The Schwarzschild radius is a concept from the general theory of relativity proposed by Albert Einstein. It refers to the radius of a spherical gravitational field, which is determined by an object’s mass and its angular momentum. For example, for a massless point particle with mass M and angular momentum J, the Schwarzschild radius—sometimes also called the gravitational radius or event horizon—is given by the formula rs = (2GM) / c², where G is the gravitational constant, c is the speed of light in a vacuum, and M is the mass of the object.
For a black hole, the Schwarzschild radius defines the boundary beyond which nothing, including light, can escape the object due to extreme gravity. For the Sun, it is about three kilometers, while for the Earth, for example, it is only 0.884 cm (see the image for an example).
If the Sun and Earth were compressed to these radii or smaller, their light would not escape. Generally speaking, the Schwarzschild radius can be calculated for any body. The smaller the body’s mass, the smaller its Schwarzschild radius. For the amount of matter that makes up a human being, this radius is so small that if expressed in centimeters, it would be zero point twenty-one, followed by twenty-one zeros, and only then would any digits appear.
If a mass equal to that of a human were compressed to such a small radius, no light would escape into outer space from it.
Who was Karl Schwarzschild?
After Albert Einstein formulated his equations of the general theory of relativity, Schwarzschild, shortly before his death, obtained the first exact solutions for them, describing, in particular, the properties of black holes. He made fundamental contributions to many areas of astrophysics.