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Dimensional analysis shows that the speed of light and Newton's constant of gravitation can be combined to define a quantity $F_* = {c^4\over G_N}$ with the dimensions of force (equivalently, tension).
K. Schwarzschild, “Über das Gravitationsfeld einer Kugel aus inkompressibler Flüssigkeit nach der Einsteinschen Theorie”, (On the gravitational field of a sphere of incompressible fluid according to Einstein’s theory), Sitzungsberichte der Königlich-Preussischen Akademie der Wissenschaften, Berlin
1916
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K. Schwarzschild, “Über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie”, (On the gravitational field of a mass point according to Einstein’s theory), Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften, Berlin
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H. A. Buchdahl, “General Relativistic Fluid Spheres”, Phys. Rev. 116
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Freeman Dyson, “Gravitational machines”, Chapter 12 in Interstellar Communication , A. G. W. Cameron, editor, New York: Benjamin Press, 1963. https://www.ifa.hawaii.edu/~barnes/ast242_s14/Dyson_Machines.pdf Also awarded 4th prize in the 1962 Gravity Research Foundation essay contest: https://www.gravityresearchfoundation.org/year https://static1.squarespace.com/static/5852e579be659442a01f27b8/t/5873d777e4fcb5de501305f7/1483986808648/dyson.pdf
1962
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Footnote 5 in reference [ 37 ] : In reply to an enquiry by Christoph Schiller, Dyson replied on 14th Feb 2011: “It is not true that I proposed the formula c 5 / G c^{5}/G as a luminosity limit for anything. I make no such claim. Perhaps this notion arose from a paper that I wrote in 1962 with the title, “Gravitational Machines”, published as Chapter 12 in the book, “Interstellar Communication” edited by Alastair Cameron, [New York, Benjamin, 1963]. Equation (11) in that paper is the well-known formula 128 V 10 / 5 G c 5 128V^{10}/5Gc^{5} for the power in gravitational waves emitted by a binary star with two equal masses moving in a circular orbit with velocity V V . As V V approaches its upper limit c c , this gravitational power approaches the upper limit 128 c 5 / 5 G 128c^{5}/5G . The remarkable thing about this upper limit is that it is independent of the masses of the stars. It may be of some relevance to the theory of gamma-ray bursts.”
1963
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H. Bondi, “Massive spheres in general relativity”, Proc. Roy. Soc. Lond. A 282 (1964) 303-317 doi: 10.1098/rspa.1964.0234
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B. Kent Harrison, Kip S. Thorne, Masami Wakano, and John Archibald Wheeler, Gravitation theory and gravitational collapse , (University of Chicago Press, Chicago, 1965)
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P. Boonserm and M. Visser, “Buchdahl-like transformations in general relativity”, Thai Journal of Mathematics 5 # 2
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D. Martin and M. Visser, “Bounds on the interior geometry and pressure profile of static fluid spheres”, Class. Quant. Grav. 20
2003
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M. Visser and N. Yunes, “Power laws, scale invariance, and generalized Frobenius series: Applications to Newtonian and TOV stars near criticality”, Int. J. Mod. Phys. A 18
2003
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C. Schiller, “Motion Mountain — A Hike Beyond Space and Time Along the Concepts of Modern Physics” ( http://www.motionmountain.net , 1997-2004), section 7: Maximum force — a simple principle encompassing general relativity
2004
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D. Martin and M. Visser, “Algorithmic construction of static perfect fluid spheres”, Phys. Rev. D 69
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C. Schiller, “General Relativity and Cosmology Derived From Principle of Maximum Power or Force”, Int J Theor Phys
2005
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P. Boonserm, M. Visser and S. Weinfurtner, “Generating perfect fluid spheres in general relativity”, Phys. Rev. D 71
2005
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J. D. Barrow and N. Dadhich, “Maximum Force in Modified Gravity Theories”, Phys. Rev. D 102
2006
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M. P. Dabrowski and H. Gohar, “Abolishing the maximum tension principle”, Phys. Lett. B 748
2015
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