The Schwarzschild radius (sometimes historically referred to as the gravitational radius) is a characteristic radius associated with every quantity of mass. It is the radius of a sphere in space, that if containing a correspondingly sufficient amount of mass (and therefore, reaches a certain density), the force of gravity from the contained mass would be so great that no known force or degeneracy pressure could stop the mass from continuing to collapse in volume into a point of infinite density: a gravitational singularity (colloquially referred to as a black hole). The term is used in physics and astronomy, especially in the theory of gravitation, and general relativity.
In 1916, Karl Schwarzschild obtained an exact solution[1][2] 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 km[3], while the Earth's is only about 9 mm, the size of a peanut. That is, if all the mass of the Sun (or Earth) were contained in a sphere with a radius of 3 km (or Earth of 9 mm), then the volume of the Sun (or Earth) would continue to collapse into a singularity, due to the force of gravity.
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 7.8 million km.
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