Chaotic Solutions and Black Hole Shadow in $f(R)$ gravity

Understand

We discuss the emergence of black hole shadow and photon-sphere in the context of $f(R)$ gravity.

• It is shown that the shadow is exponentially sensitive to linear instabilities of metric coming from some $f(R)$ solutions.
• Thus, the instabilities of photon circular trajectories, delimiting the black hole photon-sphere, are double exponentialized.
• Specifically we individuate two Lyapunov exponents, rather than only one, related to two different sources of chaos in geodesic orbits as a sort of butterfly effect.