"...look into all things with a searching eye” - Baha'u'llah (Prophet Founder of the Baha'i Faith)


Mar 28, 2015

The Gravitational Radius, also known as Schwarzschild Radius

Defined by German astronomer, Karl Schwarzschild the gravitational radius is the distance that defines the size at which a spherical astronomical object such as a star becomes a black hole. A black hole is an object so dense that not even light can escape the pull of its gravitational force. If an object collapses to within its Schwarzschild radius, it becomes a black hole. Karl Schwarzschild derived the first model of a black hole in 1916.

Nothing, not even a particle moving at the speed of light, can escape the gravitational pull of a black hole. Therefore, the Schwarzschild radius is the largest radius that a body with a specific mass can have and still keep light from escaping. The formula for the Schwarzschild radius of a body is Rs = GM/c2, where Rs is the Schwarzschild radius of the body, G is a constant known as the universal constant of gravitation, M is the mass of the object, and c is the speed of light.

To find the equation for the Schwarzschild radius of an object, Schwarzschild needed to know how massive a body has to be to keep light from escaping and how light behaves in such a strong gravitational field. French astronomer Pierre Laplace found the equation for escape velocity, or the speed an object needs to overcome the gravitational force of a body. Laplace noted in 1800 that the escape velocity would be greater than the speed of light for an object leaving a very small, dense body. German American physicist Albert Einstein explained how light behaves in a strong gravitational field in his general theory of relativity, published in 1916. In 1916 Karl Schwarzschild derived the first model of a black hole with help from the work of Laplace and Einstein.

The Schwarzschild radius of a black hole marks its ‘event horizon’, or the boundary past which light can enter but not escape. Astronomers believe that once an object collapses to within its Schwarzschild radius, it continues collapsing until it becomes a singularity, or a point with infinite density and a radius of zero.

The sun has a mass of 2×10 (to the power 30) kg (4×10 [to the power 30 lb]) and a radius of about 700,000 km (about 400,000 mi). Its Schwarzschild radius is about 3 km (about 2 mi). If the sun were to collapse into a sphere with a radius of less than 3 km, light from the sun would be trapped and the sun would become a black hole. The sun, however, is not massive enough for it to collapse to this size and become a black hole.

An object with a mass equal to that of the earth would have a Schwarzschild radius of about 3 mm (about 0.1 in). For an object with Mount Everest’s mass, the Schwarzschild radius is only about 1×10 (to the power minus 11) mm (4×10 [to the power minus 13] in). Some astronomers believe that any black hole smaller than this would be relatively unstable and would evaporate quickly, releasing gamma rays. Astronomers have speculated that the mysterious sources of celestial gamma ray bursts may be evaporating primordial black holes. 
(Adapted from Encarta Encyclopedia)