Schwarzschild radius

How small would you have to squeeze something before it became a black hole? There is an exact answer, and it is the Schwarzschild radius: the radius to which a given mass must be compressed for its gravity to trap light, forming an event horizon. Squeeze any object inside this radius and it becomes a black hole; stay larger than it and you do not. It is the precise dividing line between an ordinary object and a hole in spacetime.

The radius depends only on mass, and the formula is beautifully simple — it is directly proportional to the mass. The Sun's Schwarzschild radius is just under 3 kilometres, so to turn the Sun into a black hole you would have to crush its entire mass into a ball smaller than a town. The Earth's is a mere 9 millimetres — squeeze our whole planet into a marble and it too would vanish behind an event horizon. A 10-solar-mass black hole has a Schwarzschild radius of about 30 kilometres. The rule of thumb: roughly 3 kilometres per solar mass.

This radius is exactly where a non-rotating black hole's event horizon sits, so the two ideas are intimately linked: the Schwarzschild radius tells you how big the point of no return is for a given mass. It was the first exact solution to Einstein's equations of general relativity, found by Karl Schwarzschild in 1916 while serving in the army during World War I, just months after Einstein published the theory. Note that real black holes usually spin, which slightly changes the horizon's size and shape from this simplest case.