On the motion of a test particle around a global monopole in a modified gravity

TL;DR

This paper investigates the motion of test particles around a global monopole within a modified gravity framework, deriving weak field solutions and revealing an attractive force exerted by the monopole.

Contribution

It introduces a method to analyze test particle motion in $f(R)$ gravity around monopoles by simplifying field equations and choosing specific functional forms for $F(R)$.

Findings

Derived weak field metric solutions in $f(R)$ gravity

Computed geodesics for massive particles

Found an attractive force exerted by the monopole

Abstract

In this paper we suggest an approach to analyse the motion of a test particle in the spacetime of a global monopole within a $f(R)$-like modified gravity. The field equations are written in a more simplified form in terms of $F(R)=\frac{df(R)}{dR}$. Since we are dealing with a spherically symmetric problem, $F(R)$ is expressed as a radial function ${\cal F}(r)\equiv{F(R(r))}$. So, the choice of a specific form for $f(R)$ will be equivalent to adopt an Ansatz for ${\cal F}(r)$. By choosing an explicit functional form for ${\cal F}(r)$ we obtain the weak field solutions for the metric tensor, compute the time-like geodesics and analyse the motion of a massive test particle. An interesting feature is an emerging attractive force exerted by the monopole on the particle.