... Schwarzschild¹

Karl Schwarzschild (October 9, 1873 - May 11, 1916) was a noted German physicist and astronomer. He was born in Frankfurt am Main. Something of a child prodigy he had a paper on orbits published when he was only sixteen. He studied at Strasbourg and Munich, obtaining his doctorate in 1896 for a work on Jules Henri Poincaré's theories. At the outbreak of World War I in 1914 he joined the German army despite being over 40 years old and served on both the western and eastern fronts, rising to the rank of lieutenant in the artillery. While serving in Russia in 1915, he wrote two main papers, one on relativity theory and one on quantum theory.(how is it possible to write a paper in a war?) His work on relativity produced the first exact solutions to the general gravitational equations - one for non-rotating spherically symmetric bodies and one for static isotropic empty space surrounding any massive body. From the second he undertook some pioneering work on classical black holes. Two properties of black holes have been given his name - the Schwarzschild metric and the Schwarzschild radius. The papers were sent to Einstein and were later published in the Sitzungsberichte der Preussischen Akademie der Wissenschaften.

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... parameter²

which will be interpreted as the proper time of the particle

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...$V(r)$³

The true energy per unit mass is E, but the effective potential for the coordinate $r$ responds to $\frac{1}{2}E^2$

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...$G=c=1$⁴

SI units are $c = 299792458.0\, m/s$, $G = 6.673 \times 10^{-11}\, m^3 /kg\, s^2$, $\hbar = 1.05457148 \times 10^{-34}\, m^2 kg / s$, $m_\odot = 1.989 \times 10^{30}\, kg$.

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