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Schwarzschild radius
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The event horizon radius of a non-rotating black hole.
r_s = 2GM/c²r_s = 2GM/c² is the horizon radius of a non-rotating black hole. For the Sun, 3 km; for Earth, 9 mm.
A 10 solar mass black hole has r_s = 30 km.
It is a radius for the horizon, not the singularity.
In more detail
The Schwarzschild radius, R = 2GM/c², gives the size of the event horizon of a non-rotating black hole. For the Sun it is about 3 km.
Real-world uses
- Estimating the size of black holes of a given mass.
- Comparing object sizes to their Schwarzschild radii to assess if they are black holes.
- A black hole of ten solar masses has a Schwarzschild radius of about 30 km, which sets its event horizon.
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Frequently asked questions
Is the Schwarzschild radius a physical surface?
It marks the event horizon, the boundary beyond which escape is impossible.
Why is it so small for the Sun?
Because the Sun is not dense enough to collapse into a black hole.
Is the Schwarzschild radius the size of a black hole?
It is the radius of the event horizon, the boundary beyond which nothing can escape, so it is the effective size.
Related topics in Gravitation & Orbits
Gravitational lensing · Gravitational waves · Black holes · Neutron stars and white dwarfs · Dark matter evidence · Newton's shell theorem