Astrophysics (Index)About

Schwarzschild radius

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

The Schwarzschild radius (sometimes RS) 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) ~44 km
Sun ~3 km
Jupiter ~2.8 m
Earth ~9 mm

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 may collapse into black holes if their structure is insufficiently "strong" to support the given mass (i.e., they produce insufficient pressure, which depends on the equation of state). A black hole appears if any spherical sub-portion of an object exceeds that portion's Schwarzschild density, the density that implies a mass is within its corresponding Schwarzschild radius.

The Schwarzschild radius formula (above) appears in various correction factors adapting classical formulas so as to approximately accommodate small general relativistic effects, and often such correction factors are cited incorporating a Schwarzschild radius.

The term gravitational radius (typically, rg) is also used for the Schwarzschild radius, but also sometimes used for half the above definition, i.e., lacking the factor of two; either of these is a convenient unit because some analysis of observational data yields distances only as multiples of GM/c².

The term Schwarzschild diameter naturally means twice the Schwarzschild radius.

(limit,black holes)
Further reading:

Referenced by pages:
event horizon (EH)
innermost stable circular orbit (ISCO)
photon sphere
primordial black hole