Cloud of strings as source in $2+1$-dimensional $f( R) = R^n$ gravity

Abstract

We present three parameters exact solutions with possible black holes in $% 2+1-$dimensional $f\left( R\right) =R^{n}$ modified gravity coupled minimally to a cloud of strings. These three parameters are $n,$ the cloud of string coupling constant $\xi $ and an integration constant $C$. Although in general one has to consider each set of parameters separately; for $n$ an even integer greater than one we give a unified picture providing black holes. For $n\geq 1$ we analyze null / timelike geodesic within the context of particle confinement.