Schwarzschild (1915)
Karl Schwarzschild 1873-1916
  • Director of the Astrophysical Observatory, Potsdam.
  • Served in the Prussian army 1914-1916.
  • Schwarzschild's metric had a “Schwarzschild singularity” at \(r = 2 G M\) (units \(c = 1\)), causing Einstein to reject the concept of black holes: \[ d s^2 = - \, ( 1 - 2 G M / r ) d t^2 + {d r^2 \over 1 - 2 G M / r} + r^2 d o^2 \ . \]

Gullstrand and Painlevé (1921)
Independently discovered a version of the Schwarzschild metric that had no singularity at the horizon: \[ d s^2 = - \, d t_{\rm ff}^2 + ( d r - v \, d t_{\rm ff} )^2 + r^2 d o^2 \ . \] where \(v = \sqrt{2 G M / r}\) is the Newtonian escape velocity, and \(t_{\rm ff}\) is the time attached to a free-fall observer. Free-fall time is related to Schwarzschild time by \(d t_{\rm ff} = d t - v \, d r / ( 1 - v^2 )\).

Allvar Gullstrand 1862-1930
  • Nobel prize 1911 in Medicine & Physiology for work on dioptrics of the human eye.
  • Nobel Physics Committee 1911-1929.
  • Gullstrand's skepticism about general relativity was instrumental in ensuring that when Einstein won the Nobel prize in 1921, it was not for relativity.
Paul Painlevé 1863-1933
  • French Prime Minister 1917 and 1925.
  • Mathematician.
  • Noting that the space was flat at constant free-fall time, Painlevé concluded that, as regards the redshift of light from the Sun and suchlike, “c'est pure imagination de prétendre tirer du \(d s^2\) des conséquences de cette nature.”
  • Einstein wrote to Painlevé “only conclusions reached after the elimination of coordinates may pretend to an objective significance ... the metrical interpretation of the quantity \(d s^2\) is not ‘pure imagination’ but the deep core of the theory itself.”

Time & Life Pictures/Getty Images 28 May 1921

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