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

TL;DR

This paper investigates particle collisions near black holes in a specific $f(R)$ gravity model, revealing conditions under which collision energies become unbounded, with implications for understanding high-energy phenomena in modified gravity theories.

Contribution

It analyzes particle collision energies near black holes in an $f(R)$ gravity model, highlighting unbounded energies for oppositely moving particles and effects of a cosmological constant.

Findings

Opposite-direction particle collisions near horizons can produce unbounded energy.

Same-direction collisions near horizons result in finite energy.

Adding a cosmological constant does not affect the unbounded energy feature.

Abstract

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.