Schwarzschild Radius of the Sun

Karl Schwarzschild solved Einstein's field equations in 1915 within weeks of their publication, while serving on the Russian front, and found that a mass squeezed inside r = 2GM/c² curves spacetime so severely that no signal can climb back out. Put the Sun's mass parameter in and the answer is 2.95 km: the Sun would have to shrink by a factor of 235 000 to reach it, which it never will; a star of one solar mass ends as a white dwarf about the size of Earth.

The radius scales linearly with mass, which makes the ratio r_s/r a handy measure of how relativistic a system is. At the Sun's actual surface that ratio is 4 × 10⁻⁶, and it is exactly what produces the 1.75-arcsecond deflection of starlight that Eddington's 1919 eclipse expedition measured, and the 43 arcseconds per century of Mercury's perihelion advance that Newton could not explain.