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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.
In the Schwarzschild coordinates, the Schwarzschild radius = is the radial coordinate of the event horizon = =. In the Kruskal–Szekeres coordinates the event horizon is given by =. Note that the metric is perfectly well defined and non-singular at the event horizon.
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 ...
Schwarzschild solution in Schwarzschild coordinates, with two space dimensions suppressed, leaving just the time t and the distance from the center r. In red the incoming null geodesics. In blue outcoming null geodesics. In green the null light cones on which borders light moves, while massive objects move inside the cones.
The equatorial (maximal) radius of an ergosphere is the Schwarzschild radius, the radius of a non-rotating black hole. The polar (minimal) radius is also the polar (minimal) radius of the event horizon which can be as little as half the Schwarzschild radius for a maximally rotating black hole. [2]
The radius of the photon sphere, which is also the lower bound for any stable orbit, is, for a Schwarzschild black hole, ... and r s is the Schwarzschild radius ...
In the theory of Lorentzian manifolds, spherically symmetric spacetimes admit a family of nested round spheres.In such a spacetime, a particularly important kind of coordinate chart is the Schwarzschild chart, a kind of polar spherical coordinate chart on a static and spherically symmetric spacetime, which is adapted to these nested round spheres.
This metric has a coordinate singularity at the Schwarzschild radius =. Georges Lemaître was the first to show that this is not a real physical singularity but simply a manifestation of the fact that the static Schwarzschild coordinates cannot be realized with material bodies inside the Schwarzschild radius.