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The Schwarzschild radius or the gravitational radius is a physical parameter in the Schwarzschild solution to Einstein's field equations that corresponds to the radius defining the event horizon of a Schwarzschild black hole. It is a characteristic radius associated with any quantity of mass.
The Schwarzschild black hole is characterized by a surrounding spherical boundary, called the event horizon, which is situated at the Schwarzschild radius (), often called the radius of a black hole. The boundary is not a physical surface, and a person who fell through the event horizon (before being torn apart by tidal forces) would not notice ...
For example, the Schwarzschild radius of a nonrotating uncharged black hole with mass m becomes r = 2m. For this reason, many books and papers on relativistic physics use geometric units. An alternative system of geometrized units is often used in particle physics and cosmology, in which 8πG = 1 instead.
In such a spacetime, a particularly important kind of coordinate chart is the Schwarzschild chart, ... is the standard Riemannian metric on the unit radius 2-sphere.
is the standard Riemannian metric of the unit 2-sphere. Note the conventions being used here are the metric signature of ( + − − − ) and the natural units where c = 1 is the dimensionless speed of light, G the gravitational constant, and M is the characteristic mass of the Schwarzschild geometry.
Lemaître coordinates are a particular set of coordinates for the Schwarzschild metric—a spherically symmetric solution to the Einstein field equations in vacuum—introduced by Georges Lemaître in 1932. [1] Changing from Schwarzschild to Lemaître coordinates removes the coordinate singularity at the Schwarzschild radius.
Free falling worldlines in classic Schwarzschild-Droste coordinates. A Schwarzschild observer is a far observer or a bookkeeper. He does not directly make measurements of events that occur in different places. Instead, he is far away from the black hole and the events.
For example, the Schwarzschild radius of the Earth is roughly 9 mm (3 ⁄ 8 inch); at the surface of the Earth, the corrections to Newtonian gravity are only one part in a billion. The Schwarzschild radius of the Sun is much larger, roughly 2953 meters, but at its surface, the ratio r s r {\textstyle {\frac {r_{\text{s}}}{r}}} is roughly 4 ...