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The **Schwarzschild radius** (or **gravitational radius**)
is the radius of a (simple) black hole's event horizon,
according to Karl Schwarzschild's solution to Einstein's field equation.
More specifically, the radius of the event horizon of a non-rotating
black hole. Rotation or electric charge would modify it.

The *Schwarzschild radius* is a function of mass and is directly
proportional to it.

r_{S}= 2GM/c²

- r
_{S}- Schwarzschild radius - G - gravitational constant.
- M - mass.
- c - speed of light in a vacuum.

Some examples:

Object | approx Schwarzschild radius |

Large SMBH | ~10^{13} m or ~100 AU |

Milky Way SMBH (Sagittarius A*) | ~1.2×10^{10} m or ~1/10 AU |

Large stellar-mass BH (e.g., 15 M_{Sun}) | ~44km |

Sun | ~3km |

Jupiter | ~2.8m |

Earth | ~9mm |

The *Schwarzschild radius* places a limit
on how small an object of a given mass can be
without becoming a black hole, but somewhat larger objects can
collapse into black holes if their structure is insufficiently
"strong" to support the given mass
(i.e., they produce insufficient pressure),
or if some spherical sub-portion of the object exceeds
that portion's **Schwarzschild density**, the density that implies
a mass is within its Schwarzschild radius.

The term **Schwarzschild diameter** naturally means twice
the Schwarzschild radius.

event horizon (EH)

innermost stable circular orbit (ISCO)