Schwarzschild radius

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The radius at which the escape velocity of a spherical non-rotating mass reaches the speed of light, r_s = 2GM/c-squared. It is linear in mass, which is the single most useful thing to know about black holes and the least intuitive: doubling the mass doubles the radius, so density falls as the square of mass and a sufficiently large black hole is not dense at all. For the Sun the value is about 2.95 km; for the Earth about 8.9 mm; for Sagittarius A* at roughly four million solar masses it is about thirteen million kilometres, a tenth of the Earth-Sun distance; for M87* at about six and a half billion solar masses it is roughly nineteen billion kilometres, wider than the orbit of Pluto. The radius is a property of the geometry, not of any material surface, and Karl Schwarzschild who derived it in 1916 did not read it as a boundary of no return - that interpretation took another four decades. Not a place on Earth.

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