathematical Foundations of the Theory of Relativistic Stellar and Black Hole Configurations. In: Carter, B., Hartle, J.B. (eds) Gravitation in Astrophysics. NATO ASI Series, vol 156. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-1897-2_2

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  • DOI: https://doi.org/10.1007/978-1-4613-1897-2_2

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