# Dynamics and center of mass energy of colliding particles around black hole in f(R) gravity

## TL;DR

This paper studies particle dynamics near a static black hole in f(R) gravity, focusing on escape velocities and trajectories after collisions, to understand how modified gravity affects particle behavior around black holes.

## Contribution

It introduces a detailed analysis of particle escape conditions and trajectories in f(R) gravity, extending understanding of black hole physics beyond General Relativity.

## Key findings

- Calculated escape velocities for particles after collisions.
- Analyzed effective potential and particle trajectories.
- Discussed conditions for particle escape in f(R) gravity.

## Abstract

We have investigated the dynamics of particles in the vicinity of a static spherically symmetric black hole in f(R) gravity. Using the Euler-Lagrange method the dynamical equations of a neutral particle are obtained. Assuming that the particle is initially moving in the innermost stable circular orbit, we have calculated its escape velocity, after a collision with some other particle. The conditions for the escape of colliding particles are discussed. The effective potential and the trajectories of the escaping particles are studied graphically.