Schwarzschild Radius

The Schwarzschild radius (sometimes historically referred to as the gravitational radius) is the distance from the center of an object such that, if all the mass of the object were compressed within that sphere, the escape speed from the surface would equal the speed of light. Once a stellar remnant collapses within this radius, light cannot escape and the object is no longer visible. It is a characteristic radius associated with every quantity of mass.

In 1915, Karl Schwarzschild obtained an exact solution to Einstein's field equations for the gravitational field outside a non-rotating, spherically symmetric body (see Schwarzschild metric). Using the definition , the solution contained a term of the form ; where the value of r making this term singular has come to be known as the Schwarzschild radius. The physical significance of this singularity, and whether this singularity could ever occur in nature, was debated for many decades; a general acceptance of the possibility of a black hole did not occur until the second half of the 20th century.

The Schwarzschild radius of an object is proportional to the mass. Accordingly, the Sun has a Schwarzschild radius of approximately 3.0 km (1.86 miles) while the Earth's is only about 9.0 mm, the size of a peanut. The observable universe's mass has Schwarzschild radius of approximately 10 billion light years.

An object smaller than its Schwarzschild radius is called a black hole. The surface at the Schwarzschild radius acts as an event horizon in a non-rotating body. (A rotating black hole operates slightly differently.) Neither light nor particles can escape through this surface from the region inside, hence the name "black hole". The Schwarzschild radius of the (currently hypothesized) supermassive black hole at our Galactic Center would be approximately 13.3 million kilometres.