## Thursday, 28 January 2021

### Photon sphere

 M87* By Event Horizon Telescope
I come across the photon sphere (or last photon orbit) which is another radius around a Schwarzschild black hole at a distance $3R_s/2$. It is the closest distance for a stable orbit and light would orbit there in an exact circle. I would like to calculate it using Carroll conventions. $R_s=2GM$ is the Schwarzschild radius.

There is a Wikipedia article on it. The proof it gives has some peculiarities. I followed it avoiding those. It is one page.
Here: Commentary 5.4 Photon Sphere.pdf

The famous picture is of M87* the black hole in our neighbour galaxy Messier 87. The black central sphere has a radius of $2.6R_s$ so the photon sphere is well inside that black bit and this is not a good illustration of a photon sphere!