The black circle with radius \(R_s\) represents the event horizon of the black hole.

Photons are emitted from the event horizon (coordinates \(r=R_s \) et \(\phi=0\)) and back to it.

The figure is plotted with Cartesian coordinates \(x=r\cos\varphi\) et \(y=r\sin\varphi\),

considering a black hole of the mass

of the sun \(M\odot\)

that is \(R_s=2 \ 953\ m \), \(b_{crit}=7\ 672.73\ m\)

and with \(b=8\ 075\ m\).

The value of \(b\) is obtained for the emission point \(r=R_s\) and \(\varphi=0\) and by choosing

a target value \(r=R_s\) for a variation \(\Delta\varphi\) of \(\pi\) (Excel spreadsheet) or with the values \(R_s\)

and \(\pi\) as input data (Python script).

For a black hole with a different mass \(M\), the plots are kept by applying the scaling factor

\(\frac{M}{M\odot}\).