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The Schwarzschild radius is given as =, where G is the gravitational constant, M is the object mass ... Jupiter: 1.90 × 10 27 kg: 2.82 m: 7.0 ...
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.
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.
In the Schwarzschild metric, free-falling objects can be in circular orbits if the orbital radius is larger than (the radius of the photon sphere). The formula for a clock at rest is given above; the formula below gives the general relativistic time dilation for a clock in a circular orbit: [11] [12]
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.
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 r s 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 is roughly 4 parts in a
where is the Schwarzschild radius of the massive object with mass . Thus, even for a non-spinning object, the ISCO radius is only three times the Schwarzschild radius , R S {\displaystyle R_{S}} , suggesting that only black holes and neutron stars have innermost stable circular orbits outside of their surfaces.