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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?

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  • $\begingroup$ See e.g. en.wikipedia.org/wiki/Buchdahl%27s_theorem $\endgroup$
    – Qmechanic
    Commented May 19, 2022 at 15:38
  • $\begingroup$ 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. $\endgroup$
    – safesphere
    Commented May 19, 2022 at 17:23

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There are radii that play a role when a black hole is observed from afar, for example by the Event Horizon Telescope.

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.

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  • $\begingroup$ 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. $\endgroup$
    – ProfRob
    Commented May 21, 2022 at 7:41

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