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

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.

Gravitational Field of a Global Monopole in a Modified Gravity

In this paper we analyze the gravitational field of a global monopole in the context of $f(R)$ gravity. More precisely, we show that the field equations obtained are expressed in terms of $F(R)=frac{df(R)}{dR}$. Since we are dealing with a spherically symmetric system, we assume that $F(R)$ is a function of the radial coordinate only. Moreover, adopting the weak field approximation, we can provide all components of the metric tensor. A comparison with the corresponding results obtained in General Relativity and in the Brans-Dicke theory is also made.