Particle Acceleration by Static Black Holes in a Model of $f(R)$ Gravity

Particle collisions are considered within the context of $f(R)$ gravity described by $f(R)=R+2\alpha\sqrt{R}$, where $R$ stands for the Ricci scalar and $\alpha$ is a non-zero constant. The center of mass (CM) energy of head-on colliding particles moving in opposite radial directions near the naked singularity/horizon are considered. Collision of particles in the same direction near the event horizon yields finite energy while the energy of oppositely moving particles grows unbounded. Addition of a cosmological constant does not change the feature. Collision of a massless outgoing photon with an infalling particle and collision of two oppositely moving photons following null-geodesics are also taken into account.