### Schwarzschild radius

**(R**_{S}, gravitational radius)
(radius of a black hole's event horizon)

The **Schwarzschild radius** (sometimes **R**_{S})
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

Some examples:

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, **r**_{g})
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:**

http://en.wikipedia.org/wiki/Schwarzschild_radius

https://astronomy.swin.edu.au/cosmos/S/Schwarzschild+Radius

**Referenced by pages:**

event horizon (EH)

innermost stable circular orbit (ISCO)

photon sphere

primordial black hole

Index