# Are there any other significant radii around Schwarzschild black holes besides the four I know of?

A Schwarzschild (non-rotating, non-charged) black hole has an event horizon with radius $$r_s = \frac{2 G M} {c^2}$$, where $$M$$ is the mass of the black hole, $$G$$ is the gravitational constant, and $$c$$ is the speed of light. I know of three additional significant radii:

• Photon Sphere Radius $$r_{ph} = \frac{3 G M} {c^2} = 1.5 r_s$$
• Marginally-Bound Orbit Radius $$r_{mb} = \frac{4 G M} {c^2} = 2 r_s$$
• Innermost Stable Circular Orbit Radius $$r_{isco} = \frac{6 G M} {c^2} = 3 r_s$$

Are there any other radii of note around a Schwarzschild black hole?

• Commented May 19, 2022 at 15:38
• The Schwarzschild “radius” is defined as a reduced circumference of the horizon. The actual radius of the horizon defined as the spacelike radial distance to the origin is zero. Commented May 19, 2022 at 17:23

For example, the event horizon appears to be $$2.6r_s$$ because the space around the black hole is not flat, and rays reaching the observer may emanate from the "rear side" of the horizon. See for example this nice video at around 3:30.
• This is not the apparent event horizon. It is a projection of the photon ring at $1.5r_s$. No rays reach the observer from behind the black hole if they originate from or travel within this radius. Commented May 21, 2022 at 7:41