Astrophysics (index)about

Schwarzschild radius

(gravitational radius)
(radius of a black hole's event horizon)

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.

rS = 2GM/c²

Some examples:

Object approx Schwarzschild radius
Large SMBH ~1013 m or ~100 AU
Milky Way SMBH (Sagittarius A*) ~1.2×1010 m or ~1/10 AU
Large stellar-mass BH (e.g., 15 MSun) ~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.

(limit,black holes)

Referenced by:
event horizon (EH)
innermost stable circular orbit (ISCO)